KILLED
proof of input_9xGM4Lc9Q7.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


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

(0) CpxRelTRS
(1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 279 ms]
(2) CpxRelTRS
(3) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
(7) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(8) CpxWeightedTrs
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CpxTypedWeightedTrs
    (11) CompletionProof [UPPER BOUND(ID), 0 ms]
    (12) CpxTypedWeightedCompleteTrs
        (13) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (14) CpxTypedWeightedCompleteTrs
        (15) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 19 ms]
        (16) CpxRNTS
        (17) InliningProof [UPPER BOUND(ID), 1118 ms]
        (18) CpxRNTS
        (19) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (20) CpxRNTS
        (21) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
        (22) CpxRNTS
        (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (24) CpxRNTS
        (25) IntTrsBoundProof [UPPER BOUND(ID), 407 ms]
        (26) CpxRNTS
        (27) IntTrsBoundProof [UPPER BOUND(ID), 139 ms]
        (28) CpxRNTS
        (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (30) CpxRNTS
        (31) IntTrsBoundProof [UPPER BOUND(ID), 263 ms]
        (32) CpxRNTS
        (33) IntTrsBoundProof [UPPER BOUND(ID), 65 ms]
        (34) CpxRNTS
        (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (36) CpxRNTS
        (37) IntTrsBoundProof [UPPER BOUND(ID), 373 ms]
        (38) CpxRNTS
        (39) IntTrsBoundProof [UPPER BOUND(ID), 76 ms]
        (40) CpxRNTS
        (41) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (42) CpxRNTS
        (43) IntTrsBoundProof [UPPER BOUND(ID), 1071 ms]
        (44) CpxRNTS
        (45) IntTrsBoundProof [UPPER BOUND(ID), 1549 ms]
        (46) CpxRNTS
        (47) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (48) CpxRNTS
        (49) IntTrsBoundProof [UPPER BOUND(ID), 304 ms]
        (50) CpxRNTS
        (51) IntTrsBoundProof [UPPER BOUND(ID), 15 ms]
        (52) CpxRNTS
        (53) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (54) CpxRNTS
        (55) IntTrsBoundProof [UPPER BOUND(ID), 869 ms]
        (56) CpxRNTS
        (57) IntTrsBoundProof [UPPER BOUND(ID), 132 ms]
        (58) CpxRNTS
        (59) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (60) CpxRNTS
        (61) IntTrsBoundProof [UPPER BOUND(ID), 5087 ms]
        (62) CpxRNTS
        (63) IntTrsBoundProof [UPPER BOUND(ID), 1077 ms]
        (64) CpxRNTS
    (65) CompletionProof [UPPER BOUND(ID), 0 ms]
    (66) CpxTypedWeightedCompleteTrs
        (67) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 17 ms]
        (68) CpxRNTS
(69) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(70) CdtProblem
    (71) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (72) CdtProblem
    (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (76) CdtProblem
    (77) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 140 ms]
    (78) CdtProblem
    (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms]
    (80) CdtProblem
    (81) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (82) CdtProblem
    (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) CdtProblem
    (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (88) CdtProblem
    (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (90) CdtProblem
    (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) CdtProblem
    (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (94) CdtProblem
    (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem
    (101) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (102) CdtProblem
    (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (104) CdtProblem
    (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (106) CdtProblem
    (107) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (108) CdtProblem
    (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 61 ms]
    (112) CdtProblem
    (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms]
    (114) CdtProblem
    (115) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 1 ms]
    (116) CdtProblem
    (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (118) CdtProblem
    (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (122) CdtProblem
    (123) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (124) CdtProblem
    (125) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (126) CdtProblem
    (127) CdtInstantiationProof [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) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (134) CdtProblem
    (135) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (136) CdtProblem
    (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (138) CdtProblem
    (139) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 104 ms]
    (140) CdtProblem
    (141) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (142) CdtProblem
    (143) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (144) CdtProblem
    (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (146) CdtProblem
    (147) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (148) CdtProblem
    (149) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (150) CdtProblem
    (151) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (152) CdtProblem
    (153) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (154) CdtProblem
    (155) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (156) CdtProblem
    (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (158) CdtProblem
    (159) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (160) CdtProblem
    (161) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (162) CdtProblem
    (163) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (164) CdtProblem
    (165) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (166) CdtProblem
    (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (168) CdtProblem
    (169) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (170) CdtProblem
    (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (172) CdtProblem
    (173) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (174) CdtProblem
    (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (176) CdtProblem
    (177) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (178) CdtProblem
    (179) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (180) CdtProblem
    (181) CdtLeafRemovalProof [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) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (188) CdtProblem
    (189) CdtLeafRemovalProof [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) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (198) CdtProblem
    (199) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (200) CdtProblem
    (201) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (202) CdtProblem
    (203) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (204) CdtProblem
    (205) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (206) CdtProblem
    (207) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (208) CdtProblem
    (209) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (210) CdtProblem
    (211) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (212) CdtProblem
    (213) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (214) CdtProblem
    (215) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (216) CdtProblem


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

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


The TRS R consists of the following rules:

   @(Cons(x, xs), ys) -> Cons(x, @(xs, ys))
   @(Nil, ys) -> ys
   gt0(Cons(x, xs), Nil) -> True
   gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs)
   gcd(Nil, Nil) -> Nil
   gcd(Nil, Cons(x, xs)) -> Nil
   gcd(Cons(x, xs), Nil) -> Nil
   gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs))
   lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs))
   eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys))
   eqList(Cons(x, xs), Nil) -> False
   eqList(Nil, Cons(y, ys)) -> False
   eqList(Nil, Nil) -> True
   lgth(Nil) -> Nil
   gt0(Nil, y) -> False
   monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y)
   goal(x, y) -> gcd(x, y)

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

   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs)
   monus[Ite](True, Cons(x, xs), y) -> xs
   gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y)
   gcd[Ite](True, x, y) -> x
   gcd[False][Ite](False, x, y) -> gcd(x, monus(y, x))
   gcd[False][Ite](True, x, y) -> gcd(monus(x, y), y)

Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

(1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
proved innermost termination of relative rules
----------------------------------------

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


The TRS R consists of the following rules:

   @(Cons(x, xs), ys) -> Cons(x, @(xs, ys))
   @(Nil, ys) -> ys
   gt0(Cons(x, xs), Nil) -> True
   gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs)
   gcd(Nil, Nil) -> Nil
   gcd(Nil, Cons(x, xs)) -> Nil
   gcd(Cons(x, xs), Nil) -> Nil
   gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs))
   lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs))
   eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys))
   eqList(Cons(x, xs), Nil) -> False
   eqList(Nil, Cons(y, ys)) -> False
   eqList(Nil, Nil) -> True
   lgth(Nil) -> Nil
   gt0(Nil, y) -> False
   monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y)
   goal(x, y) -> gcd(x, y)

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

   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs)
   monus[Ite](True, Cons(x, xs), y) -> xs
   gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y)
   gcd[Ite](True, x, y) -> x
   gcd[False][Ite](False, x, y) -> gcd(x, monus(y, x))
   gcd[False][Ite](True, x, y) -> gcd(monus(x, y), y)

Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

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

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


The TRS R consists of the following rules:

   @(Cons(x, xs), ys) -> Cons(x, @(xs, ys))
   @(Nil, ys) -> ys
   gt0(Cons(x, xs), Nil) -> True
   gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs)
   gcd(Nil, Nil) -> Nil
   gcd(Nil, Cons(x, xs)) -> Nil
   gcd(Cons(x, xs), Nil) -> Nil
   gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs))
   lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs))
   eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys))
   eqList(Cons(x, xs), Nil) -> False
   eqList(Nil, Cons(y, ys)) -> False
   eqList(Nil, Nil) -> True
   lgth(Nil) -> Nil
   gt0(Nil, y) -> False
   monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y)
   goal(x, y) -> gcd(x, y)

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

   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs)
   monus[Ite](True, Cons(x, xs), y) -> xs
   gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y)
   gcd[Ite](True, x, y) -> x
   gcd[False][Ite](False, x, y) -> gcd(x, monus(y, x))
   gcd[False][Ite](True, x, y) -> gcd(monus(x, y), y)

Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

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

(6)
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:

   @(Cons(x, xs), ys) -> Cons(x, @(xs, ys))
   @(Nil, ys) -> ys
   gt0(Cons(x, xs), Nil) -> True
   gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs)
   gcd(Nil, Nil) -> Nil
   gcd(Nil, Cons(x, xs)) -> Nil
   gcd(Cons(x, xs), Nil) -> Nil
   gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs))
   lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs))
   eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys))
   eqList(Cons(x, xs), Nil) -> False
   eqList(Nil, Cons(y, ys)) -> False
   eqList(Nil, Nil) -> True
   lgth(Nil) -> Nil
   gt0(Nil, y) -> False
   monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y)
   goal(x, y) -> gcd(x, y)
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs)
   monus[Ite](True, Cons(x, xs), y) -> xs
   gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y)
   gcd[Ite](True, x, y) -> x
   gcd[False][Ite](False, x, y) -> gcd(x, monus(y, x))
   gcd[False][Ite](True, x, y) -> gcd(monus(x, y), y)

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

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

(8)
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:

   @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) [1]
   @(Nil, ys) -> ys [1]
   gt0(Cons(x, xs), Nil) -> True [1]
   gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) [1]
   gcd(Nil, Nil) -> Nil [1]
   gcd(Nil, Cons(x, xs)) -> Nil [1]
   gcd(Cons(x, xs), Nil) -> Nil [1]
   gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) [1]
   lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) [1]
   eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) [1]
   eqList(Cons(x, xs), Nil) -> False [1]
   eqList(Nil, Cons(y, ys)) -> False [1]
   eqList(Nil, Nil) -> True [1]
   lgth(Nil) -> Nil [1]
   gt0(Nil, y) -> False [1]
   monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) [1]
   goal(x, y) -> gcd(x, y) [1]
   and(False, False) -> False [0]
   and(True, False) -> False [0]
   and(False, True) -> False [0]
   and(True, True) -> True [0]
   monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) [0]
   monus[Ite](True, Cons(x, xs), y) -> xs [0]
   gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) [0]
   gcd[Ite](True, x, y) -> x [0]
   gcd[False][Ite](False, x, y) -> gcd(x, monus(y, x)) [0]
   gcd[False][Ite](True, x, y) -> gcd(monus(x, y), y) [0]

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

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

(10)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) [1]
   @(Nil, ys) -> ys [1]
   gt0(Cons(x, xs), Nil) -> True [1]
   gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) [1]
   gcd(Nil, Nil) -> Nil [1]
   gcd(Nil, Cons(x, xs)) -> Nil [1]
   gcd(Cons(x, xs), Nil) -> Nil [1]
   gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) [1]
   lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) [1]
   eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) [1]
   eqList(Cons(x, xs), Nil) -> False [1]
   eqList(Nil, Cons(y, ys)) -> False [1]
   eqList(Nil, Nil) -> True [1]
   lgth(Nil) -> Nil [1]
   gt0(Nil, y) -> False [1]
   monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) [1]
   goal(x, y) -> gcd(x, y) [1]
   and(False, False) -> False [0]
   and(True, False) -> False [0]
   and(False, True) -> False [0]
   and(True, True) -> True [0]
   monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) [0]
   monus[Ite](True, Cons(x, xs), y) -> xs [0]
   gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) [0]
   gcd[Ite](True, x, y) -> x [0]
   gcd[False][Ite](False, x, y) -> gcd(x, monus(y, x)) [0]
   gcd[False][Ite](True, x, y) -> gcd(monus(x, y), y) [0]

The TRS has the following type information:
@ :: Cons:Nil -> Cons:Nil -> Cons:Nil
Cons :: Cons:Nil -> Cons:Nil -> Cons:Nil
Nil :: Cons:Nil
gt0 :: Cons:Nil -> Cons:Nil -> True:False
True :: True:False
gcd :: Cons:Nil -> Cons:Nil -> Cons:Nil
gcd[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil
eqList :: Cons:Nil -> Cons:Nil -> True:False
lgth :: Cons:Nil -> Cons:Nil
and :: True:False -> True:False -> True:False
False :: True:False
monus :: Cons:Nil -> Cons:Nil -> Cons:Nil
monus[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil
goal :: Cons:Nil -> Cons:Nil -> Cons:Nil
gcd[False][Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil

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

(11) 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:

   gcd_2
   goal_2

(c) The following functions are completely defined:

   monus_2
   gt0_2
   lgth_1
   eqList_2
   @_2
   and_2
   monus[Ite]_3
   gcd[Ite]_3
   gcd[False][Ite]_3

Due to the following rules being added:

   and(v0, v1) -> null_and [0]
   monus[Ite](v0, v1, v2) -> Nil [0]
   gcd[Ite](v0, v1, v2) -> Nil [0]
   gcd[False][Ite](v0, v1, v2) -> Nil [0]

And the following fresh constants:    null_and

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

(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:

   @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) [1]
   @(Nil, ys) -> ys [1]
   gt0(Cons(x, xs), Nil) -> True [1]
   gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) [1]
   gcd(Nil, Nil) -> Nil [1]
   gcd(Nil, Cons(x, xs)) -> Nil [1]
   gcd(Cons(x, xs), Nil) -> Nil [1]
   gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) [1]
   lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) [1]
   eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) [1]
   eqList(Cons(x, xs), Nil) -> False [1]
   eqList(Nil, Cons(y, ys)) -> False [1]
   eqList(Nil, Nil) -> True [1]
   lgth(Nil) -> Nil [1]
   gt0(Nil, y) -> False [1]
   monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) [1]
   goal(x, y) -> gcd(x, y) [1]
   and(False, False) -> False [0]
   and(True, False) -> False [0]
   and(False, True) -> False [0]
   and(True, True) -> True [0]
   monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) [0]
   monus[Ite](True, Cons(x, xs), y) -> xs [0]
   gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) [0]
   gcd[Ite](True, x, y) -> x [0]
   gcd[False][Ite](False, x, y) -> gcd(x, monus(y, x)) [0]
   gcd[False][Ite](True, x, y) -> gcd(monus(x, y), y) [0]
   and(v0, v1) -> null_and [0]
   monus[Ite](v0, v1, v2) -> Nil [0]
   gcd[Ite](v0, v1, v2) -> Nil [0]
   gcd[False][Ite](v0, v1, v2) -> Nil [0]

