KILLED
proof of input_7cQP8kKlYM.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


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

(0) CpxTRS
(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
(3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(4) CpxTRS
(5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxWeightedTrs
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxTypedWeightedTrs
    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
        (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (12) CpxTypedWeightedCompleteTrs
        (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 4 ms]
        (14) CpxRNTS
        (15) InliningProof [UPPER BOUND(ID), 177 ms]
        (16) CpxRNTS
        (17) SimplificationProof [BOTH BOUNDS(ID, ID), 6 ms]
        (18) CpxRNTS
        (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
        (20) CpxRNTS
        (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (22) CpxRNTS
        (23) IntTrsBoundProof [UPPER BOUND(ID), 250 ms]
        (24) CpxRNTS
        (25) IntTrsBoundProof [UPPER BOUND(ID), 120 ms]
        (26) CpxRNTS
        (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (28) CpxRNTS
        (29) IntTrsBoundProof [UPPER BOUND(ID), 348 ms]
        (30) CpxRNTS
        (31) IntTrsBoundProof [UPPER BOUND(ID), 125 ms]
        (32) CpxRNTS
        (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (34) CpxRNTS
        (35) IntTrsBoundProof [UPPER BOUND(ID), 271 ms]
        (36) CpxRNTS
        (37) IntTrsBoundProof [UPPER BOUND(ID), 73 ms]
        (38) CpxRNTS
        (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (40) CpxRNTS
        (41) IntTrsBoundProof [UPPER BOUND(ID), 170 ms]
        (42) CpxRNTS
        (43) IntTrsBoundProof [UPPER BOUND(ID), 65 ms]
        (44) CpxRNTS
        (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (46) CpxRNTS
        (47) IntTrsBoundProof [UPPER BOUND(ID), 338 ms]
        (48) CpxRNTS
        (49) IntTrsBoundProof [UPPER BOUND(ID), 348 ms]
        (50) CpxRNTS
        (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (52) CpxRNTS
        (53) IntTrsBoundProof [UPPER BOUND(ID), 382 ms]
        (54) CpxRNTS
        (55) IntTrsBoundProof [UPPER BOUND(ID), 419 ms]
        (56) CpxRNTS
        (57) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (58) CpxRNTS
        (59) IntTrsBoundProof [UPPER BOUND(ID), 7468 ms]
        (60) CpxRNTS
        (61) IntTrsBoundProof [UPPER BOUND(ID), 2977 ms]
        (62) CpxRNTS
    (63) CompletionProof [UPPER BOUND(ID), 0 ms]
    (64) CpxTypedWeightedCompleteTrs
        (65) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (66) CpxRNTS
(67) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(68) CdtProblem
    (69) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (70) CdtProblem
    (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
    (73) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (76) CdtProblem
    (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) CdtProblem
    (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 54 ms]
    (84) CdtProblem
    (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (88) CdtProblem
    (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (90) CdtProblem
    (91) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) CdtProblem
    (93) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (94) CdtProblem
    (95) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 52 ms]
    (98) CdtProblem
    (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem
    (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (102) CdtProblem
    (103) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (104) CdtProblem
    (105) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 89 ms]
    (106) CdtProblem
    (107) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 59 ms]
    (108) CdtProblem
    (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (112) CdtProblem
    (113) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 62 ms]
    (114) CdtProblem
    (115) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 65 ms]
    (116) CdtProblem
    (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (118) CdtProblem
    (119) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (122) CdtProblem
    (123) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 86 ms]
    (124) CdtProblem
    (125) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 92 ms]
    (126) CdtProblem
    (127) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (128) CdtProblem
    (129) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (130) CdtProblem
    (131) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (132) CdtProblem
    (133) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (134) CdtProblem
    (135) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 84 ms]
    (136) CdtProblem
    (137) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (138) CdtProblem
    (139) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (140) CdtProblem
    (141) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (142) CdtProblem
    (143) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (144) CdtProblem
    (145) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (146) CdtProblem
    (147) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (148) CdtProblem
    (149) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (150) CdtProblem
    (151) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (152) CdtProblem
    (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 33 ms]
    (154) CdtProblem
    (155) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (156) CdtProblem
    (157) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (158) CdtProblem
    (159) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 135 ms]
    (160) CdtProblem
    (161) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (162) CdtProblem
    (163) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (164) CdtProblem
    (165) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (166) CdtProblem
    (167) CdtRewritingProof [BOTH BOUNDS(ID, ID), 3 ms]
    (168) CdtProblem
    (169) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (170) CdtProblem
    (171) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (172) CdtProblem
    (173) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (174) CdtProblem
    (175) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (176) CdtProblem
    (177) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (178) CdtProblem
    (179) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (180) CdtProblem
    (181) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (182) CdtProblem
    (183) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (184) CdtProblem
    (185) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (186) CdtProblem
    (187) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (188) CdtProblem
    (189) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (190) CdtProblem
    (191) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (192) CdtProblem
    (193) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (194) CdtProblem
    (195) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (196) CdtProblem
    (197) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (198) CdtProblem
    (199) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (200) CdtProblem
    (201) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (202) CdtProblem
    (203) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (204) CdtProblem
    (205) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (206) CdtProblem
    (207) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (208) CdtProblem
    (209) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (210) CdtProblem
    (211) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1 ms]
    (212) CdtProblem


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

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


The TRS R consists of the following rules:

   sort(l) -> st(0, l)
   st(n, l) -> cond1(member(n, l), n, l)
   cond1(true, n, l) -> cons(n, st(s(n), l))
   cond1(false, n, l) -> cond2(gt(n, max(l)), n, l)
   cond2(true, n, l) -> nil
   cond2(false, n, l) -> st(s(n), l)
   member(n, nil) -> false
   member(n, cons(m, l)) -> or(equal(n, m), member(n, l))
   or(x, true) -> true
   or(x, false) -> x
   equal(0, 0) -> true
   equal(s(x), 0) -> false
   equal(0, s(y)) -> false
   equal(s(x), s(y)) -> equal(x, y)
   gt(0, v) -> false
   gt(s(u), 0) -> true
   gt(s(u), s(v)) -> gt(u, v)
   max(nil) -> 0
   max(cons(u, l)) -> if(gt(u, max(l)), u, max(l))
   if(true, u, v) -> u
   if(false, u, v) -> v

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

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

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


The TRS R consists of the following rules:

   sort(l) -> st(0', l)
   st(n, l) -> cond1(member(n, l), n, l)
   cond1(true, n, l) -> cons(n, st(s(n), l))
   cond1(false, n, l) -> cond2(gt(n, max(l)), n, l)
   cond2(true, n, l) -> nil
   cond2(false, n, l) -> st(s(n), l)
   member(n, nil) -> false
   member(n, cons(m, l)) -> or(equal(n, m), member(n, l))
   or(x, true) -> true
   or(x, false) -> x
   equal(0', 0') -> true
   equal(s(x), 0') -> false
   equal(0', s(y)) -> false
   equal(s(x), s(y)) -> equal(x, y)
   gt(0', v) -> false
   gt(s(u), 0') -> true
   gt(s(u), s(v)) -> gt(u, v)
   max(nil) -> 0'
   max(cons(u, l)) -> if(gt(u, max(l)), u, max(l))
   if(true, u, v) -> u
   if(false, u, v) -> v

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

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

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


The TRS R consists of the following rules:

   sort(l) -> st(0, l)
   st(n, l) -> cond1(member(n, l), n, l)
   cond1(true, n, l) -> cons(n, st(s(n), l))
   cond1(false, n, l) -> cond2(gt(n, max(l)), n, l)
   cond2(true, n, l) -> nil
   cond2(false, n, l) -> st(s(n), l)
   member(n, nil) -> false
   member(n, cons(m, l)) -> or(equal(n, m), member(n, l))
   or(x, true) -> true
   or(x, false) -> x
   equal(0, 0) -> true
   equal(s(x), 0) -> false
   equal(0, s(y)) -> false
   equal(s(x), s(y)) -> equal(x, y)
   gt(0, v) -> false
   gt(s(u), 0) -> true
   gt(s(u), s(v)) -> gt(u, v)
   max(nil) -> 0
   max(cons(u, l)) -> if(gt(u, max(l)), u, max(l))
   if(true, u, v) -> u
   if(false, u, v) -> v

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

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

(6)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   sort(l) -> st(0, l) [1]
   st(n, l) -> cond1(member(n, l), n, l) [1]
   cond1(true, n, l) -> cons(n, st(s(n), l)) [1]
   cond1(false, n, l) -> cond2(gt(n, max(l)), n, l) [1]
   cond2(true, n, l) -> nil [1]
   cond2(false, n, l) -> st(s(n), l) [1]
   member(n, nil) -> false [1]
   member(n, cons(m, l)) -> or(equal(n, m), member(n, l)) [1]
   or(x, true) -> true [1]
   or(x, false) -> x [1]
   equal(0, 0) -> true [1]
   equal(s(x), 0) -> false [1]
   equal(0, s(y)) -> false [1]
   equal(s(x), s(y)) -> equal(x, y) [1]
   gt(0, v) -> false [1]
   gt(s(u), 0) -> true [1]
   gt(s(u), s(v)) -> gt(u, v) [1]
   max(nil) -> 0 [1]
   max(cons(u, l)) -> if(gt(u, max(l)), u, max(l)) [1]
   if(true, u, v) -> u [1]
   if(false, u, v) -> v [1]

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

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

(8)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   sort(l) -> st(0, l) [1]
   st(n, l) -> cond1(member(n, l), n, l) [1]
   cond1(true, n, l) -> cons(n, st(s(n), l)) [1]
   cond1(false, n, l) -> cond2(gt(n, max(l)), n, l) [1]
   cond2(true, n, l) -> nil [1]
   cond2(false, n, l) -> st(s(n), l) [1]
   member(n, nil) -> false [1]
   member(n, cons(m, l)) -> or(equal(n, m), member(n, l)) [1]
   or(x, true) -> true [1]
   or(x, false) -> x [1]
   equal(0, 0) -> true [1]
   equal(s(x), 0) -> false [1]
   equal(0, s(y)) -> false [1]
   equal(s(x), s(y)) -> equal(x, y) [1]
   gt(0, v) -> false [1]
   gt(s(u), 0) -> true [1]
   gt(s(u), s(v)) -> gt(u, v) [1]
   max(nil) -> 0 [1]
   max(cons(u, l)) -> if(gt(u, max(l)), u, max(l)) [1]
   if(true, u, v) -> u [1]
   if(false, u, v) -> v [1]

The TRS has the following type information:
sort :: cons:nil -> cons:nil
st :: 0:s -> cons:nil -> cons:nil
0 :: 0:s
cond1 :: true:false -> 0:s -> cons:nil -> cons:nil
member :: 0:s -> cons:nil -> true:false
true :: true:false
cons :: 0:s -> cons:nil -> cons:nil
s :: 0:s -> 0:s
false :: true:false
cond2 :: true:false -> 0:s -> cons:nil -> cons:nil
gt :: 0:s -> 0:s -> true:false
max :: cons:nil -> 0:s
nil :: cons:nil
or :: true:false -> true:false -> true:false
equal :: 0:s -> 0:s -> true:false
if :: true:false -> 0:s -> 0:s -> 0:s

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

(9) 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:

   sort_1
   st_2
   cond1_3
   cond2_3

(c) The following functions are completely defined:

   gt_2
   max_1
   member_2
   equal_2
   if_3
   or_2

Due to the following rules being added:
none

And the following fresh constants: none

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

(10)
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:

   sort(l) -> st(0, l) [1]
   st(n, l) -> cond1(member(n, l), n, l) [1]
   cond1(true, n, l) -> cons(n, st(s(n), l)) [1]
   cond1(false, n, l) -> cond2(gt(n, max(l)), n, l) [1]
   cond2(true, n, l) -> nil [1]
   cond2(false, n, l) -> st(s(n), l) [1]
   member(n, nil) -> false [1]
   member(n, cons(m, l)) -> or(equal(n, m), member(n, l)) [1]
   or(x, true) -> true [1]
   or(x, false) -> x [1]
   equal(0, 0) -> true [1]
   equal(s(x), 0) -> false [1]
   equal(0, s(y)) -> false [1]
   equal(s(x), s(y)) -> equal(x, y) [1]
   gt(0, v) -> false [1]
   gt(s(u), 0) -> true [1]
   gt(s(u), s(v)) -> gt(u, v) [1]
   max(nil) -> 0 [1]
   max(cons(u, l)) -> if(gt(u, max(l)), u, max(l)) [1]
   if(true, u, v) -> u [1]
   if(false, u, v) -> v [1]

The TRS has the following type information:
sort :: cons:nil -> cons:nil
st :: 0:s -> cons:nil -> cons:nil
0 :: 0:s
cond1 :: true:false -> 0:s -> cons:nil -> cons:nil
member :: 0:s -> cons:nil -> true:false
true :: true:false
cons :: 0:s -> cons:nil -> cons:nil
s :: 0:s -> 0:s
false :: true:false
cond2 :: true:false -> 0:s -> cons:nil -> cons:nil
gt :: 0:s -> 0:s -> true:false
max :: cons:nil -> 0:s
nil :: cons:nil
or :: true:false -> true:false -> true:false
equal :: 0:s -> 0:s -> true:false
if :: true:false -> 0:s -> 0:s -> 0:s

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

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

(12)
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:

   sort(l) -> st(0, l) [1]
   st(n, nil) -> cond1(false, n, nil) [2]
   st(n, cons(m', l')) -> cond1(or(equal(n, m'), member(n, l')), n, cons(m', l')) [2]
   cond1(true, n, l) -> cons(n, st(s(n), l)) [1]
   cond1(false, n, nil) -> cond2(gt(n, 0), n, nil) [2]
   cond1(false, n, cons(u', l'')) -> cond2(gt(n, if(gt(u', max(l'')), u', max(l''))), n, cons(u', l'')) [2]
   cond2(true, n, l) -> nil [1]
   cond2(false, n, l) -> st(s(n), l) [1]
   member(n, nil) -> false [1]
   member(0, cons(0, nil)) -> or(true, false) [3]
   member(0, cons(0, cons(m'', l1))) -> or(true, or(equal(0, m''), member(0, l1))) [3]
   member(s(x'), cons(0, nil)) -> or(false, false) [3]
   member(s(x'), cons(0, cons(m1, l2))) -> or(false, or(equal(s(x'), m1), member(s(x'), l2))) [3]
   member(0, cons(s(y'), nil)) -> or(false, false) [3]
   member(0, cons(s(y'), cons(m2, l3))) -> or(false, or(equal(0, m2), member(0, l3))) [3]
   member(s(x''), cons(s(y''), nil)) -> or(equal(x'', y''), false) [3]
   member(s(x''), cons(s(y''), cons(m3, l4))) -> or(equal(x'', y''), or(equal(s(x''), m3), member(s(x''), l4))) [3]
   or(x, true) -> true [1]
   or(x, false) -> x [1]
   equal(0, 0) -> true [1]
   equal(s(x), 0) -> false [1]
   equal(0, s(y)) -> false [1]
   equal(s(x), s(y)) -> equal(x, y) [1]
   gt(0, v) -> false [1]
   gt(s(u), 0) -> true [1]
   gt(s(u), s(v)) -> gt(u, v) [1]
   max(nil) -> 0 [1]
   max(cons(u, nil)) -> if(gt(u, 0), u, 0) [3]
   max(cons(u, cons(u'', l5))) -> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) [3]
   if(true, u, v) -> u [1]
   if(false, u, v) -> v [1]

The TRS has the following type information:
sort :: cons:nil -> cons:nil
st :: 0:s -> cons:nil -> cons:nil
0 :: 0:s
cond1 :: true:false -> 0:s -> cons:nil -> cons:nil
member :: 0:s -> cons:nil -> true:false
true :: true:false
cons :: 0:s -> cons:nil -> cons:nil
s :: 0:s -> 0:s
false :: true:false
cond2 :: true:false -> 0:s -> cons:nil -> cons:nil
gt :: 0:s -> 0:s -> true:false
max :: cons:nil -> 0:s
nil :: cons:nil
or :: true:false -> true:false -> true:false
equal :: 0:s -> 0:s -> true:false
if :: true:false -> 0:s -> 0:s -> 0:s

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

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

   0 => 0
   true => 1
   false => 0
   nil => 0

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

(14)
Obligation:
Complexity RNTS consisting of the following rules:

   cond1(z, z', z'') -{ 2 }-> cond2(gt(n, if(gt(u', max(l'')), u', max(l''))), n, 1 + u' + l'') :|: n >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z' = n, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(n, 0), n, 0) :|: z'' = 0, n >= 0, z' = n, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + n + st(1 + n, l) :|: n >= 0, z = 1, z' = n, l >= 0, z'' = l
   cond2(z, z', z'') -{ 1 }-> st(1 + n, l) :|: n >= 0, z' = n, l >= 0, z = 0, z'' = l
   cond2(z, z', z'') -{ 1 }-> 0 :|: n >= 0, z = 1, z' = n, l >= 0, z'' = l
   equal(z, z') -{ 1 }-> equal(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: x >= 0, z = 1 + x, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' = 1 + y, y >= 0, z = 0
   gt(z, z') -{ 1 }-> gt(u, v) :|: v >= 0, z' = 1 + v, z = 1 + u, u >= 0
   gt(z, z') -{ 1 }-> 1 :|: z = 1 + u, z' = 0, u >= 0
   gt(z, z') -{ 1 }-> 0 :|: v >= 0, z' = v, z = 0
   if(z, z', z'') -{ 1 }-> u :|: z'' = v, v >= 0, z = 1, z' = u, u >= 0
   if(z, z', z'') -{ 1 }-> v :|: z'' = v, v >= 0, z' = u, z = 0, u >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 3 }-> if(gt(u, 0), u, 0) :|: z = 1 + u + 0, u >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 3 }-> or(equal(x'', y''), or(equal(1 + x'', m3), member(1 + x'', l4))) :|: z = 1 + x'', y'' >= 0, x'' >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 3 }-> or(equal(x'', y''), 0) :|: z = 1 + x'', z' = 1 + (1 + y'') + 0, y'' >= 0, x'' >= 0
   member(z, z') -{ 3 }-> or(1, or(equal(0, m''), member(0, l1))) :|: m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 3 }-> or(1, 0) :|: z' = 1 + 0 + 0, z = 0
   member(z, z') -{ 3 }-> or(0, or(equal(0, m2), member(0, l3))) :|: y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 3 }-> or(0, or(equal(1 + x', m1), member(1 + x', l2))) :|: z = 1 + x', x' >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 3 }-> or(0, 0) :|: z = 1 + x', z' = 1 + 0 + 0, x' >= 0
   member(z, z') -{ 3 }-> or(0, 0) :|: z' = 1 + (1 + y') + 0, y' >= 0, z = 0
   member(z, z') -{ 1 }-> 0 :|: n >= 0, z = n, z' = 0
   or(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0
   or(z, z') -{ 1 }-> 1 :|: x >= 0, z' = 1, z = x
   sort(z) -{ 1 }-> st(0, l) :|: z = l, l >= 0
   st(z, z') -{ 2 }-> cond1(or(equal(n, m'), member(n, l')), n, 1 + m' + l') :|: n >= 0, z = n, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, n, 0) :|: n >= 0, z = n, z' = 0