The TRS has the following type information:
@ :: Cons:Nil -> Cons:Nil -> Cons:Nil
Cons :: Cons:Nil -> Cons:Nil -> Cons:Nil
Nil :: Cons:Nil
gt0 :: Cons:Nil -> Cons:Nil -> True:False:null_and
True :: True:False:null_and
gcd :: Cons:Nil -> Cons:Nil -> Cons:Nil
gcd[Ite] :: True:False:null_and -> Cons:Nil -> Cons:Nil -> Cons:Nil
eqList :: Cons:Nil -> Cons:Nil -> True:False:null_and
lgth :: Cons:Nil -> Cons:Nil
and :: True:False:null_and -> True:False:null_and -> True:False:null_and
False :: True:False:null_and
monus :: Cons:Nil -> Cons:Nil -> Cons:Nil
monus[Ite] :: True:False:null_and -> Cons:Nil -> Cons:Nil -> Cons:Nil
goal :: Cons:Nil -> Cons:Nil -> Cons:Nil
gcd[False][Ite] :: True:False:null_and -> Cons:Nil -> Cons:Nil -> Cons:Nil
null_and :: True:False:null_and

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

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

(14)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) [1]
   @(Nil, ys) -> ys [1]
   gt0(Cons(x, xs), Nil) -> True [1]
   gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) [1]
   gcd(Nil, Nil) -> Nil [1]
   gcd(Nil, Cons(x, xs)) -> Nil [1]
   gcd(Cons(x, xs), Nil) -> Nil [1]
   gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), Cons(x', xs'), Cons(x, xs)) [2]
   lgth(Cons(x, Cons(x'', xs''))) -> @(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(xs''))) [2]
   lgth(Cons(x, Nil)) -> @(Cons(Nil, Nil), Nil) [2]
   eqList(Cons(Cons(x1, xs1), Cons(x3, xs3)), Cons(Cons(y', ys'), Cons(y1, ys1))) -> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) [3]
   eqList(Cons(Cons(x1, xs1), Cons(x4, xs4)), Cons(Cons(y', ys'), Nil)) -> and(and(eqList(x1, y'), eqList(xs1, ys')), False) [3]
   eqList(Cons(Cons(x1, xs1), Nil), Cons(Cons(y', ys'), Cons(y2, ys2))) -> and(and(eqList(x1, y'), eqList(xs1, ys')), False) [3]
   eqList(Cons(Cons(x1, xs1), Nil), Cons(Cons(y', ys'), Nil)) -> and(and(eqList(x1, y'), eqList(xs1, ys')), True) [3]
   eqList(Cons(Cons(x2, xs2), Cons(x5, xs5)), Cons(Nil, Cons(y3, ys3))) -> and(False, and(eqList(x5, y3), eqList(xs5, ys3))) [3]
   eqList(Cons(Cons(x2, xs2), Cons(x6, xs6)), Cons(Nil, Nil)) -> and(False, False) [3]
   eqList(Cons(Cons(x2, xs2), Nil), Cons(Nil, Cons(y4, ys4))) -> and(False, False) [3]
   eqList(Cons(Cons(x2, xs2), Nil), Cons(Nil, Nil)) -> and(False, True) [3]
   eqList(Cons(Nil, Cons(x7, xs7)), Cons(Cons(y'', ys''), Cons(y5, ys5))) -> and(False, and(eqList(x7, y5), eqList(xs7, ys5))) [3]
   eqList(Cons(Nil, Cons(x8, xs8)), Cons(Cons(y'', ys''), Nil)) -> and(False, False) [3]
   eqList(Cons(Nil, Nil), Cons(Cons(y'', ys''), Cons(y6, ys6))) -> and(False, False) [3]
   eqList(Cons(Nil, Nil), Cons(Cons(y'', ys''), Nil)) -> and(False, True) [3]
   eqList(Cons(Nil, Cons(x9, xs9)), Cons(Nil, Cons(y7, ys7))) -> and(True, and(eqList(x9, y7), eqList(xs9, ys7))) [3]
   eqList(Cons(Nil, Cons(x10, xs10)), Cons(Nil, Nil)) -> and(True, False) [3]
   eqList(Cons(Nil, Nil), Cons(Nil, Cons(y8, ys8))) -> and(True, False) [3]
   eqList(Cons(Nil, Nil), Cons(Nil, Nil)) -> and(True, True) [3]
   eqList(Cons(x, xs), Nil) -> False [1]
   eqList(Nil, Cons(y, ys)) -> False [1]
   eqList(Nil, Nil) -> True [1]
   lgth(Nil) -> Nil [1]
   gt0(Nil, y) -> False [1]
   monus(x, Cons(x11, xs11)) -> monus[Ite](eqList(@(Cons(Nil, Nil), lgth(xs11)), Cons(Nil, Nil)), x, Cons(x11, xs11)) [2]
   monus(x, Nil) -> monus[Ite](eqList(Nil, Cons(Nil, Nil)), x, Nil) [2]
   goal(x, y) -> gcd(x, y) [1]
   and(False, False) -> False [0]
   and(True, False) -> False [0]
   and(False, True) -> False [0]
   and(True, True) -> True [0]
   monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) [0]
   monus[Ite](True, Cons(x, xs), y) -> xs [0]
   gcd[Ite](False, Cons(x12, xs12), Nil) -> gcd[False][Ite](True, Cons(x12, xs12), Nil) [1]
   gcd[Ite](False, Cons(x''', xs'''), Cons(x13, xs13)) -> gcd[False][Ite](gt0(xs''', xs13), Cons(x''', xs'''), Cons(x13, xs13)) [1]
   gcd[Ite](False, Nil, y) -> gcd[False][Ite](False, Nil, y) [1]
   gcd[Ite](True, x, y) -> x [0]
   gcd[False][Ite](False, x, y) -> gcd(x, monus[Ite](eqList(lgth(x), Cons(Nil, Nil)), y, x)) [1]
   gcd[False][Ite](True, x, y) -> gcd(monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y), y) [1]
   and(v0, v1) -> null_and [0]
   monus[Ite](v0, v1, v2) -> Nil [0]
   gcd[Ite](v0, v1, v2) -> Nil [0]
   gcd[False][Ite](v0, v1, v2) -> Nil [0]

The TRS has the following type information:
@ :: Cons:Nil -> Cons:Nil -> Cons:Nil
Cons :: Cons:Nil -> Cons:Nil -> Cons:Nil
Nil :: Cons:Nil
gt0 :: Cons:Nil -> Cons:Nil -> True:False:null_and
True :: True:False:null_and
gcd :: Cons:Nil -> Cons:Nil -> Cons:Nil
gcd[Ite] :: True:False:null_and -> Cons:Nil -> Cons:Nil -> Cons:Nil
eqList :: Cons:Nil -> Cons:Nil -> True:False:null_and
lgth :: Cons:Nil -> Cons:Nil
and :: True:False:null_and -> True:False:null_and -> True:False:null_and
False :: True:False:null_and
monus :: Cons:Nil -> Cons:Nil -> Cons:Nil
monus[Ite] :: True:False:null_and -> Cons:Nil -> Cons:Nil -> Cons:Nil
goal :: Cons:Nil -> Cons:Nil -> Cons:Nil
gcd[False][Ite] :: True:False:null_and -> Cons:Nil -> Cons:Nil -> Cons:Nil
null_and :: True:False:null_and

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

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

   Nil => 0
   True => 2
   False => 1
   null_and => 0

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

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

   @(z, z') -{ 1 }-> ys :|: z' = ys, ys >= 0, z = 0
   @(z, z') -{ 1 }-> 1 + x + @(xs, ys) :|: z = 1 + x + xs, xs >= 0, z' = ys, ys >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) :|: y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 2) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 3 }-> and(2, and(eqList(x9, y7), eqList(xs9, ys7))) :|: z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 3 }-> and(2, 2) :|: z = 1 + 0 + 0, z' = 1 + 0 + 0
   eqList(z, z') -{ 3 }-> and(2, 1) :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10)
   eqList(z, z') -{ 3 }-> and(2, 1) :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8)
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x5, y3), eqList(xs5, ys3))) :|: xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x7, y5), eqList(xs7, ys5))) :|: y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 3 }-> and(1, 2) :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, 2) :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0
   eqList(z, z') -{ 3 }-> and(1, 1) :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, 1) :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, 1) :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0
   eqList(z, z') -{ 3 }-> and(1, 1) :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6)
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   gcd(z, z') -{ 2 }-> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(x, monus[Ite](eqList(lgth(x), 1 + 0 + 0), y, x)) :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(y), 1 + 0 + 0), x, y), y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> x :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](gt0(xs''', xs13), 1 + x''' + xs''', 1 + x13 + xs13) :|: xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, y) :|: z'' = y, z = 1, y >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   goal(z, z') -{ 1 }-> gcd(x, y) :|: x >= 0, y >= 0, z = x, z' = y
   gt0(z, z') -{ 1 }-> gt0(xs', xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: y >= 0, z = 0, z' = y
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, 0) :|: x >= 0, z = 1 + x + 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), x, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, x >= 0, xs11 >= 0, x11 >= 0, z = x
   monus(z, z') -{ 2 }-> monus[Ite](eqList(0, 1 + 0 + 0), x, 0) :|: x >= 0, z = x, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, z'' = y, x >= 0, y >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0


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

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

   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1

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

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

   @(z, z') -{ 1 }-> ys :|: z' = ys, ys >= 0, z = 0
   @(z, z') -{ 1 }-> 1 + x + @(xs, ys) :|: z = 1 + x + xs, xs >= 0, z' = ys, ys >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) :|: y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 2) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 3 }-> and(2, and(eqList(x9, y7), eqList(xs9, ys7))) :|: z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x5, y3), eqList(xs5, ys3))) :|: xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x7, y5), eqList(xs7, ys5))) :|: y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 2 }-> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(x, monus[Ite](eqList(lgth(x), 1 + 0 + 0), y, x)) :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(y), 1 + 0 + 0), x, y), y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> x :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](gt0(xs''', xs13), 1 + x''' + xs''', 1 + x13 + xs13) :|: xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, y) :|: z'' = y, z = 1, y >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   goal(z, z') -{ 1 }-> gcd(x, y) :|: x >= 0, y >= 0, z = x, z' = y
   gt0(z, z') -{ 1 }-> gt0(xs', xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: y >= 0, z = 0, z' = y
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, 0) :|: x >= 0, z = 1 + x + 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), x, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, x >= 0, xs11 >= 0, x11 >= 0, z = x
   monus(z, z') -{ 2 }-> monus[Ite](eqList(0, 1 + 0 + 0), x, 0) :|: x >= 0, z = x, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, z'' = y, x >= 0, y >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0


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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 1 }-> 1 + x + @(xs, z') :|: z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) :|: y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 2) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 3 }-> and(2, and(eqList(x9, y7), eqList(xs9, ys7))) :|: z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x5, y3), eqList(xs5, ys3))) :|: xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x7, y5), eqList(xs7, ys5))) :|: y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 2 }-> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](gt0(xs''', xs13), 1 + x''' + xs''', 1 + x13 + xs13) :|: xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 1 }-> gt0(xs', xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, 0) :|: z - 1 >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(0, 1 + 0 + 0), z, 0) :|: z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0


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

   { gt0 }
   { and }
   { @ }
   { eqList }
   { lgth }
   { monus[Ite], monus }
   { gcd, gcd[Ite], gcd[False][Ite] }
   { goal }

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 1 }-> 1 + x + @(xs, z') :|: z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) :|: y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 2) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 3 }-> and(2, and(eqList(x9, y7), eqList(xs9, ys7))) :|: z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x5, y3), eqList(xs5, ys3))) :|: xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x7, y5), eqList(xs7, ys5))) :|: y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 2 }-> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](gt0(xs''', xs13), 1 + x''' + xs''', 1 + x13 + xs13) :|: xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 1 }-> gt0(xs', xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, 0) :|: z - 1 >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(0, 1 + 0 + 0), z, 0) :|: z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {gt0}, {and}, {@}, {eqList}, {lgth}, {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 1 }-> 1 + x + @(xs, z') :|: z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) :|: y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 2) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 3 }-> and(2, and(eqList(x9, y7), eqList(xs9, ys7))) :|: z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x5, y3), eqList(xs5, ys3))) :|: xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x7, y5), eqList(xs7, ys5))) :|: y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 2 }-> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](gt0(xs''', xs13), 1 + x''' + xs''', 1 + x13 + xs13) :|: xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 1 }-> gt0(xs', xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, 0) :|: z - 1 >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(0, 1 + 0 + 0), z, 0) :|: z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {gt0}, {and}, {@}, {eqList}, {lgth}, {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}

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(25) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: gt0
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 1 }-> 1 + x + @(xs, z') :|: z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) :|: y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 2) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 3 }-> and(2, and(eqList(x9, y7), eqList(xs9, ys7))) :|: z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x5, y3), eqList(xs5, ys3))) :|: xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x7, y5), eqList(xs7, ys5))) :|: y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 2 }-> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](gt0(xs''', xs13), 1 + x''' + xs''', 1 + x13 + xs13) :|: xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 1 }-> gt0(xs', xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, 0) :|: z - 1 >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(0, 1 + 0 + 0), z, 0) :|: z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {gt0}, {and}, {@}, {eqList}, {lgth}, {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: ?, size: O(1) [2]

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

(27) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: gt0
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z'

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 1 }-> 1 + x + @(xs, z') :|: z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) :|: y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 2) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 3 }-> and(2, and(eqList(x9, y7), eqList(xs9, ys7))) :|: z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x5, y3), eqList(xs5, ys3))) :|: xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x7, y5), eqList(xs7, ys5))) :|: y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 2 }-> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](gt0(xs''', xs13), 1 + x''' + xs''', 1 + x13 + xs13) :|: xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 1 }-> gt0(xs', xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, 0) :|: z - 1 >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(0, 1 + 0 + 0), z, 0) :|: z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {and}, {@}, {eqList}, {lgth}, {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]

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

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 1 }-> 1 + x + @(xs, z') :|: z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) :|: y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 2) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 3 }-> and(2, and(eqList(x9, y7), eqList(xs9, ys7))) :|: z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x5, y3), eqList(xs5, ys3))) :|: xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x7, y5), eqList(xs7, ys5))) :|: y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 2 }-> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, 0) :|: z - 1 >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(0, 1 + 0 + 0), z, 0) :|: z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {and}, {@}, {eqList}, {lgth}, {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]

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

(31) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 1 }-> 1 + x + @(xs, z') :|: z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) :|: y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 2) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 3 }-> and(2, and(eqList(x9, y7), eqList(xs9, ys7))) :|: z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x5, y3), eqList(xs5, ys3))) :|: xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x7, y5), eqList(xs7, ys5))) :|: y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 2 }-> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, 0) :|: z - 1 >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(0, 1 + 0 + 0), z, 0) :|: z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {and}, {@}, {eqList}, {lgth}, {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: ?, size: O(1) [2]

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

(33) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 1 }-> 1 + x + @(xs, z') :|: z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) :|: y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 2) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 3 }-> and(2, and(eqList(x9, y7), eqList(xs9, ys7))) :|: z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x5, y3), eqList(xs5, ys3))) :|: xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x7, y5), eqList(xs7, ys5))) :|: y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 2 }-> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, 0) :|: z - 1 >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(0, 1 + 0 + 0), z, 0) :|: z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {@}, {eqList}, {lgth}, {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: O(1) [0], size: O(1) [2]

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

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 1 }-> 1 + x + @(xs, z') :|: z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) :|: y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 2) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 3 }-> and(2, and(eqList(x9, y7), eqList(xs9, ys7))) :|: z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x5, y3), eqList(xs5, ys3))) :|: xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x7, y5), eqList(xs7, ys5))) :|: y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 2 }-> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, 0) :|: z - 1 >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(0, 1 + 0 + 0), z, 0) :|: z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {@}, {eqList}, {lgth}, {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: O(1) [0], size: O(1) [2]

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

(37) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 1 }-> 1 + x + @(xs, z') :|: z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) :|: y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 2) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 3 }-> and(2, and(eqList(x9, y7), eqList(xs9, ys7))) :|: z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x5, y3), eqList(xs5, ys3))) :|: xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x7, y5), eqList(xs7, ys5))) :|: y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 2 }-> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, 0) :|: z - 1 >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(0, 1 + 0 + 0), z, 0) :|: z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {@}, {eqList}, {lgth}, {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: O(1) [0], size: O(1) [2]
  @: runtime: ?, size: O(n^1) [z + z']

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

(39) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 1 }-> 1 + x + @(xs, z') :|: z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) :|: y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 2) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 3 }-> and(2, and(eqList(x9, y7), eqList(xs9, ys7))) :|: z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x5, y3), eqList(xs5, ys3))) :|: xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x7, y5), eqList(xs7, ys5))) :|: y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 2 }-> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, 0) :|: z - 1 >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(0, 1 + 0 + 0), z, 0) :|: z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {eqList}, {lgth}, {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: O(1) [0], size: O(1) [2]
  @: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']

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

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 2 + xs }-> 1 + x + s'' :|: s'' >= 0, s'' <= xs + z', z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) :|: y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 2) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 3 }-> and(2, and(eqList(x9, y7), eqList(xs9, ys7))) :|: z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x5, y3), eqList(xs5, ys3))) :|: xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x7, y5), eqList(xs7, ys5))) :|: y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 2 }-> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 1 + 0 + 0 + 0, z - 1 >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(0, 1 + 0 + 0), z, 0) :|: z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {eqList}, {lgth}, {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: O(1) [0], size: O(1) [2]
  @: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']

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

(43) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 2 + xs }-> 1 + x + s'' :|: s'' >= 0, s'' <= xs + z', z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) :|: y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 2) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 3 }-> and(2, and(eqList(x9, y7), eqList(xs9, ys7))) :|: z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x5, y3), eqList(xs5, ys3))) :|: xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x7, y5), eqList(xs7, ys5))) :|: y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 2 }-> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 1 + 0 + 0 + 0, z - 1 >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(0, 1 + 0 + 0), z, 0) :|: z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {eqList}, {lgth}, {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: O(1) [0], size: O(1) [2]
  @: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  eqList: runtime: ?, size: O(1) [2]

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

(45) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: eqList
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 78 + 156*z'

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 2 + xs }-> 1 + x + s'' :|: s'' >= 0, s'' <= xs + z', z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), and(eqList(x3, y1), eqList(xs3, ys1))) :|: y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 2) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 3 }-> and(and(eqList(x1, y'), eqList(xs1, ys')), 1) :|: z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 3 }-> and(2, and(eqList(x9, y7), eqList(xs9, ys7))) :|: z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x5, y3), eqList(xs5, ys3))) :|: xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 3 }-> and(1, and(eqList(x7, y5), eqList(xs7, ys5))) :|: y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 2 }-> gcd[Ite](and(eqList(x', x), eqList(xs', xs)), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 1 + 0 + 0 + 0, z - 1 >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(0, 1 + 0 + 0), z, 0) :|: z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {lgth}, {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: O(1) [0], size: O(1) [2]
  @: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  eqList: runtime: O(n^1) [78 + 156*z'], size: O(1) [2]

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

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 2 + xs }-> 1 + x + s'' :|: s'' >= 0, s'' <= xs + z', z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s16 :|: s13 >= 0, s13 <= 2, s14 >= 0, s14 <= 2, s15 >= 0, s15 <= 2, s16 >= 0, s16 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s20 :|: s17 >= 0, s17 <= 2, s18 >= 0, s18 <= 2, s19 >= 0, s19 <= 2, s20 >= 0, s20 <= 2, z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s24 :|: s21 >= 0, s21 <= 2, s22 >= 0, s22 <= 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 159 + 156*y3 + 156*ys3 }-> s28 :|: s25 >= 0, s25 <= 2, s26 >= 0, s26 <= 2, s27 >= 0, s27 <= 2, s28 >= 0, s28 <= 2, xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 159 + 156*y5 + 156*ys5 }-> s32 :|: s29 >= 0, s29 <= 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 2, s32 >= 0, s32 <= 2, y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 159 + 156*y7 + 156*ys7 }-> s36 :|: s33 >= 0, s33 <= 2, s34 >= 0, s34 <= 2, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= 2, z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 315 + 156*y' + 156*y1 + 156*ys' + 156*ys1 }-> s8 :|: s2 >= 0, s2 <= 2, s3 >= 0, s3 <= 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, s8 >= 0, s8 <= 2, y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 158 + 156*x + 156*xs }-> gcd[Ite](s12, 1 + x' + xs', 1 + x + xs) :|: s10 >= 0, s10 <= 2, s11 >= 0, s11 <= 2, s12 >= 0, s12 <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 1 + 0 + 0 + 0, z - 1 >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 236 }-> monus[Ite](s9, z, 0) :|: s9 >= 0, s9 <= 2, z >= 0, z' = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {lgth}, {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: O(1) [0], size: O(1) [2]
  @: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  eqList: runtime: O(n^1) [78 + 156*z'], size: O(1) [2]

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

(49) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 2 + xs }-> 1 + x + s'' :|: s'' >= 0, s'' <= xs + z', z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s16 :|: s13 >= 0, s13 <= 2, s14 >= 0, s14 <= 2, s15 >= 0, s15 <= 2, s16 >= 0, s16 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s20 :|: s17 >= 0, s17 <= 2, s18 >= 0, s18 <= 2, s19 >= 0, s19 <= 2, s20 >= 0, s20 <= 2, z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s24 :|: s21 >= 0, s21 <= 2, s22 >= 0, s22 <= 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 159 + 156*y3 + 156*ys3 }-> s28 :|: s25 >= 0, s25 <= 2, s26 >= 0, s26 <= 2, s27 >= 0, s27 <= 2, s28 >= 0, s28 <= 2, xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 159 + 156*y5 + 156*ys5 }-> s32 :|: s29 >= 0, s29 <= 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 2, s32 >= 0, s32 <= 2, y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 159 + 156*y7 + 156*ys7 }-> s36 :|: s33 >= 0, s33 <= 2, s34 >= 0, s34 <= 2, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= 2, z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 315 + 156*y' + 156*y1 + 156*ys' + 156*ys1 }-> s8 :|: s2 >= 0, s2 <= 2, s3 >= 0, s3 <= 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, s8 >= 0, s8 <= 2, y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 158 + 156*x + 156*xs }-> gcd[Ite](s12, 1 + x' + xs', 1 + x + xs) :|: s10 >= 0, s10 <= 2, s11 >= 0, s11 <= 2, s12 >= 0, s12 <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 1 + 0 + 0 + 0, z - 1 >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 236 }-> monus[Ite](s9, z, 0) :|: s9 >= 0, s9 <= 2, z >= 0, z' = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {lgth}, {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: O(1) [0], size: O(1) [2]
  @: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  eqList: runtime: O(n^1) [78 + 156*z'], size: O(1) [2]
  lgth: runtime: ?, size: O(n^1) [z]

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

(51) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 2 + xs }-> 1 + x + s'' :|: s'' >= 0, s'' <= xs + z', z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s16 :|: s13 >= 0, s13 <= 2, s14 >= 0, s14 <= 2, s15 >= 0, s15 <= 2, s16 >= 0, s16 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s20 :|: s17 >= 0, s17 <= 2, s18 >= 0, s18 <= 2, s19 >= 0, s19 <= 2, s20 >= 0, s20 <= 2, z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s24 :|: s21 >= 0, s21 <= 2, s22 >= 0, s22 <= 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 159 + 156*y3 + 156*ys3 }-> s28 :|: s25 >= 0, s25 <= 2, s26 >= 0, s26 <= 2, s27 >= 0, s27 <= 2, s28 >= 0, s28 <= 2, xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 159 + 156*y5 + 156*ys5 }-> s32 :|: s29 >= 0, s29 <= 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 2, s32 >= 0, s32 <= 2, y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 159 + 156*y7 + 156*ys7 }-> s36 :|: s33 >= 0, s33 <= 2, s34 >= 0, s34 <= 2, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= 2, z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 315 + 156*y' + 156*y1 + 156*ys' + 156*ys1 }-> s8 :|: s2 >= 0, s2 <= 2, s3 >= 0, s3 <= 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, s8 >= 0, s8 <= 2, y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 158 + 156*x + 156*xs }-> gcd[Ite](s12, 1 + x' + xs', 1 + x + xs) :|: s10 >= 0, s10 <= 2, s11 >= 0, s11 <= 2, s12 >= 0, s12 <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(z', monus[Ite](eqList(lgth(z'), 1 + 0 + 0), z'', z')) :|: z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 1 }-> gcd(monus[Ite](eqList(lgth(z''), 1 + 0 + 0), z', z''), z'') :|: z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 1 + 0 + 0 + 0, z - 1 >= 0
   lgth(z) -{ 2 }-> @(1 + 0 + 0, @(1 + 0 + 0, lgth(xs''))) :|: z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 236 }-> monus[Ite](s9, z, 0) :|: s9 >= 0, s9 <= 2, z >= 0, z' = 0
   monus(z, z') -{ 2 }-> monus[Ite](eqList(@(1 + 0 + 0, lgth(xs11)), 1 + 0 + 0), z, 1 + x11 + xs11) :|: z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: O(1) [0], size: O(1) [2]
  @: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  eqList: runtime: O(n^1) [78 + 156*z'], size: O(1) [2]
  lgth: runtime: O(n^1) [5 + 6*z], size: O(n^1) [z]

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

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 2 + xs }-> 1 + x + s'' :|: s'' >= 0, s'' <= xs + z', z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s16 :|: s13 >= 0, s13 <= 2, s14 >= 0, s14 <= 2, s15 >= 0, s15 <= 2, s16 >= 0, s16 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s20 :|: s17 >= 0, s17 <= 2, s18 >= 0, s18 <= 2, s19 >= 0, s19 <= 2, s20 >= 0, s20 <= 2, z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s24 :|: s21 >= 0, s21 <= 2, s22 >= 0, s22 <= 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 159 + 156*y3 + 156*ys3 }-> s28 :|: s25 >= 0, s25 <= 2, s26 >= 0, s26 <= 2, s27 >= 0, s27 <= 2, s28 >= 0, s28 <= 2, xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 159 + 156*y5 + 156*ys5 }-> s32 :|: s29 >= 0, s29 <= 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 2, s32 >= 0, s32 <= 2, y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 159 + 156*y7 + 156*ys7 }-> s36 :|: s33 >= 0, s33 <= 2, s34 >= 0, s34 <= 2, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= 2, z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 315 + 156*y' + 156*y1 + 156*ys' + 156*ys1 }-> s8 :|: s2 >= 0, s2 <= 2, s3 >= 0, s3 <= 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, s8 >= 0, s8 <= 2, y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 158 + 156*x + 156*xs }-> gcd[Ite](s12, 1 + x' + xs', 1 + x + xs) :|: s10 >= 0, s10 <= 2, s11 >= 0, s11 <= 2, s12 >= 0, s12 <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 240 + 6*z' }-> gcd(z', monus[Ite](s44, z'', z')) :|: s43 >= 0, s43 <= z', s44 >= 0, s44 <= 2, z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 240 + 6*z'' }-> gcd(monus[Ite](s46, z', z''), z'') :|: s45 >= 0, s45 <= z'', s46 >= 0, s46 <= 2, z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 1 + 0 + 0 + 0, z - 1 >= 0
   lgth(z) -{ 11 + 6*xs'' }-> s39 :|: s37 >= 0, s37 <= xs'', s38 >= 0, s38 <= 1 + 0 + 0 + s37, s39 >= 0, s39 <= 1 + 0 + 0 + s38, z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 243 + 6*xs11 }-> monus[Ite](s42, z, 1 + x11 + xs11) :|: s40 >= 0, s40 <= xs11, s41 >= 0, s41 <= 1 + 0 + 0 + s40, s42 >= 0, s42 <= 2, z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 236 }-> monus[Ite](s9, z, 0) :|: s9 >= 0, s9 <= 2, z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: O(1) [0], size: O(1) [2]
  @: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  eqList: runtime: O(n^1) [78 + 156*z'], size: O(1) [2]
  lgth: runtime: O(n^1) [5 + 6*z], size: O(n^1) [z]