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

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

   or(z, z') -{ 1 }-> 1 :|: x >= 0, z' = 1, z = x
   or(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0
   if(z, z', z'') -{ 1 }-> u :|: z'' = v, v >= 0, z = 1, z' = u, u >= 0
   if(z, z', z'') -{ 1 }-> v :|: z'' = v, v >= 0, z' = u, z = 0, u >= 0

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

(16)
Obligation:
Complexity RNTS consisting of the following rules:

   cond1(z, z', z'') -{ 2 }-> cond2(gt(n, if(gt(u', max(l'')), u', max(l''))), n, 1 + u' + l'') :|: n >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z' = n, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(n, 0), n, 0) :|: z'' = 0, n >= 0, z' = n, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + n + st(1 + n, l) :|: n >= 0, z = 1, z' = n, l >= 0, z'' = l
   cond2(z, z', z'') -{ 1 }-> st(1 + n, l) :|: n >= 0, z' = n, l >= 0, z = 0, z'' = l
   cond2(z, z', z'') -{ 1 }-> 0 :|: n >= 0, z = 1, z' = n, l >= 0, z'' = l
   equal(z, z') -{ 1 }-> equal(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: x >= 0, z = 1 + x, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' = 1 + y, y >= 0, z = 0
   gt(z, z') -{ 1 }-> gt(u, v) :|: v >= 0, z' = 1 + v, z = 1 + u, u >= 0
   gt(z, z') -{ 1 }-> 1 :|: z = 1 + u, z' = 0, u >= 0
   gt(z, z') -{ 1 }-> 0 :|: v >= 0, z' = v, z = 0
   if(z, z', z'') -{ 1 }-> u :|: z'' = v, v >= 0, z = 1, z' = u, u >= 0
   if(z, z', z'') -{ 1 }-> v :|: z'' = v, v >= 0, z' = u, z = 0, u >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 3 }-> if(gt(u, 0), u, 0) :|: z = 1 + u + 0, u >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z = 1 + x', z' = 1 + 0 + 0, x' >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + (1 + y') + 0, y' >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 3 }-> or(equal(x'', y''), or(equal(1 + x'', m3), member(1 + x'', l4))) :|: z = 1 + x'', y'' >= 0, x'' >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 3 }-> or(equal(x'', y''), 0) :|: z = 1 + x'', z' = 1 + (1 + y'') + 0, y'' >= 0, x'' >= 0
   member(z, z') -{ 3 }-> or(1, or(equal(0, m''), member(0, l1))) :|: m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 3 }-> or(0, or(equal(0, m2), member(0, l3))) :|: y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 3 }-> or(0, or(equal(1 + x', m1), member(1 + x', l2))) :|: z = 1 + x', x' >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 1 }-> 0 :|: n >= 0, z = n, z' = 0
   or(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0
   or(z, z') -{ 1 }-> 1 :|: x >= 0, z' = 1, z = x
   sort(z) -{ 1 }-> st(0, l) :|: z = l, l >= 0
   st(z, z') -{ 2 }-> cond1(or(equal(n, m'), member(n, l')), n, 1 + m' + l') :|: n >= 0, z = n, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, n, 0) :|: n >= 0, z = n, z' = 0


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

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', 0), z', 0) :|: z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 1 }-> equal(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 1 }-> gt(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 3 }-> if(gt(z - 1, 0), z - 1, 0) :|: z - 1 >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 3 }-> or(equal(z - 1, y''), or(equal(1 + (z - 1), m3), member(1 + (z - 1), l4))) :|: y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 3 }-> or(equal(z - 1, z' - 2), 0) :|: z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 3 }-> or(1, or(equal(0, m''), member(0, l1))) :|: m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 3 }-> or(0, or(equal(0, m2), member(0, l3))) :|: y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 3 }-> or(0, or(equal(1 + (z - 1), m1), member(1 + (z - 1), l2))) :|: z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 2 }-> cond1(or(equal(z, m'), member(z, l')), z, 1 + m' + l') :|: z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0


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

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

   { gt }
   { equal }
   { if }
   { or }
   { max }
   { member }
   { cond1, cond2, st }
   { sort }

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', 0), z', 0) :|: z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 1 }-> equal(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 1 }-> gt(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 3 }-> if(gt(z - 1, 0), z - 1, 0) :|: z - 1 >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 3 }-> or(equal(z - 1, y''), or(equal(1 + (z - 1), m3), member(1 + (z - 1), l4))) :|: y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 3 }-> or(equal(z - 1, z' - 2), 0) :|: z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 3 }-> or(1, or(equal(0, m''), member(0, l1))) :|: m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 3 }-> or(0, or(equal(0, m2), member(0, l3))) :|: y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 3 }-> or(0, or(equal(1 + (z - 1), m1), member(1 + (z - 1), l2))) :|: z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 2 }-> cond1(or(equal(z, m'), member(z, l')), z, 1 + m' + l') :|: z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {gt}, {equal}, {if}, {or}, {max}, {member}, {cond1,cond2,st}, {sort}

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

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', 0), z', 0) :|: z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 1 }-> equal(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 1 }-> gt(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 3 }-> if(gt(z - 1, 0), z - 1, 0) :|: z - 1 >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 3 }-> or(equal(z - 1, y''), or(equal(1 + (z - 1), m3), member(1 + (z - 1), l4))) :|: y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 3 }-> or(equal(z - 1, z' - 2), 0) :|: z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 3 }-> or(1, or(equal(0, m''), member(0, l1))) :|: m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 3 }-> or(0, or(equal(0, m2), member(0, l3))) :|: y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 3 }-> or(0, or(equal(1 + (z - 1), m1), member(1 + (z - 1), l2))) :|: z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 2 }-> cond1(or(equal(z, m'), member(z, l')), z, 1 + m' + l') :|: z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {gt}, {equal}, {if}, {or}, {max}, {member}, {cond1,cond2,st}, {sort}

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

(23) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', 0), z', 0) :|: z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 1 }-> equal(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 1 }-> gt(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 3 }-> if(gt(z - 1, 0), z - 1, 0) :|: z - 1 >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 3 }-> or(equal(z - 1, y''), or(equal(1 + (z - 1), m3), member(1 + (z - 1), l4))) :|: y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 3 }-> or(equal(z - 1, z' - 2), 0) :|: z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 3 }-> or(1, or(equal(0, m''), member(0, l1))) :|: m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 3 }-> or(0, or(equal(0, m2), member(0, l3))) :|: y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 3 }-> or(0, or(equal(1 + (z - 1), m1), member(1 + (z - 1), l2))) :|: z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 2 }-> cond1(or(equal(z, m'), member(z, l')), z, 1 + m' + l') :|: z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {gt}, {equal}, {if}, {or}, {max}, {member}, {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: ?, size: O(1) [1]

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

(25) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', 0), z', 0) :|: z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 1 }-> equal(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 1 }-> gt(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 3 }-> if(gt(z - 1, 0), z - 1, 0) :|: z - 1 >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 3 }-> or(equal(z - 1, y''), or(equal(1 + (z - 1), m3), member(1 + (z - 1), l4))) :|: y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 3 }-> or(equal(z - 1, z' - 2), 0) :|: z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 3 }-> or(1, or(equal(0, m''), member(0, l1))) :|: m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 3 }-> or(0, or(equal(0, m2), member(0, l3))) :|: y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 3 }-> or(0, or(equal(1 + (z - 1), m1), member(1 + (z - 1), l2))) :|: z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 2 }-> cond1(or(equal(z, m'), member(z, l')), z, 1 + m' + l') :|: z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {equal}, {if}, {or}, {max}, {member}, {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]

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

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 1 }-> equal(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 5 }-> if(s'', z - 1, 0) :|: s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 3 }-> or(equal(z - 1, y''), or(equal(1 + (z - 1), m3), member(1 + (z - 1), l4))) :|: y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 3 }-> or(equal(z - 1, z' - 2), 0) :|: z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 3 }-> or(1, or(equal(0, m''), member(0, l1))) :|: m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 3 }-> or(0, or(equal(0, m2), member(0, l3))) :|: y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 3 }-> or(0, or(equal(1 + (z - 1), m1), member(1 + (z - 1), l2))) :|: z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 2 }-> cond1(or(equal(z, m'), member(z, l')), z, 1 + m' + l') :|: z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {equal}, {if}, {or}, {max}, {member}, {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]

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

(29) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 1 }-> equal(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 5 }-> if(s'', z - 1, 0) :|: s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 3 }-> or(equal(z - 1, y''), or(equal(1 + (z - 1), m3), member(1 + (z - 1), l4))) :|: y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 3 }-> or(equal(z - 1, z' - 2), 0) :|: z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 3 }-> or(1, or(equal(0, m''), member(0, l1))) :|: m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 3 }-> or(0, or(equal(0, m2), member(0, l3))) :|: y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 3 }-> or(0, or(equal(1 + (z - 1), m1), member(1 + (z - 1), l2))) :|: z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 2 }-> cond1(or(equal(z, m'), member(z, l')), z, 1 + m' + l') :|: z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {equal}, {if}, {or}, {max}, {member}, {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: ?, size: O(1) [1]

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

(31) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 1 }-> equal(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 5 }-> if(s'', z - 1, 0) :|: s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 3 }-> or(equal(z - 1, y''), or(equal(1 + (z - 1), m3), member(1 + (z - 1), l4))) :|: y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 3 }-> or(equal(z - 1, z' - 2), 0) :|: z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 3 }-> or(1, or(equal(0, m''), member(0, l1))) :|: m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 3 }-> or(0, or(equal(0, m2), member(0, l3))) :|: y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 3 }-> or(0, or(equal(1 + (z - 1), m1), member(1 + (z - 1), l2))) :|: z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 2 }-> cond1(or(equal(z, m'), member(z, l')), z, 1 + m' + l') :|: z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {if}, {or}, {max}, {member}, {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: O(n^1) [3 + z], size: O(1) [1]

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

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 3 + z }-> s1 :|: s1 >= 0, s1 <= 1, z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 5 }-> if(s'', z - 1, 0) :|: s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 5 + z }-> or(s6, 0) :|: s6 >= 0, s6 <= 1, z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 8 + 2*z }-> or(s7, or(s8, member(1 + (z - 1), l4))) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 6 }-> or(1, or(s3, member(0, l1))) :|: s3 >= 0, s3 <= 1, m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 6 + z }-> or(0, or(s4, member(1 + (z - 1), l2))) :|: s4 >= 0, s4 <= 1, z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 6 }-> or(0, or(s5, member(0, l3))) :|: s5 >= 0, s5 <= 1, y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 5 + z }-> cond1(or(s2, member(z, l')), z, 1 + m' + l') :|: s2 >= 0, s2 <= 1, z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {if}, {or}, {max}, {member}, {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: O(n^1) [3 + z], size: O(1) [1]

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

(35) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 3 + z }-> s1 :|: s1 >= 0, s1 <= 1, z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 5 }-> if(s'', z - 1, 0) :|: s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 5 + z }-> or(s6, 0) :|: s6 >= 0, s6 <= 1, z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 8 + 2*z }-> or(s7, or(s8, member(1 + (z - 1), l4))) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 6 }-> or(1, or(s3, member(0, l1))) :|: s3 >= 0, s3 <= 1, m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 6 + z }-> or(0, or(s4, member(1 + (z - 1), l2))) :|: s4 >= 0, s4 <= 1, z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 6 }-> or(0, or(s5, member(0, l3))) :|: s5 >= 0, s5 <= 1, y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 5 + z }-> cond1(or(s2, member(z, l')), z, 1 + m' + l') :|: s2 >= 0, s2 <= 1, z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {if}, {or}, {max}, {member}, {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: O(n^1) [3 + z], size: O(1) [1]
  if: runtime: ?, size: O(n^1) [z' + z'']

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

(37) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 3 + z }-> s1 :|: s1 >= 0, s1 <= 1, z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 5 }-> if(s'', z - 1, 0) :|: s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 5 + z }-> or(s6, 0) :|: s6 >= 0, s6 <= 1, z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 8 + 2*z }-> or(s7, or(s8, member(1 + (z - 1), l4))) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 6 }-> or(1, or(s3, member(0, l1))) :|: s3 >= 0, s3 <= 1, m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 6 + z }-> or(0, or(s4, member(1 + (z - 1), l2))) :|: s4 >= 0, s4 <= 1, z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 6 }-> or(0, or(s5, member(0, l3))) :|: s5 >= 0, s5 <= 1, y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 5 + z }-> cond1(or(s2, member(z, l')), z, 1 + m' + l') :|: s2 >= 0, s2 <= 1, z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {or}, {max}, {member}, {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: O(n^1) [3 + z], size: O(1) [1]
  if: runtime: O(1) [1], size: O(n^1) [z' + z'']

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

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 3 + z }-> s1 :|: s1 >= 0, s1 <= 1, z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 6 }-> s9 :|: s9 >= 0, s9 <= 0 + (z - 1), s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 5 + z }-> or(s6, 0) :|: s6 >= 0, s6 <= 1, z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 8 + 2*z }-> or(s7, or(s8, member(1 + (z - 1), l4))) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 6 }-> or(1, or(s3, member(0, l1))) :|: s3 >= 0, s3 <= 1, m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 6 + z }-> or(0, or(s4, member(1 + (z - 1), l2))) :|: s4 >= 0, s4 <= 1, z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 6 }-> or(0, or(s5, member(0, l3))) :|: s5 >= 0, s5 <= 1, y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 5 + z }-> cond1(or(s2, member(z, l')), z, 1 + m' + l') :|: s2 >= 0, s2 <= 1, z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {or}, {max}, {member}, {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: O(n^1) [3 + z], size: O(1) [1]
  if: runtime: O(1) [1], size: O(n^1) [z' + z'']

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

(41) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 3 + z }-> s1 :|: s1 >= 0, s1 <= 1, z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 6 }-> s9 :|: s9 >= 0, s9 <= 0 + (z - 1), s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 5 + z }-> or(s6, 0) :|: s6 >= 0, s6 <= 1, z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 8 + 2*z }-> or(s7, or(s8, member(1 + (z - 1), l4))) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 6 }-> or(1, or(s3, member(0, l1))) :|: s3 >= 0, s3 <= 1, m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 6 + z }-> or(0, or(s4, member(1 + (z - 1), l2))) :|: s4 >= 0, s4 <= 1, z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 6 }-> or(0, or(s5, member(0, l3))) :|: s5 >= 0, s5 <= 1, y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 5 + z }-> cond1(or(s2, member(z, l')), z, 1 + m' + l') :|: s2 >= 0, s2 <= 1, z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {or}, {max}, {member}, {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: O(n^1) [3 + z], size: O(1) [1]
  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
  or: runtime: ?, size: O(n^1) [1 + z]

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

(43) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 3 + z }-> s1 :|: s1 >= 0, s1 <= 1, z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 6 }-> s9 :|: s9 >= 0, s9 <= 0 + (z - 1), s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 5 + z }-> or(s6, 0) :|: s6 >= 0, s6 <= 1, z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 8 + 2*z }-> or(s7, or(s8, member(1 + (z - 1), l4))) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 6 }-> or(1, or(s3, member(0, l1))) :|: s3 >= 0, s3 <= 1, m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 6 + z }-> or(0, or(s4, member(1 + (z - 1), l2))) :|: s4 >= 0, s4 <= 1, z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 6 }-> or(0, or(s5, member(0, l3))) :|: s5 >= 0, s5 <= 1, y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 5 + z }-> cond1(or(s2, member(z, l')), z, 1 + m' + l') :|: s2 >= 0, s2 <= 1, z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {max}, {member}, {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: O(n^1) [3 + z], size: O(1) [1]
  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
  or: runtime: O(1) [1], size: O(n^1) [1 + z]

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

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 3 + z }-> s1 :|: s1 >= 0, s1 <= 1, z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 6 }-> s9 :|: s9 >= 0, s9 <= 0 + (z - 1), s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 6 + z }-> s10 :|: s10 >= 0, s10 <= s6 + 1, s6 >= 0, s6 <= 1, z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 8 + 2*z }-> or(s7, or(s8, member(1 + (z - 1), l4))) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 6 }-> or(1, or(s3, member(0, l1))) :|: s3 >= 0, s3 <= 1, m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 6 + z }-> or(0, or(s4, member(1 + (z - 1), l2))) :|: s4 >= 0, s4 <= 1, z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 6 }-> or(0, or(s5, member(0, l3))) :|: s5 >= 0, s5 <= 1, y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 5 + z }-> cond1(or(s2, member(z, l')), z, 1 + m' + l') :|: s2 >= 0, s2 <= 1, z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {max}, {member}, {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: O(n^1) [3 + z], size: O(1) [1]
  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
  or: runtime: O(1) [1], size: O(n^1) [1 + z]