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

(55) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 2 + xs }-> 1 + x + s'' :|: s'' >= 0, s'' <= xs + z', z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s16 :|: s13 >= 0, s13 <= 2, s14 >= 0, s14 <= 2, s15 >= 0, s15 <= 2, s16 >= 0, s16 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s20 :|: s17 >= 0, s17 <= 2, s18 >= 0, s18 <= 2, s19 >= 0, s19 <= 2, s20 >= 0, s20 <= 2, z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s24 :|: s21 >= 0, s21 <= 2, s22 >= 0, s22 <= 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 159 + 156*y3 + 156*ys3 }-> s28 :|: s25 >= 0, s25 <= 2, s26 >= 0, s26 <= 2, s27 >= 0, s27 <= 2, s28 >= 0, s28 <= 2, xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 159 + 156*y5 + 156*ys5 }-> s32 :|: s29 >= 0, s29 <= 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 2, s32 >= 0, s32 <= 2, y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 159 + 156*y7 + 156*ys7 }-> s36 :|: s33 >= 0, s33 <= 2, s34 >= 0, s34 <= 2, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= 2, z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 315 + 156*y' + 156*y1 + 156*ys' + 156*ys1 }-> s8 :|: s2 >= 0, s2 <= 2, s3 >= 0, s3 <= 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, s8 >= 0, s8 <= 2, y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 158 + 156*x + 156*xs }-> gcd[Ite](s12, 1 + x' + xs', 1 + x + xs) :|: s10 >= 0, s10 <= 2, s11 >= 0, s11 <= 2, s12 >= 0, s12 <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 240 + 6*z' }-> gcd(z', monus[Ite](s44, z'', z')) :|: s43 >= 0, s43 <= z', s44 >= 0, s44 <= 2, z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 240 + 6*z'' }-> gcd(monus[Ite](s46, z', z''), z'') :|: s45 >= 0, s45 <= z'', s46 >= 0, s46 <= 2, z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 1 + 0 + 0 + 0, z - 1 >= 0
   lgth(z) -{ 11 + 6*xs'' }-> s39 :|: s37 >= 0, s37 <= xs'', s38 >= 0, s38 <= 1 + 0 + 0 + s37, s39 >= 0, s39 <= 1 + 0 + 0 + s38, z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 243 + 6*xs11 }-> monus[Ite](s42, z, 1 + x11 + xs11) :|: s40 >= 0, s40 <= xs11, s41 >= 0, s41 <= 1 + 0 + 0 + s40, s42 >= 0, s42 <= 2, z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 236 }-> monus[Ite](s9, z, 0) :|: s9 >= 0, s9 <= 2, z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {monus[Ite],monus}, {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: O(1) [0], size: O(1) [2]
  @: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  eqList: runtime: O(n^1) [78 + 156*z'], size: O(1) [2]
  lgth: runtime: O(n^1) [5 + 6*z], size: O(n^1) [z]
  monus[Ite]: runtime: ?, size: O(n^1) [z']
  monus: runtime: ?, size: O(n^1) [z]

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

(57) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: monus[Ite]
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 958*z'' + 12*z''^2

Computed RUNTIME bound using KoAT for: monus
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 1449 + 1970*z' + 48*z'^2

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 2 + xs }-> 1 + x + s'' :|: s'' >= 0, s'' <= xs + z', z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s16 :|: s13 >= 0, s13 <= 2, s14 >= 0, s14 <= 2, s15 >= 0, s15 <= 2, s16 >= 0, s16 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s20 :|: s17 >= 0, s17 <= 2, s18 >= 0, s18 <= 2, s19 >= 0, s19 <= 2, s20 >= 0, s20 <= 2, z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s24 :|: s21 >= 0, s21 <= 2, s22 >= 0, s22 <= 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 159 + 156*y3 + 156*ys3 }-> s28 :|: s25 >= 0, s25 <= 2, s26 >= 0, s26 <= 2, s27 >= 0, s27 <= 2, s28 >= 0, s28 <= 2, xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 159 + 156*y5 + 156*ys5 }-> s32 :|: s29 >= 0, s29 <= 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 2, s32 >= 0, s32 <= 2, y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 159 + 156*y7 + 156*ys7 }-> s36 :|: s33 >= 0, s33 <= 2, s34 >= 0, s34 <= 2, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= 2, z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 315 + 156*y' + 156*y1 + 156*ys' + 156*ys1 }-> s8 :|: s2 >= 0, s2 <= 2, s3 >= 0, s3 <= 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, s8 >= 0, s8 <= 2, y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 158 + 156*x + 156*xs }-> gcd[Ite](s12, 1 + x' + xs', 1 + x + xs) :|: s10 >= 0, s10 <= 2, s11 >= 0, s11 <= 2, s12 >= 0, s12 <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 240 + 6*z' }-> gcd(z', monus[Ite](s44, z'', z')) :|: s43 >= 0, s43 <= z', s44 >= 0, s44 <= 2, z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 240 + 6*z'' }-> gcd(monus[Ite](s46, z', z''), z'') :|: s45 >= 0, s45 <= z'', s46 >= 0, s46 <= 2, z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 1 + 0 + 0 + 0, z - 1 >= 0
   lgth(z) -{ 11 + 6*xs'' }-> s39 :|: s37 >= 0, s37 <= xs'', s38 >= 0, s38 <= 1 + 0 + 0 + s37, s39 >= 0, s39 <= 1 + 0 + 0 + s38, z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 243 + 6*xs11 }-> monus[Ite](s42, z, 1 + x11 + xs11) :|: s40 >= 0, s40 <= xs11, s41 >= 0, s41 <= 1 + 0 + 0 + s40, s42 >= 0, s42 <= 2, z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 236 }-> monus[Ite](s9, z, 0) :|: s9 >= 0, s9 <= 2, z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: O(1) [0], size: O(1) [2]
  @: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  eqList: runtime: O(n^1) [78 + 156*z'], size: O(1) [2]
  lgth: runtime: O(n^1) [5 + 6*z], size: O(n^1) [z]
  monus[Ite]: runtime: O(n^2) [958*z'' + 12*z''^2], size: O(n^1) [z']
  monus: runtime: O(n^2) [1449 + 1970*z' + 48*z'^2], size: O(n^1) [z]

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

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 2 + xs }-> 1 + x + s'' :|: s'' >= 0, s'' <= xs + z', z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s16 :|: s13 >= 0, s13 <= 2, s14 >= 0, s14 <= 2, s15 >= 0, s15 <= 2, s16 >= 0, s16 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s20 :|: s17 >= 0, s17 <= 2, s18 >= 0, s18 <= 2, s19 >= 0, s19 <= 2, s20 >= 0, s20 <= 2, z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s24 :|: s21 >= 0, s21 <= 2, s22 >= 0, s22 <= 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 159 + 156*y3 + 156*ys3 }-> s28 :|: s25 >= 0, s25 <= 2, s26 >= 0, s26 <= 2, s27 >= 0, s27 <= 2, s28 >= 0, s28 <= 2, xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 159 + 156*y5 + 156*ys5 }-> s32 :|: s29 >= 0, s29 <= 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 2, s32 >= 0, s32 <= 2, y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 159 + 156*y7 + 156*ys7 }-> s36 :|: s33 >= 0, s33 <= 2, s34 >= 0, s34 <= 2, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= 2, z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 315 + 156*y' + 156*y1 + 156*ys' + 156*ys1 }-> s8 :|: s2 >= 0, s2 <= 2, s3 >= 0, s3 <= 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, s8 >= 0, s8 <= 2, y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 158 + 156*x + 156*xs }-> gcd[Ite](s12, 1 + x' + xs', 1 + x + xs) :|: s10 >= 0, s10 <= 2, s11 >= 0, s11 <= 2, s12 >= 0, s12 <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 240 + 964*z'' + 12*z''^2 }-> gcd(s51, z'') :|: s51 >= 0, s51 <= z', s45 >= 0, s45 <= z'', s46 >= 0, s46 <= 2, z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 240 + 964*z' + 12*z'^2 }-> gcd(z', s50) :|: s50 >= 0, s50 <= z'', s43 >= 0, s43 <= z', s44 >= 0, s44 <= 2, z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 1 + 0 + 0 + 0, z - 1 >= 0
   lgth(z) -{ 11 + 6*xs'' }-> s39 :|: s37 >= 0, s37 <= xs'', s38 >= 0, s38 <= 1 + 0 + 0 + s37, s39 >= 0, s39 <= 1 + 0 + 0 + s38, z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 1213 + 982*x11 + 24*x11*xs11 + 12*x11^2 + 988*xs11 + 12*xs11^2 }-> s47 :|: s47 >= 0, s47 <= z, s40 >= 0, s40 <= xs11, s41 >= 0, s41 <= 1 + 0 + 0 + s40, s42 >= 0, s42 <= 2, z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 236 }-> s48 :|: s48 >= 0, s48 <= z, s9 >= 0, s9 <= 2, z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 1449 + 1970*xs + 48*xs^2 }-> s49 :|: s49 >= 0, s49 <= xs', xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: O(1) [0], size: O(1) [2]
  @: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  eqList: runtime: O(n^1) [78 + 156*z'], size: O(1) [2]
  lgth: runtime: O(n^1) [5 + 6*z], size: O(n^1) [z]
  monus[Ite]: runtime: O(n^2) [958*z'' + 12*z''^2], size: O(n^1) [z']
  monus: runtime: O(n^2) [1449 + 1970*z' + 48*z'^2], size: O(n^1) [z]

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

(61) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 2 + xs }-> 1 + x + s'' :|: s'' >= 0, s'' <= xs + z', z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s16 :|: s13 >= 0, s13 <= 2, s14 >= 0, s14 <= 2, s15 >= 0, s15 <= 2, s16 >= 0, s16 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s20 :|: s17 >= 0, s17 <= 2, s18 >= 0, s18 <= 2, s19 >= 0, s19 <= 2, s20 >= 0, s20 <= 2, z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s24 :|: s21 >= 0, s21 <= 2, s22 >= 0, s22 <= 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 159 + 156*y3 + 156*ys3 }-> s28 :|: s25 >= 0, s25 <= 2, s26 >= 0, s26 <= 2, s27 >= 0, s27 <= 2, s28 >= 0, s28 <= 2, xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 159 + 156*y5 + 156*ys5 }-> s32 :|: s29 >= 0, s29 <= 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 2, s32 >= 0, s32 <= 2, y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 159 + 156*y7 + 156*ys7 }-> s36 :|: s33 >= 0, s33 <= 2, s34 >= 0, s34 <= 2, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= 2, z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 315 + 156*y' + 156*y1 + 156*ys' + 156*ys1 }-> s8 :|: s2 >= 0, s2 <= 2, s3 >= 0, s3 <= 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, s8 >= 0, s8 <= 2, y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 158 + 156*x + 156*xs }-> gcd[Ite](s12, 1 + x' + xs', 1 + x + xs) :|: s10 >= 0, s10 <= 2, s11 >= 0, s11 <= 2, s12 >= 0, s12 <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 240 + 964*z'' + 12*z''^2 }-> gcd(s51, z'') :|: s51 >= 0, s51 <= z', s45 >= 0, s45 <= z'', s46 >= 0, s46 <= 2, z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 240 + 964*z' + 12*z'^2 }-> gcd(z', s50) :|: s50 >= 0, s50 <= z'', s43 >= 0, s43 <= z', s44 >= 0, s44 <= 2, z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 1 + 0 + 0 + 0, z - 1 >= 0
   lgth(z) -{ 11 + 6*xs'' }-> s39 :|: s37 >= 0, s37 <= xs'', s38 >= 0, s38 <= 1 + 0 + 0 + s37, s39 >= 0, s39 <= 1 + 0 + 0 + s38, z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 1213 + 982*x11 + 24*x11*xs11 + 12*x11^2 + 988*xs11 + 12*xs11^2 }-> s47 :|: s47 >= 0, s47 <= z, s40 >= 0, s40 <= xs11, s41 >= 0, s41 <= 1 + 0 + 0 + s40, s42 >= 0, s42 <= 2, z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 236 }-> s48 :|: s48 >= 0, s48 <= z, s9 >= 0, s9 <= 2, z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 1449 + 1970*xs + 48*xs^2 }-> s49 :|: s49 >= 0, s49 <= xs', xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: O(1) [0], size: O(1) [2]
  @: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  eqList: runtime: O(n^1) [78 + 156*z'], size: O(1) [2]
  lgth: runtime: O(n^1) [5 + 6*z], size: O(n^1) [z]
  monus[Ite]: runtime: O(n^2) [958*z'' + 12*z''^2], size: O(n^1) [z']
  monus: runtime: O(n^2) [1449 + 1970*z' + 48*z'^2], size: O(n^1) [z]
  gcd: runtime: ?, size: O(n^1) [z]
  gcd[Ite]: runtime: ?, size: O(n^1) [z']
  gcd[False][Ite]: runtime: ?, size: O(n^1) [z']

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

(63) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   @(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   @(z, z') -{ 2 + xs }-> 1 + x + s'' :|: s'' >= 0, s'' <= xs + z', z = 1 + x + xs, xs >= 0, z' >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s16 :|: s13 >= 0, s13 <= 2, s14 >= 0, s14 <= 2, s15 >= 0, s15 <= 2, s16 >= 0, s16 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, x4 >= 0, ys' >= 0, y' >= 0, xs4 >= 0, xs1 >= 0, z = 1 + (1 + x1 + xs1) + (1 + x4 + xs4)
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s20 :|: s17 >= 0, s17 <= 2, s18 >= 0, s18 <= 2, s19 >= 0, s19 <= 2, s20 >= 0, s20 <= 2, z' = 1 + (1 + y' + ys') + (1 + y2 + ys2), x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0, y2 >= 0, ys2 >= 0
   eqList(z, z') -{ 159 + 156*y' + 156*ys' }-> s24 :|: s21 >= 0, s21 <= 2, s22 >= 0, s22 <= 2, s23 >= 0, s23 <= 2, s24 >= 0, s24 <= 2, z' = 1 + (1 + y' + ys') + 0, x1 >= 0, z = 1 + (1 + x1 + xs1) + 0, ys' >= 0, y' >= 0, xs1 >= 0
   eqList(z, z') -{ 159 + 156*y3 + 156*ys3 }-> s28 :|: s25 >= 0, s25 <= 2, s26 >= 0, s26 <= 2, s27 >= 0, s27 <= 2, s28 >= 0, s28 <= 2, xs2 >= 0, x5 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x5 + xs5), y3 >= 0, z' = 1 + 0 + (1 + y3 + ys3), ys3 >= 0, xs5 >= 0, x2 >= 0
   eqList(z, z') -{ 159 + 156*y5 + 156*ys5 }-> s32 :|: s29 >= 0, s29 <= 2, s30 >= 0, s30 <= 2, s31 >= 0, s31 <= 2, s32 >= 0, s32 <= 2, y5 >= 0, ys5 >= 0, z = 1 + 0 + (1 + x7 + xs7), x7 >= 0, xs7 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y5 + ys5)
   eqList(z, z') -{ 159 + 156*y7 + 156*ys7 }-> s36 :|: s33 >= 0, s33 <= 2, s34 >= 0, s34 <= 2, s35 >= 0, s35 <= 2, s36 >= 0, s36 <= 2, z' = 1 + 0 + (1 + y7 + ys7), z = 1 + 0 + (1 + x9 + xs9), y7 >= 0, ys7 >= 0, xs9 >= 0, x9 >= 0
   eqList(z, z') -{ 315 + 156*y' + 156*y1 + 156*ys' + 156*ys1 }-> s8 :|: s2 >= 0, s2 <= 2, s3 >= 0, s3 <= 2, s4 >= 0, s4 <= 2, s5 >= 0, s5 <= 2, s6 >= 0, s6 <= 2, s7 >= 0, s7 <= 2, s8 >= 0, s8 <= 2, y1 >= 0, ys1 >= 0, x1 >= 0, ys' >= 0, z = 1 + (1 + x1 + xs1) + (1 + x3 + xs3), y' >= 0, xs1 >= 0, z' = 1 + (1 + y' + ys') + (1 + y1 + ys1), x3 >= 0, xs3 >= 0
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 3 }-> 2 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, 2 = 2
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 3 }-> 1 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 1 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), 2 = 2, 1 = 1
   eqList(z, z') -{ 3 }-> 0 :|: xs6 >= 0, z = 1 + (1 + x2 + xs2) + (1 + x6 + xs6), xs2 >= 0, z' = 1 + 0 + 0, x6 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z = 1 + (1 + x2 + xs2) + 0, z' = 1 + 0 + (1 + y4 + ys4), ys4 >= 0, y4 >= 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: xs2 >= 0, z' = 1 + 0 + 0, z = 1 + (1 + x2 + xs2) + 0, x2 >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: x8 >= 0, z' = 1 + (1 + y'' + ys'') + 0, z = 1 + 0 + (1 + x8 + xs8), y'' >= 0, xs8 >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y6 >= 0, ys6 >= 0, y'' >= 0, ys'' >= 0, z' = 1 + (1 + y'' + ys'') + (1 + y6 + ys6), v0 >= 0, v1 >= 0, 1 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + (1 + y'' + ys'') + 0, y'' >= 0, ys'' >= 0, v0 >= 0, v1 >= 0, 1 = v0, 2 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z' = 1 + 0 + 0, x10 >= 0, xs10 >= 0, z = 1 + 0 + (1 + x10 + xs10), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, y8 >= 0, ys8 >= 0, z' = 1 + 0 + (1 + y8 + ys8), v0 >= 0, v1 >= 0, 2 = v0, 1 = v1
   eqList(z, z') -{ 3 }-> 0 :|: z = 1 + 0 + 0, z' = 1 + 0 + 0, v0 >= 0, v1 >= 0, 2 = v0, 2 = v1
   gcd(z, z') -{ 158 + 156*x + 156*xs }-> gcd[Ite](s12, 1 + x' + xs', 1 + x + xs) :|: s10 >= 0, s10 <= 2, s11 >= 0, s11 <= 2, s12 >= 0, s12 <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd[False][Ite](z, z', z'') -{ 240 + 964*z'' + 12*z''^2 }-> gcd(s51, z'') :|: s51 >= 0, s51 <= z', s45 >= 0, s45 <= z'', s46 >= 0, s46 <= 2, z = 2, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 240 + 964*z' + 12*z'^2 }-> gcd(z', s50) :|: s50 >= 0, s50 <= z'', s43 >= 0, s43 <= z', s44 >= 0, s44 <= 2, z = 1, z' >= 0, z'' >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> z' :|: z = 2, z' >= 0, z'' >= 0
   gcd[Ite](z, z', z'') -{ 2 + xs13 }-> gcd[False][Ite](s', 1 + x''' + xs''', 1 + x13 + xs13) :|: s' >= 0, s' <= 2, xs13 >= 0, x13 >= 0, z = 1, z'' = 1 + x13 + xs13, xs''' >= 0, z' = 1 + x''' + xs''', x''' >= 0
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](2, 1 + x12 + xs12, 0) :|: z'' = 0, z = 1, x12 >= 0, xs12 >= 0, z' = 1 + x12 + xs12
   gcd[Ite](z, z', z'') -{ 1 }-> gcd[False][Ite](1, 0, z'') :|: z = 1, z'' >= 0, z' = 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   goal(z, z') -{ 1 }-> gcd(z, z') :|: z >= 0, z' >= 0
   gt0(z, z') -{ 2 + xs }-> s :|: s >= 0, s <= 2, xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 0
   lgth(z) -{ 4 }-> s1 :|: s1 >= 0, s1 <= 1 + 0 + 0 + 0, z - 1 >= 0
   lgth(z) -{ 11 + 6*xs'' }-> s39 :|: s37 >= 0, s37 <= xs'', s38 >= 0, s38 <= 1 + 0 + 0 + s37, s39 >= 0, s39 <= 1 + 0 + 0 + s38, z = 1 + x + (1 + x'' + xs''), x >= 0, xs'' >= 0, x'' >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   monus(z, z') -{ 1213 + 982*x11 + 24*x11*xs11 + 12*x11^2 + 988*xs11 + 12*xs11^2 }-> s47 :|: s47 >= 0, s47 <= z, s40 >= 0, s40 <= xs11, s41 >= 0, s41 <= 1 + 0 + 0 + s40, s42 >= 0, s42 <= 2, z' = 1 + x11 + xs11, z >= 0, xs11 >= 0, x11 >= 0
   monus(z, z') -{ 236 }-> s48 :|: s48 >= 0, s48 <= z, s9 >= 0, s9 <= 2, z >= 0, z' = 0
   monus[Ite](z, z', z'') -{ 1449 + 1970*xs + 48*xs^2 }-> s49 :|: s49 >= 0, s49 <= xs', xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, x >= 0, z'' >= 0
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0

Function symbols to be analyzed: {gcd,gcd[Ite],gcd[False][Ite]}, {goal}
Previous analysis results are:
  gt0: runtime: O(n^1) [1 + z'], size: O(1) [2]
  and: runtime: O(1) [0], size: O(1) [2]
  @: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  eqList: runtime: O(n^1) [78 + 156*z'], size: O(1) [2]
  lgth: runtime: O(n^1) [5 + 6*z], size: O(n^1) [z]
  monus[Ite]: runtime: O(n^2) [958*z'' + 12*z''^2], size: O(n^1) [z']
  monus: runtime: O(n^2) [1449 + 1970*z' + 48*z'^2], size: O(n^1) [z]
  gcd: runtime: INF, size: O(n^1) [z]
  gcd[Ite]: runtime: ?, size: O(n^1) [z']
  gcd[False][Ite]: runtime: ?, size: O(n^1) [z']

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

(65) 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:

   and(v0, v1) -> null_and [0]
   monus[Ite](v0, v1, v2) -> null_monus[Ite] [0]
   gcd[Ite](v0, v1, v2) -> null_gcd[Ite] [0]
   gcd[False][Ite](v0, v1, v2) -> null_gcd[False][Ite] [0]
   @(v0, v1) -> null_@ [0]
   gt0(v0, v1) -> null_gt0 [0]
   gcd(v0, v1) -> null_gcd [0]
   lgth(v0) -> null_lgth [0]
   eqList(v0, v1) -> null_eqList [0]

And the following fresh constants:    null_and, null_monus[Ite], null_gcd[Ite], null_gcd[False][Ite], null_@, null_gt0, null_gcd, null_lgth, null_eqList

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

(66)
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:

   @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) [1]
   @(Nil, ys) -> ys [1]
   gt0(Cons(x, xs), Nil) -> True [1]
   gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) [1]
   gcd(Nil, Nil) -> Nil [1]
   gcd(Nil, Cons(x, xs)) -> Nil [1]
   gcd(Cons(x, xs), Nil) -> Nil [1]
   gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) [1]
   lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) [1]
   eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) [1]
   eqList(Cons(x, xs), Nil) -> False [1]
   eqList(Nil, Cons(y, ys)) -> False [1]
   eqList(Nil, Nil) -> True [1]
   lgth(Nil) -> Nil [1]
   gt0(Nil, y) -> False [1]
   monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) [1]
   goal(x, y) -> gcd(x, y) [1]
   and(False, False) -> False [0]
   and(True, False) -> False [0]
   and(False, True) -> False [0]
   and(True, True) -> True [0]
   monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) [0]
   monus[Ite](True, Cons(x, xs), y) -> xs [0]
   gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) [0]
   gcd[Ite](True, x, y) -> x [0]
   gcd[False][Ite](False, x, y) -> gcd(x, monus(y, x)) [0]
   gcd[False][Ite](True, x, y) -> gcd(monus(x, y), y) [0]
   and(v0, v1) -> null_and [0]
   monus[Ite](v0, v1, v2) -> null_monus[Ite] [0]
   gcd[Ite](v0, v1, v2) -> null_gcd[Ite] [0]
   gcd[False][Ite](v0, v1, v2) -> null_gcd[False][Ite] [0]
   @(v0, v1) -> null_@ [0]
   gt0(v0, v1) -> null_gt0 [0]
   gcd(v0, v1) -> null_gcd [0]
   lgth(v0) -> null_lgth [0]
   eqList(v0, v1) -> null_eqList [0]

The TRS has the following type information:
@ :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth
Cons :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth
Nil :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth
gt0 :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> True:False:null_and:null_gt0:null_eqList
True :: True:False:null_and:null_gt0:null_eqList
gcd :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth
gcd[Ite] :: True:False:null_and:null_gt0:null_eqList -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth
eqList :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> True:False:null_and:null_gt0:null_eqList
lgth :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth
and :: True:False:null_and:null_gt0:null_eqList -> True:False:null_and:null_gt0:null_eqList -> True:False:null_and:null_gt0:null_eqList
False :: True:False:null_and:null_gt0:null_eqList
monus :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth
monus[Ite] :: True:False:null_and:null_gt0:null_eqList -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth
goal :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth
gcd[False][Ite] :: True:False:null_and:null_gt0:null_eqList -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth
null_and :: True:False:null_and:null_gt0:null_eqList
null_monus[Ite] :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth
null_gcd[Ite] :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth
null_gcd[False][Ite] :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth
null_@ :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth
null_gt0 :: True:False:null_and:null_gt0:null_eqList
null_gcd :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth
null_lgth :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth
null_eqList :: True:False:null_and:null_gt0:null_eqList

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

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

   Nil => 0
   True => 2
   False => 1
   null_and => 0
   null_monus[Ite] => 0
   null_gcd[Ite] => 0
   null_gcd[False][Ite] => 0
   null_@ => 0
   null_gt0 => 0
   null_gcd => 0
   null_lgth => 0
   null_eqList => 0

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

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

   @(z, z') -{ 1 }-> ys :|: z' = ys, ys >= 0, z = 0
   @(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   @(z, z') -{ 1 }-> 1 + x + @(xs, ys) :|: z = 1 + x + xs, xs >= 0, z' = ys, ys >= 0, x >= 0
   and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2
   and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1
   and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1
   and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   eqList(z, z') -{ 1 }-> and(eqList(x, y), eqList(xs, ys)) :|: z = 1 + x + xs, xs >= 0, ys >= 0, x >= 0, y >= 0, z' = 1 + y + ys
   eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys
   eqList(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   gcd(z, z') -{ 1 }-> gcd[Ite](eqList(1 + x' + xs', 1 + x + xs), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0
   gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0
   gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gcd(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   gcd[False][Ite](z, z', z'') -{ 0 }-> gcd(x, monus(y, x)) :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> gcd(monus(x, y), y) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0
   gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> x :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> gcd[False][Ite](gt0(x, y), x, y) :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0
   gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   goal(z, z') -{ 1 }-> gcd(x, y) :|: x >= 0, y >= 0, z = x, z' = y
   gt0(z, z') -{ 1 }-> gt0(xs', xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs'
   gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0
   gt0(z, z') -{ 1 }-> 1 :|: y >= 0, z = 0, z' = y
   gt0(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   lgth(z) -{ 1 }-> @(1 + 0 + 0, lgth(xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0
   lgth(z) -{ 1 }-> 0 :|: z = 0
   lgth(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   monus(z, z') -{ 1 }-> monus[Ite](eqList(lgth(y), 1 + 0 + 0), x, y) :|: x >= 0, y >= 0, z = x, z' = y
   monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, z'' = y, x >= 0, y >= 0
   monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs
   monus[Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0

Only complete derivations are relevant for the runtime complexity.

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

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   gcd[Ite](False, z0, z1) -> gcd[False][Ite](gt0(z0, z1), z0, z1)
   gcd[Ite](True, z0, z1) -> z0
   gcd[False][Ite](False, z0, z1) -> gcd(z0, monus(z1, z0))
   gcd[False][Ite](True, z0, z1) -> gcd(monus(z0, z1), z1)
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   gcd(Nil, Nil) -> Nil
   gcd(Nil, Cons(z0, z1)) -> Nil
   gcd(Cons(z0, z1), Nil) -> Nil
   gcd(Cons(z0, z1), Cons(z2, z3)) -> gcd[Ite](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3))
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Nil, Nil) -> True
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   goal(z0, z1) -> gcd(z0, z1)
Tuples:
   AND(False, False) -> c
   AND(True, False) -> c1
   AND(False, True) -> c2
   AND(True, True) -> c3
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   MONUS[ITE](True, Cons(z0, z1), z2) -> c5
   GCD[ITE](False, z0, z1) -> c6(GCD[FALSE][ITE](gt0(z0, z1), z0, z1), GT0(z0, z1))
   GCD[ITE](True, z0, z1) -> c7
   GCD[FALSE][ITE](False, z0, z1) -> c8(GCD(z0, monus(z1, z0)), MONUS(z1, z0))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus(z0, z1), z1), MONUS(z0, z1))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   @'(Nil, z0) -> c11
   GT0(Cons(z0, z1), Nil) -> c12
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GT0(Nil, z0) -> c14
   GCD(Nil, Nil) -> c15
   GCD(Nil, Cons(z0, z1)) -> c16
   GCD(Cons(z0, z1), Nil) -> c17
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   LGTH(Nil) -> c20
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(AND(eqList(z0, z2), eqList(z1, z3)), EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(AND(eqList(z0, z2), eqList(z1, z3)), EQLIST(z1, z3))
   EQLIST(Cons(z0, z1), Nil) -> c23
   EQLIST(Nil, Cons(z0, z1)) -> c24
   EQLIST(Nil, Nil) -> c25
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   GOAL(z0, z1) -> c27(GCD(z0, z1))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   @'(Nil, z0) -> c11
   GT0(Cons(z0, z1), Nil) -> c12
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GT0(Nil, z0) -> c14
   GCD(Nil, Nil) -> c15
   GCD(Nil, Cons(z0, z1)) -> c16
   GCD(Cons(z0, z1), Nil) -> c17
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   LGTH(Nil) -> c20
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(AND(eqList(z0, z2), eqList(z1, z3)), EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(AND(eqList(z0, z2), eqList(z1, z3)), EQLIST(z1, z3))
   EQLIST(Cons(z0, z1), Nil) -> c23
   EQLIST(Nil, Cons(z0, z1)) -> c24
   EQLIST(Nil, Nil) -> c25
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   GOAL(z0, z1) -> c27(GCD(z0, z1))
K tuples:none
Defined Rule Symbols:   @_2, gt0_2, gcd_2, lgth_1, eqList_2, monus_2, goal_2, and_2, monus[Ite]_3, gcd[Ite]_3, gcd[False][Ite]_3