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

(47) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 3 + z }-> s1 :|: s1 >= 0, s1 <= 1, z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 6 }-> s9 :|: s9 >= 0, s9 <= 0 + (z - 1), s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 6 + z }-> s10 :|: s10 >= 0, s10 <= s6 + 1, s6 >= 0, s6 <= 1, z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 8 + 2*z }-> or(s7, or(s8, member(1 + (z - 1), l4))) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 6 }-> or(1, or(s3, member(0, l1))) :|: s3 >= 0, s3 <= 1, m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 6 + z }-> or(0, or(s4, member(1 + (z - 1), l2))) :|: s4 >= 0, s4 <= 1, z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 6 }-> or(0, or(s5, member(0, l3))) :|: s5 >= 0, s5 <= 1, y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 5 + z }-> cond1(or(s2, member(z, l')), z, 1 + m' + l') :|: s2 >= 0, s2 <= 1, z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {max}, {member}, {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: O(n^1) [3 + z], size: O(1) [1]
  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
  or: runtime: O(1) [1], size: O(n^1) [1 + z]
  max: runtime: ?, size: O(n^1) [z]

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

(49) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 2 }-> cond2(gt(z', if(gt(u', max(l'')), u', max(l''))), z', 1 + u' + l'') :|: z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 3 + z }-> s1 :|: s1 >= 0, s1 <= 1, z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 6 }-> s9 :|: s9 >= 0, s9 <= 0 + (z - 1), s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 3 }-> if(gt(u, if(gt(u'', max(l5)), u'', max(l5))), u, if(gt(u'', max(l5)), u'', max(l5))) :|: u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 6 + z }-> s10 :|: s10 >= 0, s10 <= s6 + 1, s6 >= 0, s6 <= 1, z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 8 + 2*z }-> or(s7, or(s8, member(1 + (z - 1), l4))) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 6 }-> or(1, or(s3, member(0, l1))) :|: s3 >= 0, s3 <= 1, m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 6 + z }-> or(0, or(s4, member(1 + (z - 1), l2))) :|: s4 >= 0, s4 <= 1, z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 6 }-> or(0, or(s5, member(0, l3))) :|: s5 >= 0, s5 <= 1, y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 5 + z }-> cond1(or(s2, member(z, l')), z, 1 + m' + l') :|: s2 >= 0, s2 <= 1, z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {member}, {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: O(n^1) [3 + z], size: O(1) [1]
  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
  or: runtime: O(1) [1], size: O(n^1) [1 + z]
  max: runtime: EXP, size: O(n^1) [z]

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

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 7 + inf + inf' + s11 + s14 }-> cond2(s15, z', 1 + u' + l'') :|: s11 >= 0, s11 <= l'', s12 >= 0, s12 <= 1, s13 >= 0, s13 <= l'', s14 >= 0, s14 <= s13 + u', s15 >= 0, s15 <= 1, z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 3 + z }-> s1 :|: s1 >= 0, s1 <= 1, z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 12 + inf'' + inf1 + inf2 + inf3 + s16 + s19 + s21 }-> s25 :|: s16 >= 0, s16 <= l5, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= l5, s19 >= 0, s19 <= s18 + u'', s20 >= 0, s20 <= 1, s21 >= 0, s21 <= l5, s22 >= 0, s22 <= 1, s23 >= 0, s23 <= l5, s24 >= 0, s24 <= s23 + u'', s25 >= 0, s25 <= s24 + u, u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 6 }-> s9 :|: s9 >= 0, s9 <= 0 + (z - 1), s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 6 + z }-> s10 :|: s10 >= 0, s10 <= s6 + 1, s6 >= 0, s6 <= 1, z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 8 + 2*z }-> or(s7, or(s8, member(1 + (z - 1), l4))) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 6 }-> or(1, or(s3, member(0, l1))) :|: s3 >= 0, s3 <= 1, m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 6 + z }-> or(0, or(s4, member(1 + (z - 1), l2))) :|: s4 >= 0, s4 <= 1, z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 6 }-> or(0, or(s5, member(0, l3))) :|: s5 >= 0, s5 <= 1, y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 5 + z }-> cond1(or(s2, member(z, l')), z, 1 + m' + l') :|: s2 >= 0, s2 <= 1, z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {member}, {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: O(n^1) [3 + z], size: O(1) [1]
  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
  or: runtime: O(1) [1], size: O(n^1) [1 + z]
  max: runtime: EXP, size: O(n^1) [z]

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

(53) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 7 + inf + inf' + s11 + s14 }-> cond2(s15, z', 1 + u' + l'') :|: s11 >= 0, s11 <= l'', s12 >= 0, s12 <= 1, s13 >= 0, s13 <= l'', s14 >= 0, s14 <= s13 + u', s15 >= 0, s15 <= 1, z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 3 + z }-> s1 :|: s1 >= 0, s1 <= 1, z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 12 + inf'' + inf1 + inf2 + inf3 + s16 + s19 + s21 }-> s25 :|: s16 >= 0, s16 <= l5, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= l5, s19 >= 0, s19 <= s18 + u'', s20 >= 0, s20 <= 1, s21 >= 0, s21 <= l5, s22 >= 0, s22 <= 1, s23 >= 0, s23 <= l5, s24 >= 0, s24 <= s23 + u'', s25 >= 0, s25 <= s24 + u, u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 6 }-> s9 :|: s9 >= 0, s9 <= 0 + (z - 1), s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 6 + z }-> s10 :|: s10 >= 0, s10 <= s6 + 1, s6 >= 0, s6 <= 1, z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 8 + 2*z }-> or(s7, or(s8, member(1 + (z - 1), l4))) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 6 }-> or(1, or(s3, member(0, l1))) :|: s3 >= 0, s3 <= 1, m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 6 + z }-> or(0, or(s4, member(1 + (z - 1), l2))) :|: s4 >= 0, s4 <= 1, z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 6 }-> or(0, or(s5, member(0, l3))) :|: s5 >= 0, s5 <= 1, y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 5 + z }-> cond1(or(s2, member(z, l')), z, 1 + m' + l') :|: s2 >= 0, s2 <= 1, z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {member}, {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: O(n^1) [3 + z], size: O(1) [1]
  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
  or: runtime: O(1) [1], size: O(n^1) [1 + z]
  max: runtime: EXP, size: O(n^1) [z]
  member: runtime: ?, size: O(1) [2]

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

(55) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: member
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 19 + z + 3*z*z' + 34*z'

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 7 + inf + inf' + s11 + s14 }-> cond2(s15, z', 1 + u' + l'') :|: s11 >= 0, s11 <= l'', s12 >= 0, s12 <= 1, s13 >= 0, s13 <= l'', s14 >= 0, s14 <= s13 + u', s15 >= 0, s15 <= 1, z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 3 + z }-> s1 :|: s1 >= 0, s1 <= 1, z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 12 + inf'' + inf1 + inf2 + inf3 + s16 + s19 + s21 }-> s25 :|: s16 >= 0, s16 <= l5, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= l5, s19 >= 0, s19 <= s18 + u'', s20 >= 0, s20 <= 1, s21 >= 0, s21 <= l5, s22 >= 0, s22 <= 1, s23 >= 0, s23 <= l5, s24 >= 0, s24 <= s23 + u'', s25 >= 0, s25 <= s24 + u, u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 6 }-> s9 :|: s9 >= 0, s9 <= 0 + (z - 1), s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 6 + z }-> s10 :|: s10 >= 0, s10 <= s6 + 1, s6 >= 0, s6 <= 1, z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 8 + 2*z }-> or(s7, or(s8, member(1 + (z - 1), l4))) :|: s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 6 }-> or(1, or(s3, member(0, l1))) :|: s3 >= 0, s3 <= 1, m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 6 + z }-> or(0, or(s4, member(1 + (z - 1), l2))) :|: s4 >= 0, s4 <= 1, z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 6 }-> or(0, or(s5, member(0, l3))) :|: s5 >= 0, s5 <= 1, y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 5 + z }-> cond1(or(s2, member(z, l')), z, 1 + m' + l') :|: s2 >= 0, s2 <= 1, z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: O(n^1) [3 + z], size: O(1) [1]
  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
  or: runtime: O(1) [1], size: O(n^1) [1 + z]
  max: runtime: EXP, size: O(n^1) [z]
  member: runtime: O(n^2) [19 + z + 3*z*z' + 34*z'], size: O(1) [2]

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

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 7 + inf + inf' + s11 + s14 }-> cond2(s15, z', 1 + u' + l'') :|: s11 >= 0, s11 <= l'', s12 >= 0, s12 <= 1, s13 >= 0, s13 <= l'', s14 >= 0, s14 <= s13 + u', s15 >= 0, s15 <= 1, z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 3 + z }-> s1 :|: s1 >= 0, s1 <= 1, z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 12 + inf'' + inf1 + inf2 + inf3 + s16 + s19 + s21 }-> s25 :|: s16 >= 0, s16 <= l5, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= l5, s19 >= 0, s19 <= s18 + u'', s20 >= 0, s20 <= 1, s21 >= 0, s21 <= l5, s22 >= 0, s22 <= 1, s23 >= 0, s23 <= l5, s24 >= 0, s24 <= s23 + u'', s25 >= 0, s25 <= s24 + u, u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 6 }-> s9 :|: s9 >= 0, s9 <= 0 + (z - 1), s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 6 + z }-> s10 :|: s10 >= 0, s10 <= s6 + 1, s6 >= 0, s6 <= 1, z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 27 + 34*l1 }-> s30 :|: s28 >= 0, s28 <= 2, s29 >= 0, s29 <= s3 + 1, s30 >= 0, s30 <= 1 + 1, s3 >= 0, s3 <= 1, m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 27 + 34*l2 + 3*l2*z + 2*z }-> s33 :|: s31 >= 0, s31 <= 2, s32 >= 0, s32 <= s4 + 1, s33 >= 0, s33 <= 0 + 1, s4 >= 0, s4 <= 1, z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 27 + 34*l3 }-> s36 :|: s34 >= 0, s34 <= 2, s35 >= 0, s35 <= s5 + 1, s36 >= 0, s36 <= 0 + 1, s5 >= 0, s5 <= 1, y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 29 + 34*l4 + 3*l4*z + 3*z }-> s39 :|: s37 >= 0, s37 <= 2, s38 >= 0, s38 <= s8 + 1, s39 >= 0, s39 <= s7 + 1, s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 25 + 34*l' + 3*l'*z + 2*z }-> cond1(s27, z, 1 + m' + l') :|: s26 >= 0, s26 <= 2, s27 >= 0, s27 <= s2 + 1, s2 >= 0, s2 <= 1, z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: O(n^1) [3 + z], size: O(1) [1]
  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
  or: runtime: O(1) [1], size: O(n^1) [1 + z]
  max: runtime: EXP, size: O(n^1) [z]
  member: runtime: O(n^2) [19 + z + 3*z*z' + 34*z'], size: O(1) [2]

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

(59) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: cond1
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

Computed SIZE bound using CoFloCo for: cond2
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

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

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 7 + inf + inf' + s11 + s14 }-> cond2(s15, z', 1 + u' + l'') :|: s11 >= 0, s11 <= l'', s12 >= 0, s12 <= 1, s13 >= 0, s13 <= l'', s14 >= 0, s14 <= s13 + u', s15 >= 0, s15 <= 1, z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 3 + z }-> s1 :|: s1 >= 0, s1 <= 1, z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 12 + inf'' + inf1 + inf2 + inf3 + s16 + s19 + s21 }-> s25 :|: s16 >= 0, s16 <= l5, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= l5, s19 >= 0, s19 <= s18 + u'', s20 >= 0, s20 <= 1, s21 >= 0, s21 <= l5, s22 >= 0, s22 <= 1, s23 >= 0, s23 <= l5, s24 >= 0, s24 <= s23 + u'', s25 >= 0, s25 <= s24 + u, u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 6 }-> s9 :|: s9 >= 0, s9 <= 0 + (z - 1), s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 6 + z }-> s10 :|: s10 >= 0, s10 <= s6 + 1, s6 >= 0, s6 <= 1, z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 27 + 34*l1 }-> s30 :|: s28 >= 0, s28 <= 2, s29 >= 0, s29 <= s3 + 1, s30 >= 0, s30 <= 1 + 1, s3 >= 0, s3 <= 1, m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 27 + 34*l2 + 3*l2*z + 2*z }-> s33 :|: s31 >= 0, s31 <= 2, s32 >= 0, s32 <= s4 + 1, s33 >= 0, s33 <= 0 + 1, s4 >= 0, s4 <= 1, z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 27 + 34*l3 }-> s36 :|: s34 >= 0, s34 <= 2, s35 >= 0, s35 <= s5 + 1, s36 >= 0, s36 <= 0 + 1, s5 >= 0, s5 <= 1, y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 29 + 34*l4 + 3*l4*z + 3*z }-> s39 :|: s37 >= 0, s37 <= 2, s38 >= 0, s38 <= s8 + 1, s39 >= 0, s39 <= s7 + 1, s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 25 + 34*l' + 3*l'*z + 2*z }-> cond1(s27, z, 1 + m' + l') :|: s26 >= 0, s26 <= 2, s27 >= 0, s27 <= s2 + 1, s2 >= 0, s2 <= 1, z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: O(n^1) [3 + z], size: O(1) [1]
  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
  or: runtime: O(1) [1], size: O(n^1) [1 + z]
  max: runtime: EXP, size: O(n^1) [z]
  member: runtime: O(n^2) [19 + z + 3*z*z' + 34*z'], size: O(1) [2]
  cond1: runtime: ?, size: INF
  cond2: runtime: ?, size: INF
  st: runtime: ?, size: INF

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

(61) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: cond1
after applying outer abstraction to obtain an ITS,
resulting in: INF with polynomial bound: ?

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

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

   cond1(z, z', z'') -{ 4 }-> cond2(s, z', 0) :|: s >= 0, s <= 1, z'' = 0, z' >= 0, z = 0
   cond1(z, z', z'') -{ 7 + inf + inf' + s11 + s14 }-> cond2(s15, z', 1 + u' + l'') :|: s11 >= 0, s11 <= l'', s12 >= 0, s12 <= 1, s13 >= 0, s13 <= l'', s14 >= 0, s14 <= s13 + u', s15 >= 0, s15 <= 1, z' >= 0, l'' >= 0, z'' = 1 + u' + l'', u' >= 0, z = 0
   cond1(z, z', z'') -{ 1 }-> 1 + z' + st(1 + z', z'') :|: z' >= 0, z = 1, z'' >= 0
   cond2(z, z', z'') -{ 1 }-> st(1 + z', z'') :|: z' >= 0, z'' >= 0, z = 0
   cond2(z, z', z'') -{ 1 }-> 0 :|: z' >= 0, z = 1, z'' >= 0
   equal(z, z') -{ 3 + z }-> s1 :|: s1 >= 0, s1 <= 1, z - 1 >= 0, z' - 1 >= 0
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z - 1 >= 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' - 1 >= 0, z = 0
   gt(z, z') -{ 2 + z' }-> s' :|: s' >= 0, s' <= 1, z' - 1 >= 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 1 :|: z' = 0, z - 1 >= 0
   gt(z, z') -{ 1 }-> 0 :|: z' >= 0, z = 0
   if(z, z', z'') -{ 1 }-> z' :|: z'' >= 0, z = 1, z' >= 0
   if(z, z', z'') -{ 1 }-> z'' :|: z'' >= 0, z = 0, z' >= 0
   max(z) -{ 12 + inf'' + inf1 + inf2 + inf3 + s16 + s19 + s21 }-> s25 :|: s16 >= 0, s16 <= l5, s17 >= 0, s17 <= 1, s18 >= 0, s18 <= l5, s19 >= 0, s19 <= s18 + u'', s20 >= 0, s20 <= 1, s21 >= 0, s21 <= l5, s22 >= 0, s22 <= 1, s23 >= 0, s23 <= l5, s24 >= 0, s24 <= s23 + u'', s25 >= 0, s25 <= s24 + u, u'' >= 0, z = 1 + u + (1 + u'' + l5), l5 >= 0, u >= 0
   max(z) -{ 6 }-> s9 :|: s9 >= 0, s9 <= 0 + (z - 1), s'' >= 0, s'' <= 1, z - 1 >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 6 + z }-> s10 :|: s10 >= 0, s10 <= s6 + 1, s6 >= 0, s6 <= 1, z' - 2 >= 0, z - 1 >= 0
   member(z, z') -{ 27 + 34*l1 }-> s30 :|: s28 >= 0, s28 <= 2, s29 >= 0, s29 <= s3 + 1, s30 >= 0, s30 <= 1 + 1, s3 >= 0, s3 <= 1, m'' >= 0, z' = 1 + 0 + (1 + m'' + l1), l1 >= 0, z = 0
   member(z, z') -{ 27 + 34*l2 + 3*l2*z + 2*z }-> s33 :|: s31 >= 0, s31 <= 2, s32 >= 0, s32 <= s4 + 1, s33 >= 0, s33 <= 0 + 1, s4 >= 0, s4 <= 1, z - 1 >= 0, z' = 1 + 0 + (1 + m1 + l2), m1 >= 0, l2 >= 0
   member(z, z') -{ 27 + 34*l3 }-> s36 :|: s34 >= 0, s34 <= 2, s35 >= 0, s35 <= s5 + 1, s36 >= 0, s36 <= 0 + 1, s5 >= 0, s5 <= 1, y' >= 0, z' = 1 + (1 + y') + (1 + m2 + l3), z = 0, m2 >= 0, l3 >= 0
   member(z, z') -{ 29 + 34*l4 + 3*l4*z + 3*z }-> s39 :|: s37 >= 0, s37 <= 2, s38 >= 0, s38 <= s8 + 1, s39 >= 0, s39 <= s7 + 1, s7 >= 0, s7 <= 1, s8 >= 0, s8 <= 1, y'' >= 0, z - 1 >= 0, z' = 1 + (1 + y'') + (1 + m3 + l4), l4 >= 0, m3 >= 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z = 0, x >= 0, 1 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' = 1 + 0 + 0, z - 1 >= 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 4 }-> x :|: z' - 2 >= 0, z = 0, x >= 0, 0 = x, 0 = 0
   member(z, z') -{ 1 }-> 0 :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> z :|: z >= 0, z' = 0
   or(z, z') -{ 1 }-> 1 :|: z >= 0, z' = 1
   sort(z) -{ 1 }-> st(0, z) :|: z >= 0
   st(z, z') -{ 25 + 34*l' + 3*l'*z + 2*z }-> cond1(s27, z, 1 + m' + l') :|: s26 >= 0, s26 <= 2, s27 >= 0, s27 <= s2 + 1, s2 >= 0, s2 <= 1, z >= 0, z' = 1 + m' + l', m' >= 0, l' >= 0
   st(z, z') -{ 2 }-> cond1(0, z, 0) :|: z >= 0, z' = 0

Function symbols to be analyzed: {cond1,cond2,st}, {sort}
Previous analysis results are:
  gt: runtime: O(n^1) [2 + z'], size: O(1) [1]
  equal: runtime: O(n^1) [3 + z], size: O(1) [1]
  if: runtime: O(1) [1], size: O(n^1) [z' + z'']
  or: runtime: O(1) [1], size: O(n^1) [1 + z]
  max: runtime: EXP, size: O(n^1) [z]
  member: runtime: O(n^2) [19 + z + 3*z*z' + 34*z'], size: O(1) [2]
  cond1: runtime: INF, size: INF
  cond2: runtime: ?, size: INF
  st: runtime: ?, size: INF

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

(63) CompletionProof (UPPER BOUND(ID))
The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:
none

And the following fresh constants: none

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

(64)
Obligation:
Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is:

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

   sort(l) -> st(0, l) [1]
   st(n, l) -> cond1(member(n, l), n, l) [1]
   cond1(true, n, l) -> cons(n, st(s(n), l)) [1]
   cond1(false, n, l) -> cond2(gt(n, max(l)), n, l) [1]
   cond2(true, n, l) -> nil [1]
   cond2(false, n, l) -> st(s(n), l) [1]
   member(n, nil) -> false [1]
   member(n, cons(m, l)) -> or(equal(n, m), member(n, l)) [1]
   or(x, true) -> true [1]
   or(x, false) -> x [1]
   equal(0, 0) -> true [1]
   equal(s(x), 0) -> false [1]
   equal(0, s(y)) -> false [1]
   equal(s(x), s(y)) -> equal(x, y) [1]
   gt(0, v) -> false [1]
   gt(s(u), 0) -> true [1]
   gt(s(u), s(v)) -> gt(u, v) [1]
   max(nil) -> 0 [1]
   max(cons(u, l)) -> if(gt(u, max(l)), u, max(l)) [1]
   if(true, u, v) -> u [1]
   if(false, u, v) -> v [1]

The TRS has the following type information:
sort :: cons:nil -> cons:nil
st :: 0:s -> cons:nil -> cons:nil
0 :: 0:s
cond1 :: true:false -> 0:s -> cons:nil -> cons:nil
member :: 0:s -> cons:nil -> true:false
true :: true:false
cons :: 0:s -> cons:nil -> cons:nil
s :: 0:s -> 0:s
false :: true:false
cond2 :: true:false -> 0:s -> cons:nil -> cons:nil
gt :: 0:s -> 0:s -> true:false
max :: cons:nil -> 0:s
nil :: cons:nil
or :: true:false -> true:false -> true:false
equal :: 0:s -> 0:s -> true:false
if :: true:false -> 0:s -> 0:s -> 0:s

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

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

   0 => 0
   true => 1
   false => 0
   nil => 0

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

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

   cond1(z, z', z'') -{ 1 }-> cond2(gt(n, max(l)), n, l) :|: n >= 0, z' = n, l >= 0, z = 0, z'' = l
   cond1(z, z', z'') -{ 1 }-> 1 + n + st(1 + n, l) :|: n >= 0, z = 1, z' = n, l >= 0, z'' = l
   cond2(z, z', z'') -{ 1 }-> st(1 + n, l) :|: n >= 0, z' = n, l >= 0, z = 0, z'' = l
   cond2(z, z', z'') -{ 1 }-> 0 :|: n >= 0, z = 1, z' = n, l >= 0, z'' = l
   equal(z, z') -{ 1 }-> equal(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x
   equal(z, z') -{ 1 }-> 1 :|: z = 0, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: x >= 0, z = 1 + x, z' = 0
   equal(z, z') -{ 1 }-> 0 :|: z' = 1 + y, y >= 0, z = 0
   gt(z, z') -{ 1 }-> gt(u, v) :|: v >= 0, z' = 1 + v, z = 1 + u, u >= 0
   gt(z, z') -{ 1 }-> 1 :|: z = 1 + u, z' = 0, u >= 0
   gt(z, z') -{ 1 }-> 0 :|: v >= 0, z' = v, z = 0
   if(z, z', z'') -{ 1 }-> u :|: z'' = v, v >= 0, z = 1, z' = u, u >= 0
   if(z, z', z'') -{ 1 }-> v :|: z'' = v, v >= 0, z' = u, z = 0, u >= 0
   max(z) -{ 1 }-> if(gt(u, max(l)), u, max(l)) :|: z = 1 + u + l, l >= 0, u >= 0
   max(z) -{ 1 }-> 0 :|: z = 0
   member(z, z') -{ 1 }-> or(equal(n, m), member(n, l)) :|: n >= 0, z = n, l >= 0, z' = 1 + m + l, m >= 0
   member(z, z') -{ 1 }-> 0 :|: n >= 0, z = n, z' = 0
   or(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0
   or(z, z') -{ 1 }-> 1 :|: x >= 0, z' = 1, z = x
   sort(z) -{ 1 }-> st(0, l) :|: z = l, l >= 0
   st(z, z') -{ 1 }-> cond1(member(n, l), n, l) :|: z' = l, n >= 0, z = n, l >= 0

Only complete derivations are relevant for the runtime complexity.

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

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   sort(z0) -> st(0, z0)
   st(z0, z1) -> cond1(member(z0, z1), z0, z1)
   cond1(true, z0, z1) -> cons(z0, st(s(z0), z1))
   cond1(false, z0, z1) -> cond2(gt(z0, max(z1)), z0, z1)
   cond2(true, z0, z1) -> nil
   cond2(false, z0, z1) -> st(s(z0), z1)
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   SORT(z0) -> c(ST(0, z0))
   ST(z0, z1) -> c1(COND1(member(z0, z1), z0, z1), MEMBER(z0, z1))
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND1(false, z0, z1) -> c3(COND2(gt(z0, max(z1)), z0, z1), GT(z0, max(z1)), MAX(z1))
   COND2(true, z0, z1) -> c4
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   MEMBER(z0, nil) -> c6
   MEMBER(z0, cons(z1, z2)) -> c7(OR(equal(z0, z1), member(z0, z2)), EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(OR(equal(z0, z1), member(z0, z2)), MEMBER(z0, z2))
   OR(z0, true) -> c9
   OR(z0, false) -> c10
   EQUAL(0, 0) -> c11
   EQUAL(s(z0), 0) -> c12
   EQUAL(0, s(z0)) -> c13
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(0, z0) -> c15
   GT(s(z0), 0) -> c16
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MAX(nil) -> c18
   MAX(cons(z0, z1)) -> c19(IF(gt(z0, max(z1)), z0, max(z1)), GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(IF(gt(z0, max(z1)), z0, max(z1)), MAX(z1))
   IF(true, z0, z1) -> c21
   IF(false, z0, z1) -> c22
S tuples:
   SORT(z0) -> c(ST(0, z0))
   ST(z0, z1) -> c1(COND1(member(z0, z1), z0, z1), MEMBER(z0, z1))
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND1(false, z0, z1) -> c3(COND2(gt(z0, max(z1)), z0, z1), GT(z0, max(z1)), MAX(z1))
   COND2(true, z0, z1) -> c4
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   MEMBER(z0, nil) -> c6
   MEMBER(z0, cons(z1, z2)) -> c7(OR(equal(z0, z1), member(z0, z2)), EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(OR(equal(z0, z1), member(z0, z2)), MEMBER(z0, z2))
   OR(z0, true) -> c9
   OR(z0, false) -> c10
   EQUAL(0, 0) -> c11
   EQUAL(s(z0), 0) -> c12
   EQUAL(0, s(z0)) -> c13
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(0, z0) -> c15
   GT(s(z0), 0) -> c16
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MAX(nil) -> c18
   MAX(cons(z0, z1)) -> c19(IF(gt(z0, max(z1)), z0, max(z1)), GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(IF(gt(z0, max(z1)), z0, max(z1)), MAX(z1))
   IF(true, z0, z1) -> c21
   IF(false, z0, z1) -> c22
K tuples:none
Defined Rule Symbols:   sort_1, st_2, cond1_3, cond2_3, member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   SORT_1, ST_2, COND1_3, COND2_3, MEMBER_2, OR_2, EQUAL_2, GT_2, MAX_1, IF_3

Compound Symbols:   c_1, c1_2, c2_1, c3_3, c4, c5_1, c6, c7_2, c8_2, c9, c10, c11, c12, c13, c14_1, c15, c16, c17_1, c18, c19_3, c20_2, c21, c22


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

(69) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   SORT(z0) -> c(ST(0, z0))
Removed 12 trailing nodes:
   EQUAL(s(z0), 0) -> c12
   GT(0, z0) -> c15
   MEMBER(z0, nil) -> c6
   GT(s(z0), 0) -> c16
   IF(false, z0, z1) -> c22
   EQUAL(0, 0) -> c11
   IF(true, z0, z1) -> c21
   MAX(nil) -> c18
   COND2(true, z0, z1) -> c4
   EQUAL(0, s(z0)) -> c13
   OR(z0, false) -> c10
   OR(z0, true) -> c9

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   sort(z0) -> st(0, z0)
   st(z0, z1) -> cond1(member(z0, z1), z0, z1)
   cond1(true, z0, z1) -> cons(z0, st(s(z0), z1))
   cond1(false, z0, z1) -> cond2(gt(z0, max(z1)), z0, z1)
   cond2(true, z0, z1) -> nil
   cond2(false, z0, z1) -> st(s(z0), z1)
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   ST(z0, z1) -> c1(COND1(member(z0, z1), z0, z1), MEMBER(z0, z1))
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND1(false, z0, z1) -> c3(COND2(gt(z0, max(z1)), z0, z1), GT(z0, max(z1)), MAX(z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   MEMBER(z0, cons(z1, z2)) -> c7(OR(equal(z0, z1), member(z0, z2)), EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(OR(equal(z0, z1), member(z0, z2)), MEMBER(z0, z2))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MAX(cons(z0, z1)) -> c19(IF(gt(z0, max(z1)), z0, max(z1)), GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(IF(gt(z0, max(z1)), z0, max(z1)), MAX(z1))
S tuples:
   ST(z0, z1) -> c1(COND1(member(z0, z1), z0, z1), MEMBER(z0, z1))
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND1(false, z0, z1) -> c3(COND2(gt(z0, max(z1)), z0, z1), GT(z0, max(z1)), MAX(z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   MEMBER(z0, cons(z1, z2)) -> c7(OR(equal(z0, z1), member(z0, z2)), EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(OR(equal(z0, z1), member(z0, z2)), MEMBER(z0, z2))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MAX(cons(z0, z1)) -> c19(IF(gt(z0, max(z1)), z0, max(z1)), GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(IF(gt(z0, max(z1)), z0, max(z1)), MAX(z1))
K tuples:none
Defined Rule Symbols:   sort_1, st_2, cond1_3, cond2_3, member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   ST_2, COND1_3, COND2_3, MEMBER_2, EQUAL_2, GT_2, MAX_1

Compound Symbols:   c1_2, c2_1, c3_3, c5_1, c7_2, c8_2, c14_1, c17_1, c19_3, c20_2


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

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   sort(z0) -> st(0, z0)
   st(z0, z1) -> cond1(member(z0, z1), z0, z1)
   cond1(true, z0, z1) -> cons(z0, st(s(z0), z1))
   cond1(false, z0, z1) -> cond2(gt(z0, max(z1)), z0, z1)
   cond2(true, z0, z1) -> nil
   cond2(false, z0, z1) -> st(s(z0), z1)
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   ST(z0, z1) -> c1(COND1(member(z0, z1), z0, z1), MEMBER(z0, z1))
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND1(false, z0, z1) -> c3(COND2(gt(z0, max(z1)), z0, z1), GT(z0, max(z1)), MAX(z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c19(GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
S tuples:
   ST(z0, z1) -> c1(COND1(member(z0, z1), z0, z1), MEMBER(z0, z1))
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND1(false, z0, z1) -> c3(COND2(gt(z0, max(z1)), z0, z1), GT(z0, max(z1)), MAX(z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c19(GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
K tuples:none
Defined Rule Symbols:   sort_1, st_2, cond1_3, cond2_3, member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   ST_2, COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1

Compound Symbols:   c1_2, c2_1, c3_3, c5_1, c14_1, c17_1, c7_1, c8_1, c19_2, c20_1


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

(73) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   sort(z0) -> st(0, z0)
   st(z0, z1) -> cond1(member(z0, z1), z0, z1)
   cond1(true, z0, z1) -> cons(z0, st(s(z0), z1))
   cond1(false, z0, z1) -> cond2(gt(z0, max(z1)), z0, z1)
   cond2(true, z0, z1) -> nil
   cond2(false, z0, z1) -> st(s(z0), z1)

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   ST(z0, z1) -> c1(COND1(member(z0, z1), z0, z1), MEMBER(z0, z1))
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND1(false, z0, z1) -> c3(COND2(gt(z0, max(z1)), z0, z1), GT(z0, max(z1)), MAX(z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c19(GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
S tuples:
   ST(z0, z1) -> c1(COND1(member(z0, z1), z0, z1), MEMBER(z0, z1))
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND1(false, z0, z1) -> c3(COND2(gt(z0, max(z1)), z0, z1), GT(z0, max(z1)), MAX(z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c19(GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
K tuples:none
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   ST_2, COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1

Compound Symbols:   c1_2, c2_1, c3_3, c5_1, c14_1, c17_1, c7_1, c8_1, c19_2, c20_1


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ST(z0, z1) -> c1(COND1(member(z0, z1), z0, z1), MEMBER(z0, z1)) by 
   ST(z0, nil) -> c1(COND1(false, z0, nil), MEMBER(z0, nil))
   ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2)))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND1(false, z0, z1) -> c3(COND2(gt(z0, max(z1)), z0, z1), GT(z0, max(z1)), MAX(z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c19(GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil), MEMBER(z0, nil))
   ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND1(false, z0, z1) -> c3(COND2(gt(z0, max(z1)), z0, z1), GT(z0, max(z1)), MAX(z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c19(GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil), MEMBER(z0, nil))
   ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2)))
K tuples:none
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c3_3, c5_1, c14_1, c17_1, c7_1, c8_1, c19_2, c20_1, c1_2


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

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND1(false, z0, z1) -> c3(COND2(gt(z0, max(z1)), z0, z1), GT(z0, max(z1)), MAX(z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c19(GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND1(false, z0, z1) -> c3(COND2(gt(z0, max(z1)), z0, z1), GT(z0, max(z1)), MAX(z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c19(GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
K tuples:none
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c3_3, c5_1, c14_1, c17_1, c7_1, c8_1, c19_2, c20_1, c1_2, c1_1


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace COND1(false, z0, z1) -> c3(COND2(gt(z0, max(z1)), z0, z1), GT(z0, max(z1)), MAX(z1)) by 
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), GT(0, max(x1)), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)), MAX(nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c19(GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), GT(0, max(x1)), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)), MAX(nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c19(GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), GT(0, max(x1)), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)), MAX(nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
K tuples:none
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c19_2, c20_1, c1_2, c1_1, c3_3


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

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c19(GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c19(GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
K tuples:none
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c19_2, c20_1, c1_2, c1_1, c3_3, c3_2


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

(83) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
We considered the (Usable) Rules:none
And the Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c19(GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = [1]
   POL(COND1(x_1, x_2, x_3)) = x_2
   POL(COND2(x_1, x_2, x_3)) = 0
   POL(EQUAL(x_1, x_2)) = 0
   POL(GT(x_1, x_2)) = 0
   POL(MAX(x_1)) = 0
   POL(MEMBER(x_1, x_2)) = 0
   POL(ST(x_1, x_2)) = x_1
   POL(c1(x_1)) = x_1
   POL(c1(x_1, x_2)) = x_1 + x_2
   POL(c14(x_1)) = x_1
   POL(c17(x_1)) = x_1
   POL(c19(x_1, x_2)) = x_1 + x_2
   POL(c2(x_1)) = x_1
   POL(c20(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c8(x_1)) = x_1
   POL(cons(x_1, x_2)) = 0
   POL(equal(x_1, x_2)) = 0
   POL(false) = 0
   POL(gt(x_1, x_2)) = 0
   POL(if(x_1, x_2, x_3)) = [1]
   POL(max(x_1)) = 0
   POL(member(x_1, x_2)) = [1] + x_1 + x_2
   POL(nil) = 0
   POL(or(x_1, x_2)) = [1] + x_1
   POL(s(x_1)) = 0
   POL(true) = 0

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c19(GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c19(GT(z0, max(z1)), MAX(z1))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c19_2, c20_1, c1_2, c1_1, c3_3, c3_2