Defined Pair Symbols:   AND_2, MONUS[ITE]_3, GCD[ITE]_3, GCD[FALSE][ITE]_3, @'_2, GT0_2, GCD_2, LGTH_1, EQLIST_2, MONUS_2, GOAL_2

Compound Symbols:   c, c1, c2, c3, c4_1, c5, c6_2, c7, c8_2, c9_2, c10_1, c11, c12, c13_1, c14, c15, c16, c17, c18_2, c19_2, c20, c21_2, c22_2, c23, c24, c25, c26_3, c27_1


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

(71) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   GOAL(z0, z1) -> c27(GCD(z0, z1))
Removed 11 trailing nodes:
   EQLIST(Nil, Cons(z0, z1)) -> c24
   AND(True, True) -> c3
   AND(True, False) -> c1
   AND(False, False) -> c
   MONUS[ITE](True, Cons(z0, z1), z2) -> c5
   AND(False, True) -> c2
   LGTH(Nil) -> c20
   @'(Nil, z0) -> c11
   GCD[ITE](True, z0, z1) -> c7
   EQLIST(Nil, Nil) -> c25
   EQLIST(Cons(z0, z1), Nil) -> c23

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   gcd[Ite](False, z0, z1) -> gcd[False][Ite](gt0(z0, z1), z0, z1)
   gcd[Ite](True, z0, z1) -> z0
   gcd[False][Ite](False, z0, z1) -> gcd(z0, monus(z1, z0))
   gcd[False][Ite](True, z0, z1) -> gcd(monus(z0, z1), z1)
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   gcd(Nil, Nil) -> Nil
   gcd(Nil, Cons(z0, z1)) -> Nil
   gcd(Cons(z0, z1), Nil) -> Nil
   gcd(Cons(z0, z1), Cons(z2, z3)) -> gcd[Ite](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3))
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Nil, Nil) -> True
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   goal(z0, z1) -> gcd(z0, z1)
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   GCD[ITE](False, z0, z1) -> c6(GCD[FALSE][ITE](gt0(z0, z1), z0, z1), GT0(z0, z1))
   GCD[FALSE][ITE](False, z0, z1) -> c8(GCD(z0, monus(z1, z0)), MONUS(z1, z0))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus(z0, z1), z1), MONUS(z0, z1))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Nil) -> c12
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GT0(Nil, z0) -> c14
   GCD(Nil, Nil) -> c15
   GCD(Nil, Cons(z0, z1)) -> c16
   GCD(Cons(z0, z1), Nil) -> c17
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(AND(eqList(z0, z2), eqList(z1, z3)), EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(AND(eqList(z0, z2), eqList(z1, z3)), EQLIST(z1, z3))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Nil) -> c12
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GT0(Nil, z0) -> c14
   GCD(Nil, Nil) -> c15
   GCD(Nil, Cons(z0, z1)) -> c16
   GCD(Cons(z0, z1), Nil) -> c17
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(AND(eqList(z0, z2), eqList(z1, z3)), EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(AND(eqList(z0, z2), eqList(z1, z3)), EQLIST(z1, z3))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
K tuples:none
Defined Rule Symbols:   @_2, gt0_2, gcd_2, lgth_1, eqList_2, monus_2, goal_2, and_2, monus[Ite]_3, gcd[Ite]_3, gcd[False][Ite]_3

Defined Pair Symbols:   MONUS[ITE]_3, GCD[ITE]_3, GCD[FALSE][ITE]_3, @'_2, GT0_2, GCD_2, LGTH_1, EQLIST_2, MONUS_2

Compound Symbols:   c4_1, c6_2, c8_2, c9_2, c10_1, c12, c13_1, c14, c15, c16, c17, c18_2, c19_2, c21_2, c22_2, c26_3


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

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   gcd[Ite](False, z0, z1) -> gcd[False][Ite](gt0(z0, z1), z0, z1)
   gcd[Ite](True, z0, z1) -> z0
   gcd[False][Ite](False, z0, z1) -> gcd(z0, monus(z1, z0))
   gcd[False][Ite](True, z0, z1) -> gcd(monus(z0, z1), z1)
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   gcd(Nil, Nil) -> Nil
   gcd(Nil, Cons(z0, z1)) -> Nil
   gcd(Cons(z0, z1), Nil) -> Nil
   gcd(Cons(z0, z1), Cons(z2, z3)) -> gcd[Ite](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3))
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Nil, Nil) -> True
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   goal(z0, z1) -> gcd(z0, z1)
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   GCD[ITE](False, z0, z1) -> c6(GCD[FALSE][ITE](gt0(z0, z1), z0, z1), GT0(z0, z1))
   GCD[FALSE][ITE](False, z0, z1) -> c8(GCD(z0, monus(z1, z0)), MONUS(z1, z0))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus(z0, z1), z1), MONUS(z0, z1))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Nil) -> c12
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GT0(Nil, z0) -> c14
   GCD(Nil, Nil) -> c15
   GCD(Nil, Cons(z0, z1)) -> c16
   GCD(Cons(z0, z1), Nil) -> c17
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Nil) -> c12
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GT0(Nil, z0) -> c14
   GCD(Nil, Nil) -> c15
   GCD(Nil, Cons(z0, z1)) -> c16
   GCD(Cons(z0, z1), Nil) -> c17
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
K tuples:none
Defined Rule Symbols:   @_2, gt0_2, gcd_2, lgth_1, eqList_2, monus_2, goal_2, and_2, monus[Ite]_3, gcd[Ite]_3, gcd[False][Ite]_3

Defined Pair Symbols:   MONUS[ITE]_3, GCD[ITE]_3, GCD[FALSE][ITE]_3, @'_2, GT0_2, GCD_2, LGTH_1, MONUS_2, EQLIST_2

Compound Symbols:   c4_1, c6_2, c8_2, c9_2, c10_1, c12, c13_1, c14, c15, c16, c17, c18_2, c19_2, c26_3, c21_1, c22_1


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

(75) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   gcd[Ite](False, z0, z1) -> gcd[False][Ite](gt0(z0, z1), z0, z1)
   gcd[Ite](True, z0, z1) -> z0
   gcd[False][Ite](False, z0, z1) -> gcd(z0, monus(z1, z0))
   gcd[False][Ite](True, z0, z1) -> gcd(monus(z0, z1), z1)
   gcd(Nil, Nil) -> Nil
   gcd(Nil, Cons(z0, z1)) -> Nil
   gcd(Cons(z0, z1), Nil) -> Nil
   gcd(Cons(z0, z1), Cons(z2, z3)) -> gcd[Ite](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3))
   goal(z0, z1) -> gcd(z0, z1)

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   GCD[ITE](False, z0, z1) -> c6(GCD[FALSE][ITE](gt0(z0, z1), z0, z1), GT0(z0, z1))
   GCD[FALSE][ITE](False, z0, z1) -> c8(GCD(z0, monus(z1, z0)), MONUS(z1, z0))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus(z0, z1), z1), MONUS(z0, z1))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Nil) -> c12
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GT0(Nil, z0) -> c14
   GCD(Nil, Nil) -> c15
   GCD(Nil, Cons(z0, z1)) -> c16
   GCD(Cons(z0, z1), Nil) -> c17
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Nil) -> c12
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GT0(Nil, z0) -> c14
   GCD(Nil, Nil) -> c15
   GCD(Nil, Cons(z0, z1)) -> c16
   GCD(Cons(z0, z1), Nil) -> c17
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
K tuples:none
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, GCD[ITE]_3, GCD[FALSE][ITE]_3, @'_2, GT0_2, GCD_2, LGTH_1, MONUS_2, EQLIST_2

Compound Symbols:   c4_1, c6_2, c8_2, c9_2, c10_1, c12, c13_1, c14, c15, c16, c17, c18_2, c19_2, c26_3, c21_1, c22_1


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

(77) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   GCD(Nil, Nil) -> c15
   GCD(Nil, Cons(z0, z1)) -> c16
   GCD(Cons(z0, z1), Nil) -> c17
We considered the (Usable) Rules:none
And the Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   GCD[ITE](False, z0, z1) -> c6(GCD[FALSE][ITE](gt0(z0, z1), z0, z1), GT0(z0, z1))
   GCD[FALSE][ITE](False, z0, z1) -> c8(GCD(z0, monus(z1, z0)), MONUS(z1, z0))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus(z0, z1), z1), MONUS(z0, z1))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Nil) -> c12
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GT0(Nil, z0) -> c14
   GCD(Nil, Nil) -> c15
   GCD(Nil, Cons(z0, z1)) -> c16
   GCD(Cons(z0, z1), Nil) -> c17
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(@(x_1, x_2)) = [1] + x_1 + x_2
   POL(@'(x_1, x_2)) = 0
   POL(Cons(x_1, x_2)) = 0
   POL(EQLIST(x_1, x_2)) = 0
   POL(False) = 0
   POL(GCD(x_1, x_2)) = [1]
   POL(GCD[FALSE][ITE](x_1, x_2, x_3)) = [1]
   POL(GCD[ITE](x_1, x_2, x_3)) = [1]
   POL(GT0(x_1, x_2)) = 0
   POL(LGTH(x_1)) = 0
   POL(MONUS(x_1, x_2)) = 0
   POL(MONUS[ITE](x_1, x_2, x_3)) = 0
   POL(Nil) = 0
   POL(True) = 0
   POL(and(x_1, x_2)) = [1]
   POL(c10(x_1)) = x_1
   POL(c12) = 0
   POL(c13(x_1)) = x_1
   POL(c14) = 0
   POL(c15) = 0
   POL(c16) = 0
   POL(c17) = 0
   POL(c18(x_1, x_2)) = x_1 + x_2
   POL(c19(x_1, x_2)) = x_1 + x_2
   POL(c21(x_1)) = x_1
   POL(c22(x_1)) = x_1
   POL(c26(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c4(x_1)) = x_1
   POL(c6(x_1, x_2)) = x_1 + x_2
   POL(c8(x_1, x_2)) = x_1 + x_2
   POL(c9(x_1, x_2)) = x_1 + x_2
   POL(eqList(x_1, x_2)) = 0
   POL(gt0(x_1, x_2)) = [1]
   POL(lgth(x_1)) = x_1
   POL(monus(x_1, x_2)) = [1] + x_1 + x_2
   POL(monus[Ite](x_1, x_2, x_3)) = [1] + x_2 + x_3

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   GCD[ITE](False, z0, z1) -> c6(GCD[FALSE][ITE](gt0(z0, z1), z0, z1), GT0(z0, z1))
   GCD[FALSE][ITE](False, z0, z1) -> c8(GCD(z0, monus(z1, z0)), MONUS(z1, z0))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus(z0, z1), z1), MONUS(z0, z1))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Nil) -> c12
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GT0(Nil, z0) -> c14
   GCD(Nil, Nil) -> c15
   GCD(Nil, Cons(z0, z1)) -> c16
   GCD(Cons(z0, z1), Nil) -> c17
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Nil) -> c12
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GT0(Nil, z0) -> c14
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
K tuples:
   GCD(Nil, Nil) -> c15
   GCD(Nil, Cons(z0, z1)) -> c16
   GCD(Cons(z0, z1), Nil) -> c17
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, GCD[ITE]_3, GCD[FALSE][ITE]_3, @'_2, GT0_2, GCD_2, LGTH_1, MONUS_2, EQLIST_2

Compound Symbols:   c4_1, c6_2, c8_2, c9_2, c10_1, c12, c13_1, c14, c15, c16, c17, c18_2, c19_2, c26_3, c21_1, c22_1


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace GCD[ITE](False, z0, z1) -> c6(GCD[FALSE][ITE](gt0(z0, z1), z0, z1), GT0(z0, z1)) by 
   GCD[ITE](False, Cons(z0, z1), Nil) -> c6(GCD[FALSE][ITE](True, Cons(z0, z1), Nil), GT0(Cons(z0, z1), Nil))
   GCD[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(z0, z1), Cons(z2, z3)), GT0(Cons(z0, z1), Cons(z2, z3)))
   GCD[ITE](False, Nil, z0) -> c6(GCD[FALSE][ITE](False, Nil, z0), GT0(Nil, z0))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   GCD[FALSE][ITE](False, z0, z1) -> c8(GCD(z0, monus(z1, z0)), MONUS(z1, z0))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus(z0, z1), z1), MONUS(z0, z1))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Nil) -> c12
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GT0(Nil, z0) -> c14
   GCD(Nil, Nil) -> c15
   GCD(Nil, Cons(z0, z1)) -> c16
   GCD(Cons(z0, z1), Nil) -> c17
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(z0, z1), Nil) -> c6(GCD[FALSE][ITE](True, Cons(z0, z1), Nil), GT0(Cons(z0, z1), Nil))
   GCD[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(z0, z1), Cons(z2, z3)), GT0(Cons(z0, z1), Cons(z2, z3)))
   GCD[ITE](False, Nil, z0) -> c6(GCD[FALSE][ITE](False, Nil, z0), GT0(Nil, z0))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Nil) -> c12
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GT0(Nil, z0) -> c14
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
K tuples:
   GCD(Nil, Nil) -> c15
   GCD(Nil, Cons(z0, z1)) -> c16
   GCD(Cons(z0, z1), Nil) -> c17
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, GCD[FALSE][ITE]_3, @'_2, GT0_2, GCD_2, LGTH_1, MONUS_2, EQLIST_2, GCD[ITE]_3

Compound Symbols:   c4_1, c8_2, c9_2, c10_1, c12, c13_1, c14, c15, c16, c17, c18_2, c19_2, c26_3, c21_1, c22_1, c6_2


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

(81) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 2 leading nodes:
   GCD[ITE](False, Cons(z0, z1), Nil) -> c6(GCD[FALSE][ITE](True, Cons(z0, z1), Nil), GT0(Cons(z0, z1), Nil))
   GCD[ITE](False, Nil, z0) -> c6(GCD[FALSE][ITE](False, Nil, z0), GT0(Nil, z0))
Removed 3 trailing nodes:
   GCD(Cons(z0, z1), Nil) -> c17
   GCD(Nil, Cons(z0, z1)) -> c16
   GCD(Nil, Nil) -> c15