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

(85) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MAX(cons(z0, z1)) -> c19(GT(z0, max(z1)), MAX(z1)) by 
   MAX(cons(x0, nil)) -> c19(GT(x0, 0), MAX(nil))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, nil)) -> c19(GT(x0, 0), MAX(nil))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, nil)) -> c19(GT(x0, 0), MAX(nil))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c3_3, c3_2, c19_2


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

(87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MAX(cons(x0, nil)) -> c19(GT(x0, 0), MAX(nil))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c3_3, c3_2, c19_2


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

(89) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ST(z0, cons(z1, z2)) -> c1(COND1(or(equal(z0, z1), member(z0, z2)), z0, cons(z1, z2)), MEMBER(z0, cons(z1, z2))) by 
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(0, cons(0, x2)) -> c1(COND1(or(true, member(0, x2)), 0, cons(0, x2)), MEMBER(0, cons(0, x2)))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c1(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)), MEMBER(0, cons(s(z0), x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(0, cons(0, x2)) -> c1(COND1(or(true, member(0, x2)), 0, cons(0, x2)), MEMBER(0, cons(0, x2)))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c1(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)), MEMBER(0, cons(s(z0), x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(0, cons(0, x2)) -> c1(COND1(or(true, member(0, x2)), 0, cons(0, x2)), MEMBER(0, cons(0, x2)))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c1(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)), MEMBER(0, cons(s(z0), x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_3, c3_2, c19_2, c1_2


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

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(0, x2)) -> c(MEMBER(0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(0, cons(s(z0), x2)) -> c(MEMBER(0, cons(s(z0), x2)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(0, x2)) -> c(MEMBER(0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(0, cons(s(z0), x2)) -> c(MEMBER(0, cons(s(z0), x2)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_3, c3_2, c19_2, c1_2, c_1


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

(93) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 2 leading nodes:
   ST(0, cons(0, x2)) -> c(MEMBER(0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(MEMBER(0, cons(s(z0), x2)))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_3, c3_2, c19_2, c1_2, c_1


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

(95) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_3, c3_2, c19_2, c1_2, c_1


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

(97) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
We considered the (Usable) Rules:none
And the Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(COND1(x_1, x_2, x_3)) = x_3
   POL(COND2(x_1, x_2, x_3)) = x_3
   POL(EQUAL(x_1, x_2)) = 0
   POL(GT(x_1, x_2)) = 0
   POL(MAX(x_1)) = 0
   POL(MEMBER(x_1, x_2)) = 0
   POL(ST(x_1, x_2)) = x_2
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c1(x_1, x_2)) = x_1 + x_2
   POL(c14(x_1)) = x_1
   POL(c17(x_1)) = x_1
   POL(c19(x_1, x_2)) = x_1 + x_2
   POL(c2(x_1)) = x_1
   POL(c20(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c8(x_1)) = x_1
   POL(cons(x_1, x_2)) = [1] + x_2
   POL(equal(x_1, x_2)) = 0
   POL(false) = 0
   POL(gt(x_1, x_2)) = 0
   POL(if(x_1, x_2, x_3)) = [1]
   POL(max(x_1)) = 0
   POL(member(x_1, x_2)) = [1] + x_1 + x_2
   POL(nil) = 0
   POL(or(x_1, x_2)) = [1]
   POL(s(x_1)) = 0
   POL(true) = 0

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1)))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_3, c3_2, c19_2, c1_2, c_1


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

(99) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace COND1(false, x0, cons(z0, z1)) -> c3(COND2(gt(x0, if(gt(z0, max(z1)), z0, max(z1))), x0, cons(z0, z1)), GT(x0, max(cons(z0, z1))), MAX(cons(z0, z1))) by 
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), GT(0, max(cons(x1, x2))), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(x1, x2)) -> c3(GT(x0, max(cons(x1, x2))), MAX(cons(x1, x2)))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), GT(0, max(cons(x1, x2))), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(x1, x2)) -> c3(GT(x0, max(cons(x1, x2))), MAX(cons(x1, x2)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), GT(0, max(cons(x1, x2))), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(x1, x2)) -> c3(GT(x0, max(cons(x1, x2))), MAX(cons(x1, x2)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c19_2, c1_2, c_1, c3_3


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

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(x1, x2)) -> c3(GT(x0, max(cons(x1, x2))), MAX(cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(x1, x2)) -> c3(GT(x0, max(cons(x1, x2))), MAX(cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c19_2, c1_2, c_1, c3_3


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

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c19_2, c1_2, c_1, c3_3, c4_1


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

(105) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
We considered the (Usable) Rules:none
And the Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = [1]
   POL(COND1(x_1, x_2, x_3)) = x_2
   POL(COND2(x_1, x_2, x_3)) = 0
   POL(EQUAL(x_1, x_2)) = 0
   POL(GT(x_1, x_2)) = 0
   POL(MAX(x_1)) = 0
   POL(MEMBER(x_1, x_2)) = 0
   POL(ST(x_1, x_2)) = x_1
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c1(x_1, x_2)) = x_1 + x_2
   POL(c14(x_1)) = x_1
   POL(c17(x_1)) = x_1
   POL(c19(x_1, x_2)) = x_1 + x_2
   POL(c2(x_1)) = x_1
   POL(c20(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c4(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c8(x_1)) = x_1
   POL(cons(x_1, x_2)) = 0
   POL(equal(x_1, x_2)) = 0
   POL(false) = 0
   POL(gt(x_1, x_2)) = 0
   POL(if(x_1, x_2, x_3)) = [1]
   POL(max(x_1)) = 0
   POL(member(x_1, x_2)) = [1] + x_1 + x_2
   POL(nil) = 0
   POL(or(x_1, x_2)) = [1]
   POL(s(x_1)) = 0
   POL(true) = 0

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c19_2, c1_2, c_1, c3_3, c4_1


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

(107) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
We considered the (Usable) Rules:none
And the Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = [1]
   POL(COND1(x_1, x_2, x_3)) = x_3
   POL(COND2(x_1, x_2, x_3)) = x_3
   POL(EQUAL(x_1, x_2)) = 0
   POL(GT(x_1, x_2)) = 0
   POL(MAX(x_1)) = 0
   POL(MEMBER(x_1, x_2)) = 0
   POL(ST(x_1, x_2)) = x_2
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c1(x_1, x_2)) = x_1 + x_2
   POL(c14(x_1)) = x_1
   POL(c17(x_1)) = x_1
   POL(c19(x_1, x_2)) = x_1 + x_2
   POL(c2(x_1)) = x_1
   POL(c20(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c4(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c8(x_1)) = x_1
   POL(cons(x_1, x_2)) = [1] + x_1
   POL(equal(x_1, x_2)) = 0
   POL(false) = 0
   POL(gt(x_1, x_2)) = 0
   POL(if(x_1, x_2, x_3)) = [1]
   POL(max(x_1)) = 0
   POL(member(x_1, x_2)) = [1] + x_1 + x_2
   POL(nil) = 0
   POL(or(x_1, x_2)) = [1]
   POL(s(x_1)) = [1]
   POL(true) = 0

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil)))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c19_2, c1_2, c_1, c3_3, c4_1


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

(109) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace COND1(false, x0, nil) -> c3(COND2(gt(x0, 0), x0, nil), GT(x0, max(nil))) by 
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil), GT(0, max(nil)))
   COND1(false, s(z0), nil) -> c3(COND2(true, s(z0), nil), GT(s(z0), max(nil)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil), GT(0, max(nil)))
   COND1(false, s(z0), nil) -> c3(COND2(true, s(z0), nil), GT(s(z0), max(nil)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil), GT(0, max(nil)))
   COND1(false, s(z0), nil) -> c3(COND2(true, s(z0), nil), GT(s(z0), max(nil)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c19_2, c1_2, c_1, c3_3, c4_1, c3_1


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

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c19_2, c1_2, c_1, c3_3, c4_1, c3_1


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

(113) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
We considered the (Usable) Rules:none
And the Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = [1]
   POL(COND1(x_1, x_2, x_3)) = x_2
   POL(COND2(x_1, x_2, x_3)) = 0
   POL(EQUAL(x_1, x_2)) = 0
   POL(GT(x_1, x_2)) = 0
   POL(MAX(x_1)) = 0
   POL(MEMBER(x_1, x_2)) = 0
   POL(ST(x_1, x_2)) = x_1
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c1(x_1, x_2)) = x_1 + x_2
   POL(c14(x_1)) = x_1
   POL(c17(x_1)) = x_1
   POL(c19(x_1, x_2)) = x_1 + x_2
   POL(c2(x_1)) = x_1
   POL(c20(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c4(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c8(x_1)) = x_1
   POL(cons(x_1, x_2)) = 0
   POL(equal(x_1, x_2)) = 0
   POL(false) = 0
   POL(gt(x_1, x_2)) = 0
   POL(if(x_1, x_2, x_3)) = [1]
   POL(max(x_1)) = 0
   POL(member(x_1, x_2)) = [1] + x_1 + x_2
   POL(nil) = 0
   POL(or(x_1, x_2)) = [1]
   POL(s(x_1)) = 0
   POL(true) = 0

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c19_2, c1_2, c_1, c3_3, c4_1, c3_1


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

(115) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
We considered the (Usable) Rules:none
And the Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(COND1(x_1, x_2, x_3)) = [1]
   POL(COND2(x_1, x_2, x_3)) = [1]
   POL(EQUAL(x_1, x_2)) = 0
   POL(GT(x_1, x_2)) = 0
   POL(MAX(x_1)) = 0
   POL(MEMBER(x_1, x_2)) = 0
   POL(ST(x_1, x_2)) = [1]
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c1(x_1, x_2)) = x_1 + x_2
   POL(c14(x_1)) = x_1
   POL(c17(x_1)) = x_1
   POL(c19(x_1, x_2)) = x_1 + x_2
   POL(c2(x_1)) = x_1
   POL(c20(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c4(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c8(x_1)) = x_1
   POL(cons(x_1, x_2)) = 0
   POL(equal(x_1, x_2)) = 0
   POL(false) = 0
   POL(gt(x_1, x_2)) = 0
   POL(if(x_1, x_2, x_3)) = [1]
   POL(max(x_1)) = 0
   POL(member(x_1, x_2)) = [1] + x_1 + x_2
   POL(nil) = 0
   POL(or(x_1, x_2)) = [1]
   POL(s(x_1)) = 0
   POL(true) = 0

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1)))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c19_2, c1_2, c_1, c3_3, c4_1, c3_1


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

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MAX(cons(x0, cons(z0, z1))) -> c19(GT(x0, if(gt(z0, max(z1)), z0, max(z1))), MAX(cons(z0, z1))) by 
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil)))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c1_2, c_1, c3_3, c4_1, c3_1, c19_2, c19_1


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

(119) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ST(z0, cons(x1, nil)) -> c1(COND1(or(equal(z0, x1), false), z0, cons(x1, nil)), MEMBER(z0, cons(x1, nil))) by ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
----------------------------------------

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
S tuples:
   COND1(true, z0, z1) -> c2(ST(s(z0), z1))
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND1_3, COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2

Compound Symbols:   c2_1, c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c1_2, c_1, c3_3, c4_1, c3_1, c19_2, c19_1


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

(121) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace COND1(true, z0, z1) -> c2(ST(s(z0), z1)) by 
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
S tuples:
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3

Compound Symbols:   c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c1_2, c_1, c3_3, c4_1, c3_1, c19_2, c19_1, c2_1


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

(123) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
We considered the (Usable) Rules:none
And the Tuples:
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = [1]
   POL(COND1(x_1, x_2, x_3)) = x_2
   POL(COND2(x_1, x_2, x_3)) = 0
   POL(EQUAL(x_1, x_2)) = 0
   POL(GT(x_1, x_2)) = 0
   POL(MAX(x_1)) = 0
   POL(MEMBER(x_1, x_2)) = 0
   POL(ST(x_1, x_2)) = x_1
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c1(x_1, x_2)) = x_1 + x_2
   POL(c14(x_1)) = x_1
   POL(c17(x_1)) = x_1
   POL(c19(x_1)) = x_1
   POL(c19(x_1, x_2)) = x_1 + x_2
   POL(c2(x_1)) = x_1
   POL(c20(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c4(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c8(x_1)) = x_1
   POL(cons(x_1, x_2)) = 0
   POL(equal(x_1, x_2)) = 0
   POL(false) = 0
   POL(gt(x_1, x_2)) = 0
   POL(if(x_1, x_2, x_3)) = [1]
   POL(max(x_1)) = 0
   POL(member(x_1, x_2)) = [1] + x_1 + x_2
   POL(nil) = 0
   POL(or(x_1, x_2)) = [1]
   POL(s(x_1)) = 0
   POL(true) = 0

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
S tuples:
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3

Compound Symbols:   c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c1_2, c_1, c3_3, c4_1, c3_1, c19_2, c19_1, c2_1


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

(125) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   ST(z0, nil) -> c1(COND1(false, z0, nil))
We considered the (Usable) Rules:
   gt(0, z0) -> false
   gt(s(z0), s(z1)) -> gt(z0, z1)
   gt(s(z0), 0) -> true
And the Tuples:
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = [1]
   POL(COND1(x_1, x_2, x_3)) = x_2 + x_3
   POL(COND2(x_1, x_2, x_3)) = x_1
   POL(EQUAL(x_1, x_2)) = 0
   POL(GT(x_1, x_2)) = 0
   POL(MAX(x_1)) = 0
   POL(MEMBER(x_1, x_2)) = 0
   POL(ST(x_1, x_2)) = [1] + x_1
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c1(x_1, x_2)) = x_1 + x_2
   POL(c14(x_1)) = x_1
   POL(c17(x_1)) = x_1
   POL(c19(x_1)) = x_1
   POL(c19(x_1, x_2)) = x_1 + x_2
   POL(c2(x_1)) = x_1
   POL(c20(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c4(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c8(x_1)) = x_1
   POL(cons(x_1, x_2)) = [1]
   POL(equal(x_1, x_2)) = 0
   POL(false) = [1]
   POL(gt(x_1, x_2)) = [1]
   POL(if(x_1, x_2, x_3)) = [1]
   POL(max(x_1)) = 0
   POL(member(x_1, x_2)) = [1] + x_1 + x_2
   POL(nil) = 0
   POL(or(x_1, x_2)) = [1]
   POL(s(x_1)) = 0
   POL(true) = [1]

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
S tuples:
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3

Compound Symbols:   c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c1_2, c_1, c3_3, c4_1, c3_1, c19_2, c19_1, c2_1


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

(127) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, max(nil)), x1, 0)), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil))) by COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
----------------------------------------

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
S tuples:
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3

Compound Symbols:   c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c1_2, c_1, c3_3, c4_1, c3_1, c19_2, c19_1, c2_1


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

(129) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1)))) by COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
----------------------------------------

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
S tuples:
   COND2(false, z0, z1) -> c5(ST(s(z0), z1))
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   COND2_3, EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3

Compound Symbols:   c5_1, c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c1_2, c_1, c3_3, c4_1, c3_1, c19_2, c19_1, c2_1


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

(131) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace COND2(false, z0, z1) -> c5(ST(s(z0), z1)) by 
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND2(false, 0, nil) -> c5(ST(s(0), nil))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND2(false, 0, nil) -> c5(ST(s(0), nil))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND2(false, 0, nil) -> c5(ST(s(0), nil))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c1_2, c_1, c3_3, c4_1, c3_1, c19_2, c19_1, c2_1, c5_1


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

(133) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   COND2(false, 0, nil) -> c5(ST(s(0), nil))
   ST(z0, nil) -> c1(COND1(false, z0, nil))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND2(false, 0, nil) -> c5(ST(s(0), nil))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND2(false, 0, nil) -> c5(ST(s(0), nil))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c1_2, c_1, c3_3, c4_1, c3_1, c19_2, c19_1, c2_1, c5_1


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

(135) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
We considered the (Usable) Rules:none
And the Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND2(false, 0, nil) -> c5(ST(s(0), nil))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = [1]
   POL(COND1(x_1, x_2, x_3)) = x_2
   POL(COND2(x_1, x_2, x_3)) = x_2
   POL(EQUAL(x_1, x_2)) = 0
   POL(GT(x_1, x_2)) = 0
   POL(MAX(x_1)) = 0
   POL(MEMBER(x_1, x_2)) = 0
   POL(ST(x_1, x_2)) = x_1
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c1(x_1, x_2)) = x_1 + x_2
   POL(c14(x_1)) = x_1
   POL(c17(x_1)) = x_1
   POL(c19(x_1)) = x_1
   POL(c19(x_1, x_2)) = x_1 + x_2
   POL(c2(x_1)) = x_1
   POL(c20(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c4(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c8(x_1)) = x_1
   POL(cons(x_1, x_2)) = 0
   POL(equal(x_1, x_2)) = 0
   POL(false) = 0
   POL(gt(x_1, x_2)) = 0
   POL(if(x_1, x_2, x_3)) = [1]
   POL(max(x_1)) = 0
   POL(member(x_1, x_2)) = [1] + x_1 + x_2
   POL(nil) = 0
   POL(or(x_1, x_2)) = [1]
   POL(s(x_1)) = 0
   POL(true) = 0

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND2(false, 0, nil) -> c5(ST(s(0), nil))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND2(false, 0, nil) -> c5(ST(s(0), nil))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c1_2, c_1, c3_3, c4_1, c3_1, c19_2, c19_1, c2_1, c5_1


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

(137) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace COND1(false, x0, cons(0, x2)) -> c3(COND2(gt(x0, if(false, 0, max(x2))), x0, cons(0, x2)), GT(x0, max(cons(0, x2))), MAX(cons(0, x2))) by COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
----------------------------------------

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND2(false, 0, nil) -> c5(ST(s(0), nil))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   ST(z0, nil) -> c1(COND1(false, z0, nil))
   COND2(false, 0, nil) -> c5(ST(s(0), nil))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c1_1, c3_2, c1_2, c_1, c3_3, c4_1, c3_1, c19_2, c19_1, c2_1, c5_1


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

(139) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace ST(z0, nil) -> c1(COND1(false, z0, nil)) by 
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND2(false, 0, nil) -> c5(ST(s(0), nil))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, nil) -> c5(ST(s(0), nil))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, COND1_3, ST_2, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c3_2, c1_2, c1_1, c_1, c3_3, c4_1, c3_1, c19_2, c19_1, c2_1, c5_1


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

(141) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   COND1(false, 0, nil) -> c3(COND2(false, 0, nil))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND2(false, 0, nil) -> c5(ST(s(0), nil))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
K tuples:
   COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, nil) -> c5(ST(s(0), nil))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, COND1_3, ST_2, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c3_2, c1_2, c1_1, c_1, c3_3, c4_1, c3_1, c19_2, c19_1, c2_1, c5_1


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

(143) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace COND1(false, 0, x1) -> c3(COND2(false, 0, x1), MAX(x1)) by 
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c3(COND2(false, 0, cons(x1, cons(x2, x3))), MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(0, x0)) -> c3(COND2(false, 0, cons(0, x0)), MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c3(COND2(false, 0, cons(s(x0), x1)), MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c3(COND2(false, 0, cons(x1, nil)), MAX(cons(x1, nil)))

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND2(false, 0, nil) -> c5(ST(s(0), nil))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c3(COND2(false, 0, cons(x1, cons(x2, x3))), MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(0, x0)) -> c3(COND2(false, 0, cons(0, x0)), MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c3(COND2(false, 0, cons(s(x0), x1)), MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c3(COND2(false, 0, cons(x1, nil)), MAX(cons(x1, nil)))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, nil) -> c5(ST(s(0), nil))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c3(COND2(false, 0, cons(x1, cons(x2, x3))), MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(0, x0)) -> c3(COND2(false, 0, cons(0, x0)), MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c3(COND2(false, 0, cons(s(x0), x1)), MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c3(COND2(false, 0, cons(x1, nil)), MAX(cons(x1, nil)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c_1, c3_3, c3_2, c4_1, c3_1, c19_2, c19_1, c2_1, c5_1


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

(145) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   COND2(false, 0, nil) -> c5(ST(s(0), nil))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c3(COND2(false, 0, cons(x1, cons(x2, x3))), MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(0, x0)) -> c3(COND2(false, 0, cons(0, x0)), MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c3(COND2(false, 0, cons(s(x0), x1)), MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c3(COND2(false, 0, cons(x1, nil)), MAX(cons(x1, nil)))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c3(COND2(false, 0, cons(x1, cons(x2, x3))), MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(0, x0)) -> c3(COND2(false, 0, cons(0, x0)), MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c3(COND2(false, 0, cons(s(x0), x1)), MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c3(COND2(false, 0, cons(x1, nil)), MAX(cons(x1, nil)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c_1, c3_3, c3_2, c4_1, c3_1, c19_2, c19_1, c2_1, c5_1


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

(147) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace COND1(false, x0, cons(x1, nil)) -> c3(COND2(gt(x0, if(gt(x1, 0), x1, max(nil))), x0, cons(x1, nil)), GT(x0, max(cons(x1, nil))), MAX(cons(x1, nil))) by COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
----------------------------------------

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c3(COND2(false, 0, cons(x1, cons(x2, x3))), MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(0, x0)) -> c3(COND2(false, 0, cons(0, x0)), MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c3(COND2(false, 0, cons(s(x0), x1)), MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c3(COND2(false, 0, cons(x1, nil)), MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2))))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c3(COND2(false, 0, cons(x1, cons(x2, x3))), MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(0, x0)) -> c3(COND2(false, 0, cons(0, x0)), MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c3(COND2(false, 0, cons(s(x0), x1)), MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c3(COND2(false, 0, cons(x1, nil)), MAX(cons(x1, nil)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c_1, c3_3, c3_2, c4_1, c3_1, c19_2, c19_1, c2_1, c5_1


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

(149) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace ST(z0, cons(x1, cons(z1, z2))) -> c1(COND1(or(equal(z0, x1), or(equal(z0, z1), member(z0, z2))), z0, cons(x1, cons(z1, z2))), MEMBER(z0, cons(x1, cons(z1, z2)))) by 
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c3(COND2(false, 0, cons(x1, cons(x2, x3))), MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(0, x0)) -> c3(COND2(false, 0, cons(0, x0)), MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c3(COND2(false, 0, cons(s(x0), x1)), MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c3(COND2(false, 0, cons(x1, nil)), MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c3(COND2(false, 0, cons(x1, cons(x2, x3))), MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(0, x0)) -> c3(COND2(false, 0, cons(0, x0)), MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c3(COND2(false, 0, cons(s(x0), x1)), MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c3(COND2(false, 0, cons(x1, nil)), MAX(cons(x1, nil)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c_1, c3_3, c3_2, c4_1, c3_1, c19_2, c19_1, c2_1, c5_1


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

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(0, x0)) -> c3(COND2(false, 0, cons(0, x0)), MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c3(COND2(false, 0, cons(s(x0), x1)), MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c3(COND2(false, 0, cons(x1, nil)), MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(0, x0)) -> c3(COND2(false, 0, cons(0, x0)), MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c3(COND2(false, 0, cons(s(x0), x1)), MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c3(COND2(false, 0, cons(x1, nil)), MAX(cons(x1, nil)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c_1, c3_3, c3_2, c4_1, c3_1, c19_2, c19_1, c2_1, c5_1, c6_1


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

(153) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ST(z0, cons(z1, nil)) -> c1(COND1(equal(z0, z1), z0, cons(z1, nil)), MEMBER(z0, cons(z1, nil))) by 
   ST(0, cons(0, nil)) -> c1(COND1(true, 0, cons(0, nil)), MEMBER(0, cons(0, nil)))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(0, cons(s(z0), nil)) -> c1(COND1(false, 0, cons(s(z0), nil)), MEMBER(0, cons(s(z0), nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(0, x0)) -> c3(COND2(false, 0, cons(0, x0)), MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c3(COND2(false, 0, cons(s(x0), x1)), MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c3(COND2(false, 0, cons(x1, nil)), MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(0, cons(0, nil)) -> c1(COND1(true, 0, cons(0, nil)), MEMBER(0, cons(0, nil)))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(0, cons(s(z0), nil)) -> c1(COND1(false, 0, cons(s(z0), nil)), MEMBER(0, cons(s(z0), nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(0, cons(0, nil)) -> c1(COND1(true, 0, cons(0, nil)), MEMBER(0, cons(0, nil)))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(0, cons(s(z0), nil)) -> c1(COND1(false, 0, cons(s(z0), nil)), MEMBER(0, cons(s(z0), nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(0, x0)) -> c3(COND2(false, 0, cons(0, x0)), MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c3(COND2(false, 0, cons(s(x0), x1)), MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c3(COND2(false, 0, cons(x1, nil)), MAX(cons(x1, nil)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c_1, c3_3, c3_2, c4_1, c3_1, c19_2, c19_1, c2_1, c5_1, c6_1


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

(155) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 2 leading nodes:
   ST(0, cons(s(z0), nil)) -> c1(COND1(false, 0, cons(s(z0), nil)), MEMBER(0, cons(s(z0), nil)))
   ST(0, cons(0, nil)) -> c1(COND1(true, 0, cons(0, nil)), MEMBER(0, cons(0, nil)))

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(0, x0)) -> c3(COND2(false, 0, cons(0, x0)), MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c3(COND2(false, 0, cons(s(x0), x1)), MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c3(COND2(false, 0, cons(x1, nil)), MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c3(COND2(false, 0, cons(x1, x2)), MAX(cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(0, x0)) -> c3(COND2(false, 0, cons(0, x0)), MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c3(COND2(false, 0, cons(s(x0), x1)), MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c3(COND2(false, 0, cons(x1, nil)), MAX(cons(x1, nil)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c_1, c3_3, c3_2, c4_1, c3_1, c19_2, c19_1, c2_1, c5_1, c6_1


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

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c_1, c3_3, c4_1, c3_1, c19_2, c19_1, c2_1, c5_1, c6_1, c9_1


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

(159) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
We considered the (Usable) Rules:none
And the Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(0) = 0
   POL(COND1(x_1, x_2, x_3)) = x_3
   POL(COND2(x_1, x_2, x_3)) = x_3
   POL(EQUAL(x_1, x_2)) = 0
   POL(GT(x_1, x_2)) = 0
   POL(MAX(x_1)) = 0
   POL(MEMBER(x_1, x_2)) = 0
   POL(ST(x_1, x_2)) = x_2
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c1(x_1, x_2)) = x_1 + x_2
   POL(c14(x_1)) = x_1
   POL(c17(x_1)) = x_1
   POL(c19(x_1)) = x_1
   POL(c19(x_1, x_2)) = x_1 + x_2
   POL(c2(x_1)) = x_1
   POL(c20(x_1)) = x_1
   POL(c3(x_1)) = x_1
   POL(c3(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c4(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c6(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(c8(x_1)) = x_1
   POL(c9(x_1)) = x_1
   POL(cons(x_1, x_2)) = x_2
   POL(equal(x_1, x_2)) = 0
   POL(false) = 0
   POL(gt(x_1, x_2)) = 0
   POL(if(x_1, x_2, x_3)) = [1]
   POL(max(x_1)) = 0
   POL(member(x_1, x_2)) = [1] + x_1 + x_2
   POL(nil) = [1]
   POL(or(x_1, x_2)) = [1]
   POL(s(x_1)) = 0
   POL(true) = 0

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c_1, c3_3, c4_1, c3_1, c19_2, c19_1, c2_1, c5_1, c6_1, c9_1


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

(161) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace COND1(false, x0, cons(x1, cons(z0, z1))) -> c3(COND2(gt(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), x0, cons(x1, cons(z0, z1))), GT(x0, max(cons(x1, cons(z0, z1)))), MAX(cons(x1, cons(z0, z1)))) by COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
----------------------------------------

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c_1, c4_1, c3_1, c19_2, c19_1, c2_1, c3_3, c5_1, c6_1, c9_1


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

(163) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace ST(s(z0), cons(s(z1), x2)) -> c1(COND1(or(equal(z0, z1), member(s(z0), x2)), s(z0), cons(s(z1), x2)), MEMBER(s(z0), cons(s(z1), x2))) by 
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
S tuples:
   EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1))
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   EQUAL_2, GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3

Compound Symbols:   c14_1, c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c_1, c4_1, c3_1, c19_2, c19_1, c2_1, c3_3, c5_1, c6_1, c9_1


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

(165) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace EQUAL(s(z0), s(z1)) -> c14(EQUAL(z0, z1)) by 
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
S tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2

Compound Symbols:   c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c_1, c4_1, c3_1, c19_2, c19_1, c2_1, c3_3, c5_1, c6_1, c9_1, c14_1


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

(167) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2)))) by COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
----------------------------------------

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
S tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2

Compound Symbols:   c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c_1, c4_1, c3_1, c19_2, c19_1, c2_1, c3_3, c5_1, c6_1, c9_1, c14_1


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

(169) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace COND1(false, x0, nil) -> c3(GT(x0, max(nil))) by COND1(false, z0, nil) -> c3(GT(z0, 0))
----------------------------------------

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   COND1(false, z0, nil) -> c3(GT(z0, 0))
S tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(GT(x0, max(cons(x1, x2))))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, x0, nil) -> c3(GT(x0, max(nil)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2

Compound Symbols:   c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c_1, c4_1, c3_1, c19_2, c19_1, c2_1, c3_3, c5_1, c6_1, c9_1, c14_1


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

(171) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   COND1(false, z0, nil) -> c3(GT(z0, 0))

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
S tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2

Compound Symbols:   c17_1, c7_1, c8_1, c20_1, c1_2, c1_1, c_1, c4_1, c3_1, c19_2, c19_1, c2_1, c3_3, c5_1, c6_1, c9_1, c14_1


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

(173) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace ST(x0, cons(x1, x2)) -> c1(MEMBER(x0, cons(x1, x2))) by 
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))

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

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
S tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2

Compound Symbols:   c17_1, c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c3_1, c19_2, c19_1, c2_1, c3_3, c5_1, c1_1, c6_1, c9_1, c14_1


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

(175) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil))) by COND1(false, s(z0), nil) -> c3(GT(s(z0), 0))
----------------------------------------

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), 0))
S tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(false, s(z0), nil) -> c3(GT(s(z0), max(nil)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2

Compound Symbols:   c17_1, c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c19_2, c19_1, c2_1, c3_3, c5_1, c1_1, c6_1, c9_1, c14_1, c3_1


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

(177) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   COND1(false, s(z0), nil) -> c3(GT(s(z0), 0))
   ST(s(0), nil) -> c1(COND1(false, s(0), nil))

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

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
S tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2

Compound Symbols:   c17_1, c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c19_2, c19_1, c2_1, c3_3, c5_1, c6_1, c1_1, c9_1, c14_1


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

(179) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, max(nil)), x1, 0)), MAX(cons(x1, nil))) by MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
----------------------------------------

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
S tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2

Compound Symbols:   c17_1, c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c19_2, c19_1, c2_1, c3_3, c5_1, c6_1, c1_1, c9_1, c14_1


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

(181) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, max(cons(z0, z1))), x1, if(gt(z0, max(z1)), z0, max(z1)))), MAX(cons(x1, cons(z0, z1)))) by MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
----------------------------------------

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
S tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2

Compound Symbols:   c17_1, c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c19_2, c19_1, c2_1, c3_3, c5_1, c6_1, c1_1, c9_1, c14_1


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

(183) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace MAX(cons(x0, cons(0, x2))) -> c19(GT(x0, if(false, 0, max(x2))), MAX(cons(0, x2))) by MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
----------------------------------------

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
S tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2

Compound Symbols:   c17_1, c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c19_2, c19_1, c2_1, c3_3, c5_1, c6_1, c1_1, c9_1, c14_1


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

(185) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace MAX(cons(x0, cons(x1, nil))) -> c19(GT(x0, if(gt(x1, 0), x1, max(nil))), MAX(cons(x1, nil))) by MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
----------------------------------------

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
S tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1))))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2

Compound Symbols:   c17_1, c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c19_2, c19_1, c2_1, c3_3, c5_1, c6_1, c1_1, c9_1, c14_1


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

(187) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace MAX(cons(x0, cons(x1, cons(z0, z1)))) -> c19(GT(x0, if(gt(x1, if(gt(z0, max(z1)), z0, max(z1))), x1, max(cons(z0, z1)))), MAX(cons(x1, cons(z0, z1)))) by MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
----------------------------------------

(188)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
S tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2

Compound Symbols:   c17_1, c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c19_1, c2_1, c3_3, c5_1, c6_1, c1_1, c9_1, c14_1, c19_2


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

(189) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil))) by COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
----------------------------------------

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
S tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2

Compound Symbols:   c17_1, c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c19_1, c2_1, c3_3, c5_1, c6_1, c1_1, c9_1, c14_1, c19_2


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

(191) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3)))) by COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
----------------------------------------

(192)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
S tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2

Compound Symbols:   c17_1, c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c19_1, c2_1, c5_1, c3_3, c6_1, c1_1, c9_1, c14_1, c19_2


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

(193) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(gt(0, max(z1)), 0, max(z1))), MAX(cons(0, z1))) by COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
----------------------------------------

(194)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
S tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2

Compound Symbols:   c17_1, c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c19_1, c2_1, c5_1, c3_3, c6_1, c1_1, c9_1, c14_1, c19_2


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

(195) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, max(nil))), MAX(cons(z1, nil))) by COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
----------------------------------------

(196)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
S tuples:
   GT(s(z0), s(z1)) -> c17(GT(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   GT_2, MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2

Compound Symbols:   c17_1, c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c19_1, c2_1, c5_1, c6_1, c1_1, c9_1, c3_3, c14_1, c19_2


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

(197) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace GT(s(z0), s(z1)) -> c17(GT(z0, z1)) by 
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))

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

(198)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))
S tuples:
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2, GT_2

Compound Symbols:   c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c19_1, c2_1, c5_1, c6_1, c1_1, c9_1, c3_3, c14_1, c19_2, c17_1


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

(199) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ST(s(s(x0)), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), 0), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(0, cons(z2, z3))), MEMBER(s(s(x0)), cons(0, cons(z2, z3)))) by ST(s(s(z0)), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(s(z0)), z1), member(s(s(z0)), z2))), s(s(z0)), cons(0, cons(z1, z2))), MEMBER(s(s(z0)), cons(0, cons(z1, z2))))
----------------------------------------

(200)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))
   ST(s(s(z0)), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(s(z0)), z1), member(s(s(z0)), z2))), s(s(z0)), cons(0, cons(z1, z2))), MEMBER(s(s(z0)), cons(0, cons(z1, z2))))
S tuples:
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))
   ST(s(s(z0)), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(s(z0)), z1), member(s(s(z0)), z2))), s(s(z0)), cons(0, cons(z1, z2))), MEMBER(s(s(z0)), cons(0, cons(z1, z2))))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2, GT_2

Compound Symbols:   c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c19_1, c2_1, c5_1, c6_1, c1_1, c9_1, c3_3, c14_1, c19_2, c17_1


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

(201) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ST(s(s(x0)), cons(s(x1), cons(z2, z3))) -> c1(COND1(or(equal(s(s(x0)), s(x1)), or(equal(s(s(x0)), z2), member(s(s(x0)), z3))), s(s(x0)), cons(s(x1), cons(z2, z3))), MEMBER(s(s(x0)), cons(s(x1), cons(z2, z3)))) by ST(s(s(z0)), cons(s(z1), cons(z2, z3))) -> c1(COND1(or(equal(s(z0), z1), or(equal(s(s(z0)), z2), member(s(s(z0)), z3))), s(s(z0)), cons(s(z1), cons(z2, z3))), MEMBER(s(s(z0)), cons(s(z1), cons(z2, z3))))
----------------------------------------