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   GCD[FALSE][ITE](False, z0, z1) -> c8(GCD(z0, monus(z1, z0)), MONUS(z1, z0))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus(z0, z1), z1), MONUS(z0, z1))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Nil) -> c12
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GT0(Nil, z0) -> c14
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(z0, z1), Cons(z2, z3)), GT0(Cons(z0, z1), Cons(z2, z3)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Nil) -> c12
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GT0(Nil, z0) -> c14
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
K tuples:none
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, GCD[FALSE][ITE]_3, @'_2, GT0_2, GCD_2, LGTH_1, MONUS_2, EQLIST_2, GCD[ITE]_3

Compound Symbols:   c4_1, c8_2, c9_2, c10_1, c12, c13_1, c14, c18_2, c19_2, c26_3, c21_1, c22_1, c6_2


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

(83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   GT0(Cons(z0, z1), Nil) -> c12
   GT0(Nil, z0) -> c14

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   GCD[FALSE][ITE](False, z0, z1) -> c8(GCD(z0, monus(z1, z0)), MONUS(z1, z0))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus(z0, z1), z1), MONUS(z0, z1))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(z0, z1), Cons(z2, z3)), GT0(Cons(z0, z1), Cons(z2, z3)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
K tuples:none
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, GCD[FALSE][ITE]_3, @'_2, GT0_2, GCD_2, LGTH_1, MONUS_2, EQLIST_2, GCD[ITE]_3

Compound Symbols:   c4_1, c8_2, c9_2, c10_1, c13_1, c18_2, c19_2, c26_3, c21_1, c22_1, c6_2


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

(85) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace GCD[FALSE][ITE](False, z0, z1) -> c8(GCD(z0, monus(z1, z0)), MONUS(z1, z0)) by 
   GCD[FALSE][ITE](False, z1, z0) -> c8(GCD(z1, monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)), MONUS(z0, z1))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus(z0, z1), z1), MONUS(z0, z1))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(z0, z1), Cons(z2, z3)), GT0(Cons(z0, z1), Cons(z2, z3)))
   GCD[FALSE][ITE](False, z1, z0) -> c8(GCD(z1, monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)), MONUS(z0, z1))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
K tuples:none
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, GCD[FALSE][ITE]_3, @'_2, GT0_2, GCD_2, LGTH_1, MONUS_2, EQLIST_2, GCD[ITE]_3

Compound Symbols:   c4_1, c9_2, c10_1, c13_1, c18_2, c19_2, c26_3, c21_1, c22_1, c6_2, c8_2


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus(z0, z1), z1), MONUS(z0, z1)) by 
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), z1), MONUS(z0, z1))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(z0, z1), Cons(z2, z3)), GT0(Cons(z0, z1), Cons(z2, z3)))
   GCD[FALSE][ITE](False, z1, z0) -> c8(GCD(z1, monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)), MONUS(z0, z1))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), z1), MONUS(z0, z1))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
K tuples:none
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, GCD_2, LGTH_1, MONUS_2, EQLIST_2, GCD[ITE]_3, GCD[FALSE][ITE]_3

Compound Symbols:   c4_1, c10_1, c13_1, c18_2, c19_2, c26_3, c21_1, c22_1, c6_2, c8_2, c9_2


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

(89) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](eqList(Cons(z0, z1), Cons(z2, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3))) by 
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(z0, z1), Cons(z2, z3)), GT0(Cons(z0, z1), Cons(z2, z3)))
   GCD[FALSE][ITE](False, z1, z0) -> c8(GCD(z1, monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)), MONUS(z0, z1))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), z1), MONUS(z0, z1))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
K tuples:none
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, MONUS_2, EQLIST_2, GCD[ITE]_3, GCD[FALSE][ITE]_3, GCD_2

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c26_3, c21_1, c22_1, c6_2, c8_2, c9_2, c18_2


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MONUS(z0, z1) -> c26(MONUS[ITE](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), EQLIST(lgth(z1), Cons(Nil, Nil)), LGTH(z1)) by 
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(MONUS[ITE](eqList(Nil, Cons(Nil, Nil)), x0, Nil), EQLIST(lgth(Nil), Cons(Nil, Nil)), LGTH(Nil))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(z0, z1), Cons(z2, z3)), GT0(Cons(z0, z1), Cons(z2, z3)))
   GCD[FALSE][ITE](False, z1, z0) -> c8(GCD(z1, monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)), MONUS(z0, z1))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), z1), MONUS(z0, z1))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(MONUS[ITE](eqList(Nil, Cons(Nil, Nil)), x0, Nil), EQLIST(lgth(Nil), Cons(Nil, Nil)), LGTH(Nil))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(MONUS[ITE](eqList(Nil, Cons(Nil, Nil)), x0, Nil), EQLIST(lgth(Nil), Cons(Nil, Nil)), LGTH(Nil))
K tuples:none
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, EQLIST_2, GCD[ITE]_3, GCD[FALSE][ITE]_3, GCD_2, MONUS_2

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c21_1, c22_1, c6_2, c8_2, c9_2, c18_2, c26_3


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

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(z0, z1), Cons(z2, z3)), GT0(Cons(z0, z1), Cons(z2, z3)))
   GCD[FALSE][ITE](False, z1, z0) -> c8(GCD(z1, monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)), MONUS(z0, z1))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), z1), MONUS(z0, z1))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
K tuples:none
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, EQLIST_2, GCD[ITE]_3, GCD[FALSE][ITE]_3, GCD_2, MONUS_2

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c21_1, c22_1, c6_2, c8_2, c9_2, c18_2, c26_3, c26_1


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

(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace GCD[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(z0, z1), Cons(z2, z3)), GT0(Cons(z0, z1), Cons(z2, z3))) by 
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[FALSE][ITE](False, z1, z0) -> c8(GCD(z1, monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)), MONUS(z0, z1))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), z1), MONUS(z0, z1))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
K tuples:none
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, EQLIST_2, GCD[FALSE][ITE]_3, GCD_2, MONUS_2, GCD[ITE]_3

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c21_1, c22_1, c8_2, c9_2, c18_2, c26_3, c26_1, c6_2, c6_1


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

(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace GCD[FALSE][ITE](False, z1, z0) -> c8(GCD(z1, monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)), MONUS(z0, z1)) by 
   GCD[FALSE][ITE](False, Cons(z0, z1), x1) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x1, Cons(z0, z1))), MONUS(x1, Cons(z0, z1)))
   GCD[FALSE][ITE](False, Nil, x1) -> c8(GCD(Nil, monus[Ite](eqList(Nil, Cons(Nil, Nil)), x1, Nil)), MONUS(x1, Nil))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), z1), MONUS(z0, z1))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](False, Cons(z0, z1), x1) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x1, Cons(z0, z1))), MONUS(x1, Cons(z0, z1)))
   GCD[FALSE][ITE](False, Nil, x1) -> c8(GCD(Nil, monus[Ite](eqList(Nil, Cons(Nil, Nil)), x1, Nil)), MONUS(x1, Nil))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
K tuples:none
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, EQLIST_2, GCD[FALSE][ITE]_3, GCD_2, MONUS_2, GCD[ITE]_3

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c21_1, c22_1, c9_2, c18_2, c26_3, c26_1, c6_2, c6_1, c8_2


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

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), z1), MONUS(z0, z1))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](False, Cons(z0, z1), x1) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x1, Cons(z0, z1))), MONUS(x1, Cons(z0, z1)))
   GCD[FALSE][ITE](False, Nil, x1) -> c8(MONUS(x1, Nil))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
K tuples:none
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, EQLIST_2, GCD[FALSE][ITE]_3, GCD_2, MONUS_2, GCD[ITE]_3

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c21_1, c22_1, c9_2, c18_2, c26_3, c26_1, c6_2, c6_1, c8_2, c8_1


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

(101) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   GCD[FALSE][ITE](False, Nil, x1) -> c8(MONUS(x1, Nil))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), z1), MONUS(z0, z1))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](False, Cons(z0, z1), x1) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x1, Cons(z0, z1))), MONUS(x1, Cons(z0, z1)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
K tuples:none
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, EQLIST_2, GCD[FALSE][ITE]_3, GCD_2, MONUS_2, GCD[ITE]_3

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c21_1, c22_1, c9_2, c18_2, c26_3, c26_1, c6_2, c6_1, c8_2


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

(103) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace GCD[FALSE][ITE](True, z0, z1) -> c9(GCD(monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1), z1), MONUS(z0, z1)) by 
   GCD[FALSE][ITE](True, x0, Cons(z0, z1)) -> c9(GCD(monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), Cons(z0, z1)), MONUS(x0, Cons(z0, z1)))
   GCD[FALSE][ITE](True, x0, Nil) -> c9(GCD(monus[Ite](eqList(Nil, Cons(Nil, Nil)), x0, Nil), Nil), MONUS(x0, Nil))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](False, Cons(z0, z1), x1) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x1, Cons(z0, z1))), MONUS(x1, Cons(z0, z1)))
   GCD[FALSE][ITE](True, x0, Cons(z0, z1)) -> c9(GCD(monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), Cons(z0, z1)), MONUS(x0, Cons(z0, z1)))
   GCD[FALSE][ITE](True, x0, Nil) -> c9(GCD(monus[Ite](eqList(Nil, Cons(Nil, Nil)), x0, Nil), Nil), MONUS(x0, Nil))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
K tuples:none
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, EQLIST_2, GCD_2, MONUS_2, GCD[ITE]_3, GCD[FALSE][ITE]_3

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c21_1, c22_1, c18_2, c26_3, c26_1, c6_2, c6_1, c8_2, c9_2


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

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](False, Cons(z0, z1), x1) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x1, Cons(z0, z1))), MONUS(x1, Cons(z0, z1)))
   GCD[FALSE][ITE](True, x0, Cons(z0, z1)) -> c9(GCD(monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), Cons(z0, z1)), MONUS(x0, Cons(z0, z1)))
   GCD[FALSE][ITE](True, x0, Nil) -> c9(MONUS(x0, Nil))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
K tuples:none
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, EQLIST_2, GCD_2, MONUS_2, GCD[ITE]_3, GCD[FALSE][ITE]_3

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c21_1, c22_1, c18_2, c26_3, c26_1, c6_2, c6_1, c8_2, c9_2, c9_1


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

(107) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   GCD[FALSE][ITE](True, x0, Nil) -> c9(MONUS(x0, Nil))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](False, Cons(z0, z1), x1) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x1, Cons(z0, z1))), MONUS(x1, Cons(z0, z1)))
   GCD[FALSE][ITE](True, x0, Cons(z0, z1)) -> c9(GCD(monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), Cons(z0, z1)), MONUS(x0, Cons(z0, z1)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3)))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
K tuples:none
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, EQLIST_2, GCD_2, MONUS_2, GCD[ITE]_3, GCD[FALSE][ITE]_3

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c21_1, c22_1, c18_2, c26_3, c26_1, c6_2, c6_1, c8_2, c9_2


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

(109) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace GCD(Cons(z0, z1), Cons(z2, z3)) -> c18(GCD[ITE](and(eqList(z0, z2), eqList(z1, z3)), Cons(z0, z1), Cons(z2, z3)), EQLIST(Cons(z0, z1), Cons(z2, z3))) by 
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](False, Cons(z0, z1), x1) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x1, Cons(z0, z1))), MONUS(x1, Cons(z0, z1)))
   GCD[FALSE][ITE](True, x0, Cons(z0, z1)) -> c9(GCD(monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), Cons(z0, z1)), MONUS(x0, Cons(z0, z1)))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
K tuples:none
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, EQLIST_2, MONUS_2, GCD[ITE]_3, GCD[FALSE][ITE]_3, GCD_2

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c21_1, c22_1, c26_3, c26_1, c6_2, c6_1, c8_2, c9_2, c18_2, c18_1


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

(111) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
We considered the (Usable) Rules:
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   gt0(Cons(z0, z1), Nil) -> True
And the Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](False, Cons(z0, z1), x1) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x1, Cons(z0, z1))), MONUS(x1, Cons(z0, z1)))
   GCD[FALSE][ITE](True, x0, Cons(z0, z1)) -> c9(GCD(monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), Cons(z0, z1)), MONUS(x0, Cons(z0, z1)))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(@(x_1, x_2)) = [1] + x_1
   POL(@'(x_1, x_2)) = 0
   POL(Cons(x_1, x_2)) = [1]
   POL(EQLIST(x_1, x_2)) = 0
   POL(False) = [1]
   POL(GCD(x_1, x_2)) = [1]
   POL(GCD[FALSE][ITE](x_1, x_2, x_3)) = x_1
   POL(GCD[ITE](x_1, x_2, x_3)) = x_3
   POL(GT0(x_1, x_2)) = 0
   POL(LGTH(x_1)) = 0
   POL(MONUS(x_1, x_2)) = 0
   POL(MONUS[ITE](x_1, x_2, x_3)) = 0
   POL(Nil) = 0
   POL(True) = [1]
   POL(and(x_1, x_2)) = 0
   POL(c10(x_1)) = x_1
   POL(c13(x_1)) = x_1
   POL(c18(x_1)) = x_1
   POL(c18(x_1, x_2)) = x_1 + x_2
   POL(c19(x_1, x_2)) = x_1 + x_2
   POL(c21(x_1)) = x_1
   POL(c22(x_1)) = x_1
   POL(c26(x_1)) = x_1
   POL(c26(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c4(x_1)) = x_1
   POL(c6(x_1)) = x_1
   POL(c6(x_1, x_2)) = x_1 + x_2
   POL(c8(x_1, x_2)) = x_1 + x_2
   POL(c9(x_1, x_2)) = x_1 + x_2
   POL(eqList(x_1, x_2)) = 0
   POL(gt0(x_1, x_2)) = [1]
   POL(lgth(x_1)) = 0
   POL(monus(x_1, x_2)) = [1] + x_1 + x_2
   POL(monus[Ite](x_1, x_2, x_3)) = [1] + x_3

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](False, Cons(z0, z1), x1) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x1, Cons(z0, z1))), MONUS(x1, Cons(z0, z1)))
   GCD[FALSE][ITE](True, x0, Cons(z0, z1)) -> c9(GCD(monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), Cons(z0, z1)), MONUS(x0, Cons(z0, z1)))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1)))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, EQLIST_2, MONUS_2, GCD[ITE]_3, GCD[FALSE][ITE]_3, GCD_2