(202)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))
   ST(s(s(z0)), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(s(z0)), z1), member(s(s(z0)), z2))), s(s(z0)), cons(0, cons(z1, z2))), MEMBER(s(s(z0)), cons(0, cons(z1, z2))))
   ST(s(s(z0)), cons(s(z1), cons(z2, z3))) -> c1(COND1(or(equal(s(z0), z1), or(equal(s(s(z0)), z2), member(s(s(z0)), z3))), s(s(z0)), cons(s(z1), cons(z2, z3))), MEMBER(s(s(z0)), cons(s(z1), cons(z2, z3))))
S tuples:
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))
   ST(s(s(z0)), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(s(z0)), z1), member(s(s(z0)), z2))), s(s(z0)), cons(0, cons(z1, z2))), MEMBER(s(s(z0)), cons(0, cons(z1, z2))))
   ST(s(s(z0)), cons(s(z1), cons(z2, z3))) -> c1(COND1(or(equal(s(z0), z1), or(equal(s(s(z0)), z2), member(s(s(z0)), z3))), s(s(z0)), cons(s(z1), cons(z2, z3))), MEMBER(s(s(z0)), cons(s(z1), cons(z2, z3))))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2, GT_2

Compound Symbols:   c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c19_1, c2_1, c5_1, c6_1, c1_1, c9_1, c3_3, c14_1, c19_2, c17_1


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

(203) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ST(s(0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(0), 0), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(0, cons(z2, z3))), MEMBER(s(0), cons(0, cons(z2, z3)))) by ST(s(0), cons(0, cons(z0, z1))) -> c1(COND1(or(false, or(equal(s(0), z0), member(s(0), z1))), s(0), cons(0, cons(z0, z1))), MEMBER(s(0), cons(0, cons(z0, z1))))
----------------------------------------

(204)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))
   ST(s(s(z0)), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(s(z0)), z1), member(s(s(z0)), z2))), s(s(z0)), cons(0, cons(z1, z2))), MEMBER(s(s(z0)), cons(0, cons(z1, z2))))
   ST(s(s(z0)), cons(s(z1), cons(z2, z3))) -> c1(COND1(or(equal(s(z0), z1), or(equal(s(s(z0)), z2), member(s(s(z0)), z3))), s(s(z0)), cons(s(z1), cons(z2, z3))), MEMBER(s(s(z0)), cons(s(z1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z0, z1))) -> c1(COND1(or(false, or(equal(s(0), z0), member(s(0), z1))), s(0), cons(0, cons(z0, z1))), MEMBER(s(0), cons(0, cons(z0, z1))))
S tuples:
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))
   ST(s(s(z0)), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(s(z0)), z1), member(s(s(z0)), z2))), s(s(z0)), cons(0, cons(z1, z2))), MEMBER(s(s(z0)), cons(0, cons(z1, z2))))
   ST(s(s(z0)), cons(s(z1), cons(z2, z3))) -> c1(COND1(or(equal(s(z0), z1), or(equal(s(s(z0)), z2), member(s(s(z0)), z3))), s(s(z0)), cons(s(z1), cons(z2, z3))), MEMBER(s(s(z0)), cons(s(z1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z0, z1))) -> c1(COND1(or(false, or(equal(s(0), z0), member(s(0), z1))), s(0), cons(0, cons(z0, z1))), MEMBER(s(0), cons(0, cons(z0, z1))))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2, GT_2

Compound Symbols:   c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c19_1, c2_1, c5_1, c6_1, c1_1, c9_1, c3_3, c14_1, c19_2, c17_1


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

(205) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ST(s(0), cons(s(x0), cons(z2, z3))) -> c1(COND1(or(equal(s(0), s(x0)), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(s(x0), cons(z2, z3))), MEMBER(s(0), cons(s(x0), cons(z2, z3)))) by ST(s(0), cons(s(z0), cons(z1, z2))) -> c1(COND1(or(equal(0, z0), or(equal(s(0), z1), member(s(0), z2))), s(0), cons(s(z0), cons(z1, z2))), MEMBER(s(0), cons(s(z0), cons(z1, z2))))
----------------------------------------

(206)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))
   ST(s(s(z0)), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(s(z0)), z1), member(s(s(z0)), z2))), s(s(z0)), cons(0, cons(z1, z2))), MEMBER(s(s(z0)), cons(0, cons(z1, z2))))
   ST(s(s(z0)), cons(s(z1), cons(z2, z3))) -> c1(COND1(or(equal(s(z0), z1), or(equal(s(s(z0)), z2), member(s(s(z0)), z3))), s(s(z0)), cons(s(z1), cons(z2, z3))), MEMBER(s(s(z0)), cons(s(z1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z0, z1))) -> c1(COND1(or(false, or(equal(s(0), z0), member(s(0), z1))), s(0), cons(0, cons(z0, z1))), MEMBER(s(0), cons(0, cons(z0, z1))))
   ST(s(0), cons(s(z0), cons(z1, z2))) -> c1(COND1(or(equal(0, z0), or(equal(s(0), z1), member(s(0), z2))), s(0), cons(s(z0), cons(z1, z2))), MEMBER(s(0), cons(s(z0), cons(z1, z2))))
S tuples:
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))
   ST(s(s(z0)), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(s(z0)), z1), member(s(s(z0)), z2))), s(s(z0)), cons(0, cons(z1, z2))), MEMBER(s(s(z0)), cons(0, cons(z1, z2))))
   ST(s(s(z0)), cons(s(z1), cons(z2, z3))) -> c1(COND1(or(equal(s(z0), z1), or(equal(s(s(z0)), z2), member(s(s(z0)), z3))), s(s(z0)), cons(s(z1), cons(z2, z3))), MEMBER(s(s(z0)), cons(s(z1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z0, z1))) -> c1(COND1(or(false, or(equal(s(0), z0), member(s(0), z1))), s(0), cons(0, cons(z0, z1))), MEMBER(s(0), cons(0, cons(z0, z1))))
   ST(s(0), cons(s(z0), cons(z1, z2))) -> c1(COND1(or(equal(0, z0), or(equal(s(0), z1), member(s(0), z2))), s(0), cons(s(z0), cons(z1, z2))), MEMBER(s(0), cons(s(z0), cons(z1, z2))))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2, GT_2

Compound Symbols:   c7_1, c8_1, c20_1, c1_2, c_1, c4_1, c19_1, c2_1, c5_1, c6_1, c1_1, c9_1, c3_3, c14_1, c19_2, c17_1


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

(207) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace COND1(false, x0, cons(x1, x2)) -> c4(MAX(cons(x1, x2))) by 
   COND1(false, s(x0), cons(0, x1)) -> c4(MAX(cons(0, x1)))
   COND1(false, 0, cons(0, x0)) -> c4(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c4(MAX(cons(s(x0), x1)))
   COND1(false, s(x0), cons(x1, cons(x2, x3))) -> c4(MAX(cons(x1, cons(x2, x3))))
   COND1(false, s(0), cons(x0, cons(x1, x2))) -> c4(MAX(cons(x0, cons(x1, x2))))
   COND1(false, s(x0), cons(0, cons(x1, x2))) -> c4(MAX(cons(0, cons(x1, x2))))
   COND1(false, s(x0), cons(0, nil)) -> c4(MAX(cons(0, nil)))
   COND1(false, s(x0), cons(s(x1), nil)) -> c4(MAX(cons(s(x1), nil)))
   COND1(false, s(x0), cons(s(x1), cons(x2, x3))) -> c4(MAX(cons(s(x1), cons(x2, x3))))
   COND1(false, s(s(x0)), cons(s(x1), x2)) -> c4(MAX(cons(s(x1), x2)))
   COND1(false, s(0), cons(s(x0), x1)) -> c4(MAX(cons(s(x0), x1)))
   COND1(false, s(s(x0)), cons(0, cons(x1, x2))) -> c4(MAX(cons(0, cons(x1, x2))))
   COND1(false, s(s(x0)), cons(s(x1), cons(x2, x3))) -> c4(MAX(cons(s(x1), cons(x2, x3))))
   COND1(false, s(0), cons(0, cons(x0, x1))) -> c4(MAX(cons(0, cons(x0, x1))))
   COND1(false, s(0), cons(s(x0), cons(x1, x2))) -> c4(MAX(cons(s(x0), cons(x1, x2))))

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

(208)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))
   ST(s(s(z0)), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(s(z0)), z1), member(s(s(z0)), z2))), s(s(z0)), cons(0, cons(z1, z2))), MEMBER(s(s(z0)), cons(0, cons(z1, z2))))
   ST(s(s(z0)), cons(s(z1), cons(z2, z3))) -> c1(COND1(or(equal(s(z0), z1), or(equal(s(s(z0)), z2), member(s(s(z0)), z3))), s(s(z0)), cons(s(z1), cons(z2, z3))), MEMBER(s(s(z0)), cons(s(z1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z0, z1))) -> c1(COND1(or(false, or(equal(s(0), z0), member(s(0), z1))), s(0), cons(0, cons(z0, z1))), MEMBER(s(0), cons(0, cons(z0, z1))))
   ST(s(0), cons(s(z0), cons(z1, z2))) -> c1(COND1(or(equal(0, z0), or(equal(s(0), z1), member(s(0), z2))), s(0), cons(s(z0), cons(z1, z2))), MEMBER(s(0), cons(s(z0), cons(z1, z2))))
   COND1(false, s(x0), cons(0, x1)) -> c4(MAX(cons(0, x1)))
   COND1(false, 0, cons(0, x0)) -> c4(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c4(MAX(cons(s(x0), x1)))
   COND1(false, s(x0), cons(x1, cons(x2, x3))) -> c4(MAX(cons(x1, cons(x2, x3))))
   COND1(false, s(0), cons(x0, cons(x1, x2))) -> c4(MAX(cons(x0, cons(x1, x2))))
   COND1(false, s(x0), cons(0, cons(x1, x2))) -> c4(MAX(cons(0, cons(x1, x2))))
   COND1(false, s(x0), cons(0, nil)) -> c4(MAX(cons(0, nil)))
   COND1(false, s(x0), cons(s(x1), nil)) -> c4(MAX(cons(s(x1), nil)))
   COND1(false, s(x0), cons(s(x1), cons(x2, x3))) -> c4(MAX(cons(s(x1), cons(x2, x3))))
   COND1(false, s(s(x0)), cons(s(x1), x2)) -> c4(MAX(cons(s(x1), x2)))
   COND1(false, s(0), cons(s(x0), x1)) -> c4(MAX(cons(s(x0), x1)))
   COND1(false, s(s(x0)), cons(0, cons(x1, x2))) -> c4(MAX(cons(0, cons(x1, x2))))
   COND1(false, s(s(x0)), cons(s(x1), cons(x2, x3))) -> c4(MAX(cons(s(x1), cons(x2, x3))))
   COND1(false, s(0), cons(0, cons(x0, x1))) -> c4(MAX(cons(0, cons(x0, x1))))
   COND1(false, s(0), cons(s(x0), cons(x1, x2))) -> c4(MAX(cons(s(x0), cons(x1, x2))))
S tuples:
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))
   ST(s(s(z0)), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(s(z0)), z1), member(s(s(z0)), z2))), s(s(z0)), cons(0, cons(z1, z2))), MEMBER(s(s(z0)), cons(0, cons(z1, z2))))
   ST(s(s(z0)), cons(s(z1), cons(z2, z3))) -> c1(COND1(or(equal(s(z0), z1), or(equal(s(s(z0)), z2), member(s(s(z0)), z3))), s(s(z0)), cons(s(z1), cons(z2, z3))), MEMBER(s(s(z0)), cons(s(z1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z0, z1))) -> c1(COND1(or(false, or(equal(s(0), z0), member(s(0), z1))), s(0), cons(0, cons(z0, z1))), MEMBER(s(0), cons(0, cons(z0, z1))))
   ST(s(0), cons(s(z0), cons(z1, z2))) -> c1(COND1(or(equal(0, z0), or(equal(s(0), z1), member(s(0), z2))), s(0), cons(s(z0), cons(z1, z2))), MEMBER(s(0), cons(s(z0), cons(z1, z2))))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   COND1(false, s(x0), cons(0, x1)) -> c4(MAX(cons(0, x1)))
   COND1(false, 0, cons(0, x0)) -> c4(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c4(MAX(cons(s(x0), x1)))
   COND1(false, s(x0), cons(x1, cons(x2, x3))) -> c4(MAX(cons(x1, cons(x2, x3))))
   COND1(false, s(0), cons(x0, cons(x1, x2))) -> c4(MAX(cons(x0, cons(x1, x2))))
   COND1(false, s(x0), cons(0, cons(x1, x2))) -> c4(MAX(cons(0, cons(x1, x2))))
   COND1(false, s(x0), cons(0, nil)) -> c4(MAX(cons(0, nil)))
   COND1(false, s(x0), cons(s(x1), nil)) -> c4(MAX(cons(s(x1), nil)))
   COND1(false, s(x0), cons(s(x1), cons(x2, x3))) -> c4(MAX(cons(s(x1), cons(x2, x3))))
   COND1(false, s(s(x0)), cons(s(x1), x2)) -> c4(MAX(cons(s(x1), x2)))
   COND1(false, s(0), cons(s(x0), x1)) -> c4(MAX(cons(s(x0), x1)))
   COND1(false, s(s(x0)), cons(0, cons(x1, x2))) -> c4(MAX(cons(0, cons(x1, x2))))
   COND1(false, s(s(x0)), cons(s(x1), cons(x2, x3))) -> c4(MAX(cons(s(x1), cons(x2, x3))))
   COND1(false, s(0), cons(0, cons(x0, x1))) -> c4(MAX(cons(0, cons(x0, x1))))
   COND1(false, s(0), cons(s(x0), cons(x1, x2))) -> c4(MAX(cons(s(x0), cons(x1, x2))))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2, GT_2

Compound Symbols:   c7_1, c8_1, c20_1, c1_2, c_1, c19_1, c2_1, c5_1, c6_1, c1_1, c9_1, c3_3, c14_1, c4_1, c19_2, c17_1


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

(209) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace ST(s(x0), cons(0, cons(z2, z3))) -> c1(COND1(or(equal(s(x0), 0), or(equal(s(x0), z2), member(s(x0), z3))), s(x0), cons(0, cons(z2, z3))), MEMBER(s(x0), cons(0, cons(z2, z3)))) by ST(s(z0), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(z0), z1), member(s(z0), z2))), s(z0), cons(0, cons(z1, z2))), MEMBER(s(z0), cons(0, cons(z1, z2))))
----------------------------------------

(210)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))
   ST(s(s(z0)), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(s(z0)), z1), member(s(s(z0)), z2))), s(s(z0)), cons(0, cons(z1, z2))), MEMBER(s(s(z0)), cons(0, cons(z1, z2))))
   ST(s(s(z0)), cons(s(z1), cons(z2, z3))) -> c1(COND1(or(equal(s(z0), z1), or(equal(s(s(z0)), z2), member(s(s(z0)), z3))), s(s(z0)), cons(s(z1), cons(z2, z3))), MEMBER(s(s(z0)), cons(s(z1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z0, z1))) -> c1(COND1(or(false, or(equal(s(0), z0), member(s(0), z1))), s(0), cons(0, cons(z0, z1))), MEMBER(s(0), cons(0, cons(z0, z1))))
   ST(s(0), cons(s(z0), cons(z1, z2))) -> c1(COND1(or(equal(0, z0), or(equal(s(0), z1), member(s(0), z2))), s(0), cons(s(z0), cons(z1, z2))), MEMBER(s(0), cons(s(z0), cons(z1, z2))))
   COND1(false, s(x0), cons(0, x1)) -> c4(MAX(cons(0, x1)))
   COND1(false, 0, cons(0, x0)) -> c4(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c4(MAX(cons(s(x0), x1)))
   COND1(false, s(x0), cons(x1, cons(x2, x3))) -> c4(MAX(cons(x1, cons(x2, x3))))
   COND1(false, s(0), cons(x0, cons(x1, x2))) -> c4(MAX(cons(x0, cons(x1, x2))))
   COND1(false, s(x0), cons(0, cons(x1, x2))) -> c4(MAX(cons(0, cons(x1, x2))))
   COND1(false, s(x0), cons(0, nil)) -> c4(MAX(cons(0, nil)))
   COND1(false, s(x0), cons(s(x1), nil)) -> c4(MAX(cons(s(x1), nil)))
   COND1(false, s(x0), cons(s(x1), cons(x2, x3))) -> c4(MAX(cons(s(x1), cons(x2, x3))))
   COND1(false, s(s(x0)), cons(s(x1), x2)) -> c4(MAX(cons(s(x1), x2)))
   COND1(false, s(0), cons(s(x0), x1)) -> c4(MAX(cons(s(x0), x1)))
   COND1(false, s(s(x0)), cons(0, cons(x1, x2))) -> c4(MAX(cons(0, cons(x1, x2))))
   COND1(false, s(s(x0)), cons(s(x1), cons(x2, x3))) -> c4(MAX(cons(s(x1), cons(x2, x3))))
   COND1(false, s(0), cons(0, cons(x0, x1))) -> c4(MAX(cons(0, cons(x0, x1))))
   COND1(false, s(0), cons(s(x0), cons(x1, x2))) -> c4(MAX(cons(s(x0), cons(x1, x2))))
   ST(s(z0), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(z0), z1), member(s(z0), z2))), s(z0), cons(0, cons(z1, z2))), MEMBER(s(z0), cons(0, cons(z1, z2))))
S tuples:
   MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1))
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))
   ST(s(s(z0)), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(s(z0)), z1), member(s(s(z0)), z2))), s(s(z0)), cons(0, cons(z1, z2))), MEMBER(s(s(z0)), cons(0, cons(z1, z2))))
   ST(s(s(z0)), cons(s(z1), cons(z2, z3))) -> c1(COND1(or(equal(s(z0), z1), or(equal(s(s(z0)), z2), member(s(s(z0)), z3))), s(s(z0)), cons(s(z1), cons(z2, z3))), MEMBER(s(s(z0)), cons(s(z1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z0, z1))) -> c1(COND1(or(false, or(equal(s(0), z0), member(s(0), z1))), s(0), cons(0, cons(z0, z1))), MEMBER(s(0), cons(0, cons(z0, z1))))
   ST(s(0), cons(s(z0), cons(z1, z2))) -> c1(COND1(or(equal(0, z0), or(equal(s(0), z1), member(s(0), z2))), s(0), cons(s(z0), cons(z1, z2))), MEMBER(s(0), cons(s(z0), cons(z1, z2))))
   ST(s(z0), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(z0), z1), member(s(z0), z2))), s(z0), cons(0, cons(z1, z2))), MEMBER(s(z0), cons(0, cons(z1, z2))))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   COND1(false, s(x0), cons(0, x1)) -> c4(MAX(cons(0, x1)))
   COND1(false, 0, cons(0, x0)) -> c4(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c4(MAX(cons(s(x0), x1)))
   COND1(false, s(x0), cons(x1, cons(x2, x3))) -> c4(MAX(cons(x1, cons(x2, x3))))
   COND1(false, s(0), cons(x0, cons(x1, x2))) -> c4(MAX(cons(x0, cons(x1, x2))))
   COND1(false, s(x0), cons(0, cons(x1, x2))) -> c4(MAX(cons(0, cons(x1, x2))))
   COND1(false, s(x0), cons(0, nil)) -> c4(MAX(cons(0, nil)))
   COND1(false, s(x0), cons(s(x1), nil)) -> c4(MAX(cons(s(x1), nil)))
   COND1(false, s(x0), cons(s(x1), cons(x2, x3))) -> c4(MAX(cons(s(x1), cons(x2, x3))))
   COND1(false, s(s(x0)), cons(s(x1), x2)) -> c4(MAX(cons(s(x1), x2)))
   COND1(false, s(0), cons(s(x0), x1)) -> c4(MAX(cons(s(x0), x1)))
   COND1(false, s(s(x0)), cons(0, cons(x1, x2))) -> c4(MAX(cons(0, cons(x1, x2))))
   COND1(false, s(s(x0)), cons(s(x1), cons(x2, x3))) -> c4(MAX(cons(s(x1), cons(x2, x3))))
   COND1(false, s(0), cons(0, cons(x0, x1))) -> c4(MAX(cons(0, cons(x0, x1))))
   COND1(false, s(0), cons(s(x0), cons(x1, x2))) -> c4(MAX(cons(s(x0), cons(x1, x2))))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2, GT_2

Compound Symbols:   c7_1, c8_1, c20_1, c1_2, c_1, c19_1, c2_1, c5_1, c6_1, c1_1, c9_1, c3_3, c14_1, c4_1, c19_2, c17_1


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

(211) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MEMBER(z0, cons(z1, z2)) -> c7(EQUAL(z0, z1)) by 
   MEMBER(s(s(y0)), cons(s(s(y1)), z2)) -> c7(EQUAL(s(s(y0)), s(s(y1))))

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

(212)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   member(z0, nil) -> false
   member(z0, cons(z1, z2)) -> or(equal(z0, z1), member(z0, z2))
   or(z0, true) -> true
   or(z0, false) -> z0
   equal(0, 0) -> true
   equal(s(z0), 0) -> false
   equal(0, s(z0)) -> false
   equal(s(z0), s(z1)) -> equal(z0, z1)
   gt(0, z0) -> false
   gt(s(z0), 0) -> true
   gt(s(z0), s(z1)) -> gt(z0, z1)
   max(nil) -> 0
   max(cons(z0, z1)) -> if(gt(z0, max(z1)), z0, max(z1))
   if(true, z0, z1) -> z0
   if(false, z0, z1) -> z1
Tuples:
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   COND1(false, z0, cons(z1, z2)) -> c4(GT(z0, if(gt(z1, max(z2)), z1, max(z2))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))
   ST(s(s(z0)), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(s(z0)), z1), member(s(s(z0)), z2))), s(s(z0)), cons(0, cons(z1, z2))), MEMBER(s(s(z0)), cons(0, cons(z1, z2))))
   ST(s(s(z0)), cons(s(z1), cons(z2, z3))) -> c1(COND1(or(equal(s(z0), z1), or(equal(s(s(z0)), z2), member(s(s(z0)), z3))), s(s(z0)), cons(s(z1), cons(z2, z3))), MEMBER(s(s(z0)), cons(s(z1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z0, z1))) -> c1(COND1(or(false, or(equal(s(0), z0), member(s(0), z1))), s(0), cons(0, cons(z0, z1))), MEMBER(s(0), cons(0, cons(z0, z1))))
   ST(s(0), cons(s(z0), cons(z1, z2))) -> c1(COND1(or(equal(0, z0), or(equal(s(0), z1), member(s(0), z2))), s(0), cons(s(z0), cons(z1, z2))), MEMBER(s(0), cons(s(z0), cons(z1, z2))))
   COND1(false, s(x0), cons(0, x1)) -> c4(MAX(cons(0, x1)))
   COND1(false, 0, cons(0, x0)) -> c4(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c4(MAX(cons(s(x0), x1)))
   COND1(false, s(x0), cons(x1, cons(x2, x3))) -> c4(MAX(cons(x1, cons(x2, x3))))
   COND1(false, s(0), cons(x0, cons(x1, x2))) -> c4(MAX(cons(x0, cons(x1, x2))))
   COND1(false, s(x0), cons(0, cons(x1, x2))) -> c4(MAX(cons(0, cons(x1, x2))))
   COND1(false, s(x0), cons(0, nil)) -> c4(MAX(cons(0, nil)))
   COND1(false, s(x0), cons(s(x1), nil)) -> c4(MAX(cons(s(x1), nil)))
   COND1(false, s(x0), cons(s(x1), cons(x2, x3))) -> c4(MAX(cons(s(x1), cons(x2, x3))))
   COND1(false, s(s(x0)), cons(s(x1), x2)) -> c4(MAX(cons(s(x1), x2)))
   COND1(false, s(0), cons(s(x0), x1)) -> c4(MAX(cons(s(x0), x1)))
   COND1(false, s(s(x0)), cons(0, cons(x1, x2))) -> c4(MAX(cons(0, cons(x1, x2))))
   COND1(false, s(s(x0)), cons(s(x1), cons(x2, x3))) -> c4(MAX(cons(s(x1), cons(x2, x3))))
   COND1(false, s(0), cons(0, cons(x0, x1))) -> c4(MAX(cons(0, cons(x0, x1))))
   COND1(false, s(0), cons(s(x0), cons(x1, x2))) -> c4(MAX(cons(s(x0), cons(x1, x2))))
   ST(s(z0), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(z0), z1), member(s(z0), z2))), s(z0), cons(0, cons(z1, z2))), MEMBER(s(z0), cons(0, cons(z1, z2))))
   MEMBER(s(s(y0)), cons(s(s(y1)), z2)) -> c7(EQUAL(s(s(y0)), s(s(y1))))
S tuples:
   MEMBER(z0, cons(z1, z2)) -> c8(MEMBER(z0, z2))
   MAX(cons(z0, z1)) -> c20(MAX(z1))
   ST(s(z0), cons(0, x2)) -> c1(COND1(or(false, member(s(z0), x2)), s(z0), cons(0, x2)), MEMBER(s(z0), cons(0, x2)))
   MAX(cons(x0, cons(x1, x2))) -> c19(MAX(cons(x1, x2)))
   COND1(true, x0, cons(x1, cons(x2, x3))) -> c2(ST(s(x0), cons(x1, cons(x2, x3))))
   COND1(true, s(x0), cons(0, x1)) -> c2(ST(s(s(x0)), cons(0, x1)))
   COND1(true, s(x0), cons(s(x1), x2)) -> c2(ST(s(s(x0)), cons(s(x1), x2)))
   COND1(true, x0, cons(x1, nil)) -> c2(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(0, x1)) -> c5(ST(s(x0), cons(0, x1)))
   COND2(false, x0, cons(x1, nil)) -> c5(ST(s(x0), cons(x1, nil)))
   COND2(false, x0, cons(x1, cons(x2, x3))) -> c5(ST(s(x0), cons(x1, cons(x2, x3))))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(COND1(or(equal(s(x0), x1), or(equal(s(x0), x2), member(s(x0), x3))), s(x0), cons(x1, cons(x2, x3))), MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(0), cons(z1, cons(z2, z3))) -> c1(COND1(or(equal(s(0), z1), or(equal(s(0), z2), member(s(0), z3))), s(0), cons(z1, cons(z2, z3))), MEMBER(s(0), cons(z1, cons(z2, z3))))
   ST(s(z0), cons(0, nil)) -> c1(COND1(false, s(z0), cons(0, nil)), MEMBER(s(z0), cons(0, nil)))
   ST(s(z0), cons(s(z1), nil)) -> c1(COND1(equal(z0, z1), s(z0), cons(s(z1), nil)), MEMBER(s(z0), cons(s(z1), nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, max(cons(z2, z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, max(cons(z2, z3)))), MAX(cons(z1, cons(z2, z3))))
   ST(s(x0), cons(s(z1), cons(x2, x3))) -> c1(COND1(or(equal(x0, z1), member(s(x0), cons(x2, x3))), s(x0), cons(s(z1), cons(x2, x3))), MEMBER(s(x0), cons(s(z1), cons(x2, x3))))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(COND1(or(equal(s(x0), x1), member(s(s(x0)), x2)), s(s(x0)), cons(s(x1), x2)), MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(s(x0), x1)) -> c1(COND1(or(equal(0, x0), member(s(0), x1)), s(0), cons(s(x0), x1)), MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(s(z1), nil)) -> c1(COND1(or(equal(x0, z1), member(s(x0), nil)), s(x0), cons(s(z1), nil)), MEMBER(s(x0), cons(s(z1), nil)))
   EQUAL(s(s(y0)), s(s(y1))) -> c14(EQUAL(s(y0), s(y1)))
   MAX(cons(z0, cons(z1, nil))) -> c19(GT(z0, if(gt(z1, 0), z1, 0)), MAX(cons(z1, nil)))
   MAX(cons(z0, cons(z1, cons(z2, z3)))) -> c19(GT(z0, if(gt(z1, if(gt(z2, max(z3)), z2, max(z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   MAX(cons(z0, cons(0, z1))) -> c19(GT(z0, max(z1)), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, max(nil)), z1, 0)), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   COND1(false, z0, cons(z1, cons(z2, z3))) -> c3(COND2(gt(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), z0, cons(z1, cons(z2, z3))), GT(z0, if(gt(z1, max(cons(z2, z3))), z1, if(gt(z2, max(z3)), z2, max(z3)))), MAX(cons(z1, cons(z2, z3))))
   COND1(false, z0, cons(0, z1)) -> c3(COND2(gt(z0, if(false, 0, max(z1))), z0, cons(0, z1)), GT(z0, if(false, 0, max(z1))), MAX(cons(0, z1)))
   COND1(false, z0, cons(z1, nil)) -> c3(COND2(gt(z0, if(gt(z1, 0), z1, max(nil))), z0, cons(z1, nil)), GT(z0, if(gt(z1, max(nil)), z1, 0)), MAX(cons(z1, nil)))
   GT(s(s(y0)), s(s(y1))) -> c17(GT(s(y0), s(y1)))
   ST(s(s(z0)), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(s(z0)), z1), member(s(s(z0)), z2))), s(s(z0)), cons(0, cons(z1, z2))), MEMBER(s(s(z0)), cons(0, cons(z1, z2))))
   ST(s(s(z0)), cons(s(z1), cons(z2, z3))) -> c1(COND1(or(equal(s(z0), z1), or(equal(s(s(z0)), z2), member(s(s(z0)), z3))), s(s(z0)), cons(s(z1), cons(z2, z3))), MEMBER(s(s(z0)), cons(s(z1), cons(z2, z3))))
   ST(s(0), cons(0, cons(z0, z1))) -> c1(COND1(or(false, or(equal(s(0), z0), member(s(0), z1))), s(0), cons(0, cons(z0, z1))), MEMBER(s(0), cons(0, cons(z0, z1))))
   ST(s(0), cons(s(z0), cons(z1, z2))) -> c1(COND1(or(equal(0, z0), or(equal(s(0), z1), member(s(0), z2))), s(0), cons(s(z0), cons(z1, z2))), MEMBER(s(0), cons(s(z0), cons(z1, z2))))
   ST(s(z0), cons(0, cons(z1, z2))) -> c1(COND1(or(false, or(equal(s(z0), z1), member(s(z0), z2))), s(z0), cons(0, cons(z1, z2))), MEMBER(s(z0), cons(0, cons(z1, z2))))
   MEMBER(s(s(y0)), cons(s(s(y1)), z2)) -> c7(EQUAL(s(s(y0)), s(s(y1))))
K tuples:
   ST(0, cons(0, x2)) -> c(COND1(or(true, member(0, x2)), 0, cons(0, x2)))
   ST(0, cons(s(z0), x2)) -> c(COND1(or(false, member(0, x2)), 0, cons(s(z0), x2)))
   COND1(true, 0, cons(0, x0)) -> c2(ST(s(0), cons(0, x0)))
   COND1(true, 0, cons(s(x0), x1)) -> c2(ST(s(0), cons(s(x0), x1)))
   COND2(false, 0, x0) -> c5(ST(s(0), x0))
   COND2(false, 0, cons(x0, x1)) -> c5(ST(s(0), cons(x0, x1)))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(COND2(false, 0, cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, cons(x2, x3))) -> c6(MAX(cons(x1, cons(x2, x3))))
   COND1(false, 0, cons(x1, x2)) -> c9(COND2(false, 0, cons(x1, x2)))
   COND1(false, 0, cons(x1, x2)) -> c9(MAX(cons(x1, x2)))
   COND1(false, 0, cons(0, x0)) -> c9(COND2(false, 0, cons(0, x0)))
   COND1(false, 0, cons(0, x0)) -> c9(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(COND2(false, 0, cons(s(x0), x1)))
   COND1(false, 0, cons(s(x0), x1)) -> c9(MAX(cons(s(x0), x1)))
   COND1(false, 0, cons(x1, nil)) -> c9(COND2(false, 0, cons(x1, nil)))
   COND1(false, 0, cons(x1, nil)) -> c9(MAX(cons(x1, nil)))
   ST(x0, cons(x1, nil)) -> c1(MEMBER(x0, cons(x1, nil)))
   ST(s(x0), cons(x1, cons(x2, x3))) -> c1(MEMBER(s(x0), cons(x1, cons(x2, x3))))
   ST(s(s(x0)), cons(0, x1)) -> c1(MEMBER(s(s(x0)), cons(0, x1)))
   ST(s(s(x0)), cons(s(x1), x2)) -> c1(MEMBER(s(s(x0)), cons(s(x1), x2)))
   ST(s(0), cons(0, x0)) -> c1(MEMBER(s(0), cons(0, x0)))
   ST(s(0), cons(s(x0), x1)) -> c1(MEMBER(s(0), cons(s(x0), x1)))
   ST(s(x0), cons(x1, nil)) -> c1(MEMBER(s(x0), cons(x1, nil)))
   ST(s(0), cons(z1, z2)) -> c1(MEMBER(s(0), cons(z1, z2)))
   ST(s(x0), cons(0, x1)) -> c1(MEMBER(s(x0), cons(0, x1)))
   COND1(false, s(x0), cons(0, x1)) -> c4(MAX(cons(0, x1)))
   COND1(false, 0, cons(0, x0)) -> c4(MAX(cons(0, x0)))
   COND1(false, 0, cons(s(x0), x1)) -> c4(MAX(cons(s(x0), x1)))
   COND1(false, s(x0), cons(x1, cons(x2, x3))) -> c4(MAX(cons(x1, cons(x2, x3))))
   COND1(false, s(0), cons(x0, cons(x1, x2))) -> c4(MAX(cons(x0, cons(x1, x2))))
   COND1(false, s(x0), cons(0, cons(x1, x2))) -> c4(MAX(cons(0, cons(x1, x2))))
   COND1(false, s(x0), cons(0, nil)) -> c4(MAX(cons(0, nil)))
   COND1(false, s(x0), cons(s(x1), nil)) -> c4(MAX(cons(s(x1), nil)))
   COND1(false, s(x0), cons(s(x1), cons(x2, x3))) -> c4(MAX(cons(s(x1), cons(x2, x3))))
   COND1(false, s(s(x0)), cons(s(x1), x2)) -> c4(MAX(cons(s(x1), x2)))
   COND1(false, s(0), cons(s(x0), x1)) -> c4(MAX(cons(s(x0), x1)))
   COND1(false, s(s(x0)), cons(0, cons(x1, x2))) -> c4(MAX(cons(0, cons(x1, x2))))
   COND1(false, s(s(x0)), cons(s(x1), cons(x2, x3))) -> c4(MAX(cons(s(x1), cons(x2, x3))))
   COND1(false, s(0), cons(0, cons(x0, x1))) -> c4(MAX(cons(0, cons(x0, x1))))
   COND1(false, s(0), cons(s(x0), cons(x1, x2))) -> c4(MAX(cons(s(x0), cons(x1, x2))))
Defined Rule Symbols:   member_2, or_2, equal_2, gt_2, max_1, if_3

Defined Pair Symbols:   MEMBER_2, MAX_1, ST_2, COND1_3, COND2_3, EQUAL_2, GT_2

Compound Symbols:   c8_1, c20_1, c1_2, c_1, c19_1, c2_1, c5_1, c6_1, c1_1, c9_1, c3_3, c14_1, c4_1, c19_2, c17_1, c7_1