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c21_1, c22_1, c26_3, c26_1, c6_2, c6_1, c8_2, c9_2, c18_2, c18_1


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

(113) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MONUS(x0, Cons(z0, z1)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), EQLIST(lgth(Cons(z0, z1)), Cons(Nil, Nil)), LGTH(Cons(z0, z1))) by 
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, Nil)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)), EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)), LGTH(Cons(x1, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c26(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](False, Cons(z0, z1), x1) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x1, Cons(z0, z1))), MONUS(x1, Cons(z0, z1)))
   GCD[FALSE][ITE](True, x0, Cons(z0, z1)) -> c9(GCD(monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), Cons(z0, z1)), MONUS(x0, Cons(z0, z1)))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, Nil)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)), EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)), LGTH(Cons(x1, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c26(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, Nil)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)), EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)), LGTH(Cons(x1, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c26(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, EQLIST_2, MONUS_2, GCD[ITE]_3, GCD[FALSE][ITE]_3, GCD_2

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c21_1, c22_1, c26_1, c6_2, c6_1, c8_2, c9_2, c18_2, c18_1, c26_3, c26_2


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

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](False, Cons(z0, z1), x1) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x1, Cons(z0, z1))), MONUS(x1, Cons(z0, z1)))
   GCD[FALSE][ITE](True, x0, Cons(z0, z1)) -> c9(GCD(monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), Cons(z0, z1)), MONUS(x0, Cons(z0, z1)))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, Nil)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)), EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)), LGTH(Cons(x1, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil)))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, Nil)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)), EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)), LGTH(Cons(x1, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, EQLIST_2, MONUS_2, GCD[ITE]_3, GCD[FALSE][ITE]_3, GCD_2

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c21_1, c22_1, c26_1, c6_2, c6_1, c8_2, c9_2, c18_2, c18_1, c26_3, c_1


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

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MONUS(x0, Nil) -> c26(EQLIST(lgth(Nil), Cons(Nil, Nil))) by 
   MONUS(x0, Nil) -> c26(EQLIST(Nil, Cons(Nil, Nil)))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](False, Cons(z0, z1), x1) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x1, Cons(z0, z1))), MONUS(x1, Cons(z0, z1)))
   GCD[FALSE][ITE](True, x0, Cons(z0, z1)) -> c9(GCD(monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), Cons(z0, z1)), MONUS(x0, Cons(z0, z1)))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, Nil)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)), EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)), LGTH(Cons(x1, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26(EQLIST(Nil, Cons(Nil, Nil)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, Nil)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)), EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)), LGTH(Cons(x1, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26(EQLIST(Nil, Cons(Nil, Nil)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, EQLIST_2, GCD[ITE]_3, GCD[FALSE][ITE]_3, GCD_2, MONUS_2

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c21_1, c22_1, c6_2, c6_1, c8_2, c9_2, c18_2, c18_1, c26_3, c_1, c26_1


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

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](False, Cons(z0, z1), x1) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x1, Cons(z0, z1))), MONUS(x1, Cons(z0, z1)))
   GCD[FALSE][ITE](True, x0, Cons(z0, z1)) -> c9(GCD(monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), Cons(z0, z1)), MONUS(x0, Cons(z0, z1)))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, Nil)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)), EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)), LGTH(Cons(x1, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, Nil)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)), EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)), LGTH(Cons(x1, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, EQLIST_2, GCD[ITE]_3, GCD[FALSE][ITE]_3, GCD_2, MONUS_2

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c21_1, c22_1, c6_2, c6_1, c8_2, c9_2, c18_2, c18_1, c26_3, c_1, c26


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

(121) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace GCD[FALSE][ITE](False, Cons(z0, z1), x1) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x1, Cons(z0, z1))), MONUS(x1, Cons(z0, z1))) by GCD[FALSE][ITE](False, Cons(z0, z1), z2) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z1))), Cons(Nil, Nil)), z2, Cons(z0, z1))), MONUS(z2, Cons(z0, z1)))
----------------------------------------

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3))
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](True, x0, Cons(z0, z1)) -> c9(GCD(monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), Cons(z0, z1)), MONUS(x0, Cons(z0, z1)))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, Nil)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)), EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)), LGTH(Cons(x1, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   GCD[FALSE][ITE](False, Cons(z0, z1), z2) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z1))), Cons(Nil, Nil)), z2, Cons(z0, z1))), MONUS(z2, Cons(z0, z1)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, Nil)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)), EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)), LGTH(Cons(x1, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   MONUS[ITE]_3, @'_2, GT0_2, LGTH_1, EQLIST_2, GCD[ITE]_3, GCD[FALSE][ITE]_3, GCD_2, MONUS_2

Compound Symbols:   c4_1, c10_1, c13_1, c19_2, c21_1, c22_1, c6_2, c6_1, c9_2, c18_2, c18_1, c26_3, c_1, c26, c8_2


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

(123) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MONUS[ITE](False, Cons(z0, z1), Cons(z2, z3)) -> c4(MONUS(z1, z3)) by 
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](True, x0, Cons(z0, z1)) -> c9(GCD(monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), Cons(z0, z1)), MONUS(x0, Cons(z0, z1)))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, Nil)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)), EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)), LGTH(Cons(x1, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   GCD[FALSE][ITE](False, Cons(z0, z1), z2) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z1))), Cons(Nil, Nil)), z2, Cons(z0, z1))), MONUS(z2, Cons(z0, z1)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, Nil)) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)), EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)), LGTH(Cons(x1, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   @'_2, GT0_2, LGTH_1, EQLIST_2, GCD[ITE]_3, GCD[FALSE][ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3

Compound Symbols:   c10_1, c13_1, c19_2, c21_1, c22_1, c6_2, c6_1, c9_2, c18_2, c18_1, c26_3, c_1, c26, c8_2, c4_1


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

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0)))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](True, x0, Cons(z0, z1)) -> c9(GCD(monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), Cons(z0, z1)), MONUS(x0, Cons(z0, z1)))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   GCD[FALSE][ITE](False, Cons(z0, z1), z2) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z1))), Cons(Nil, Nil)), z2, Cons(z0, z1))), MONUS(z2, Cons(z0, z1)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   @'_2, GT0_2, LGTH_1, EQLIST_2, GCD[ITE]_3, GCD[FALSE][ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3

Compound Symbols:   c10_1, c13_1, c19_2, c21_1, c22_1, c6_2, c6_1, c9_2, c18_2, c18_1, c26_3, c_1, c26, c8_2, c4_1, c1_1


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

(127) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace GCD[ITE](False, Cons(x0, Nil), Cons(x2, z0)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x2, z0)), GT0(Cons(x0, Nil), Cons(x2, z0))) by 
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))), GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)), GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)), GT0(Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)), GT0(Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)), GT0(Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)), GT0(Cons(Nil, Nil), Cons(Nil, x1)))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD[FALSE][ITE](True, x0, Cons(z0, z1)) -> c9(GCD(monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), Cons(z0, z1)), MONUS(x0, Cons(z0, z1)))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   GCD[FALSE][ITE](False, Cons(z0, z1), z2) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z1))), Cons(Nil, Nil)), z2, Cons(z0, z1))), MONUS(z2, Cons(z0, z1)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))), GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)), GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)), GT0(Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)), GT0(Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)), GT0(Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)), GT0(Cons(Nil, Nil), Cons(Nil, x1)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   @'_2, GT0_2, LGTH_1, EQLIST_2, GCD[ITE]_3, GCD[FALSE][ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3

Compound Symbols:   c10_1, c13_1, c19_2, c21_1, c22_1, c6_2, c6_1, c9_2, c18_2, c18_1, c26_3, c_1, c26, c8_2, c4_1, c1_1


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

(129) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace GCD[FALSE][ITE](True, x0, Cons(z0, z1)) -> c9(GCD(monus[Ite](eqList(@(Cons(Nil, Nil), lgth(z1)), Cons(Nil, Nil)), x0, Cons(z0, z1)), Cons(z0, z1)), MONUS(x0, Cons(z0, z1))) by GCD[FALSE][ITE](True, z0, Cons(z1, z2)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), Cons(z1, z2)), MONUS(z0, Cons(z1, z2)))
----------------------------------------

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3)))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   GCD[FALSE][ITE](False, Cons(z0, z1), z2) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z1))), Cons(Nil, Nil)), z2, Cons(z0, z1))), MONUS(z2, Cons(z0, z1)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))), GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)), GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)), GT0(Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)), GT0(Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)), GT0(Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)), GT0(Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](True, z0, Cons(z1, z2)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), Cons(z1, z2)), MONUS(z0, Cons(z1, z2)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   @'_2, GT0_2, LGTH_1, EQLIST_2, GCD[ITE]_3, GCD_2, MONUS_2, GCD[FALSE][ITE]_3, MONUS[ITE]_3

Compound Symbols:   c10_1, c13_1, c19_2, c21_1, c22_1, c6_2, c6_1, c18_2, c18_1, c26_3, c_1, c26, c8_2, c4_1, c1_1, c9_2


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

(131) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace GCD[ITE](False, Cons(x0, x1), Cons(x2, x3)) -> c6(GT0(Cons(x0, x1), Cons(x2, x3))) by 
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   GCD[FALSE][ITE](False, Cons(z0, z1), z2) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z1))), Cons(Nil, Nil)), z2, Cons(z0, z1))), MONUS(z2, Cons(z0, z1)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))), GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)), GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)), GT0(Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)), GT0(Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)), GT0(Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)), GT0(Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](True, z0, Cons(z1, z2)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), Cons(z1, z2)), MONUS(z0, Cons(z1, z2)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   @'_2, GT0_2, LGTH_1, EQLIST_2, GCD[ITE]_3, GCD_2, MONUS_2, GCD[FALSE][ITE]_3, MONUS[ITE]_3

Compound Symbols:   c10_1, c13_1, c19_2, c21_1, c22_1, c6_2, c18_2, c18_1, c26_3, c_1, c26, c8_2, c4_1, c1_1, c9_2, c6_1


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

(133) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace MONUS(x0, Cons(x1, x2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(x2))), Cons(Nil, Nil)), x0, Cons(x1, x2)), EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)), LGTH(Cons(x1, x2))) by MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
----------------------------------------

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   GCD[FALSE][ITE](False, Cons(z0, z1), z2) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z1))), Cons(Nil, Nil)), z2, Cons(z0, z1))), MONUS(z2, Cons(z0, z1)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))), GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)), GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)), GT0(Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)), GT0(Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)), GT0(Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)), GT0(Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](True, z0, Cons(z1, z2)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), Cons(z1, z2)), MONUS(z0, Cons(z1, z2)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
S tuples:
   @'(Cons(z0, z1), z2) -> c10(@'(z1, z2))
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   @'_2, GT0_2, LGTH_1, EQLIST_2, GCD[ITE]_3, GCD_2, MONUS_2, GCD[FALSE][ITE]_3, MONUS[ITE]_3

Compound Symbols:   c10_1, c13_1, c19_2, c21_1, c22_1, c6_2, c18_2, c18_1, c26_3, c_1, c26, c8_2, c4_1, c1_1, c9_2, c6_1


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

(135) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace @'(Cons(z0, z1), z2) -> c10(@'(z1, z2)) by 
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   GCD[FALSE][ITE](False, Cons(z0, z1), z2) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z1))), Cons(Nil, Nil)), z2, Cons(z0, z1))), MONUS(z2, Cons(z0, z1)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))), GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)), GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)), GT0(Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)), GT0(Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)), GT0(Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)), GT0(Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](True, z0, Cons(z1, z2)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), Cons(z1, z2)), MONUS(z0, Cons(z1, z2)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
S tuples:
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   LGTH(Cons(z0, z1)) -> c19(@'(Cons(Nil, Nil), lgth(z1)), LGTH(z1))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GT0_2, LGTH_1, EQLIST_2, GCD[ITE]_3, GCD_2, MONUS_2, GCD[FALSE][ITE]_3, MONUS[ITE]_3, @'_2

Compound Symbols:   c13_1, c19_2, c21_1, c22_1, c6_2, c18_2, c18_1, c26_3, c_1, c26, c8_2, c4_1, c1_1, c9_2, c6_1, c10_1


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

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   GCD[FALSE][ITE](False, Cons(z0, z1), z2) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z1))), Cons(Nil, Nil)), z2, Cons(z0, z1))), MONUS(z2, Cons(z0, z1)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))), GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)), GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)), GT0(Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)), GT0(Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)), GT0(Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)), GT0(Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](True, z0, Cons(z1, z2)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), Cons(z1, z2)), MONUS(z0, Cons(z1, z2)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
S tuples:
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GT0_2, EQLIST_2, GCD[ITE]_3, GCD_2, MONUS_2, GCD[FALSE][ITE]_3, MONUS[ITE]_3, @'_2, LGTH_1

Compound Symbols:   c13_1, c21_1, c22_1, c6_2, c18_2, c18_1, c26_3, c_1, c26, c8_2, c4_1, c1_1, c9_2, c6_1, c10_1, c19_1


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

(139) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
We considered the (Usable) Rules:none
And the Tuples:
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   GCD[FALSE][ITE](False, Cons(z0, z1), z2) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z1))), Cons(Nil, Nil)), z2, Cons(z0, z1))), MONUS(z2, Cons(z0, z1)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))), GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)), GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)), GT0(Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)), GT0(Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)), GT0(Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)), GT0(Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](True, z0, Cons(z1, z2)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), Cons(z1, z2)), MONUS(z0, Cons(z1, z2)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(@(x_1, x_2)) = 0
   POL(@'(x_1, x_2)) = x_1
   POL(Cons(x_1, x_2)) = [1] + x_2
   POL(EQLIST(x_1, x_2)) = 0
   POL(False) = 0
   POL(GCD(x_1, x_2)) = 0
   POL(GCD[FALSE][ITE](x_1, x_2, x_3)) = 0
   POL(GCD[ITE](x_1, x_2, x_3)) = 0
   POL(GT0(x_1, x_2)) = 0
   POL(LGTH(x_1)) = 0
   POL(MONUS(x_1, x_2)) = 0
   POL(MONUS[ITE](x_1, x_2, x_3)) = 0
   POL(Nil) = 0
   POL(True) = 0
   POL(and(x_1, x_2)) = 0
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c10(x_1)) = x_1
   POL(c13(x_1)) = x_1
   POL(c18(x_1)) = x_1
   POL(c18(x_1, x_2)) = x_1 + x_2
   POL(c19(x_1)) = x_1
   POL(c21(x_1)) = x_1
   POL(c22(x_1)) = x_1
   POL(c26) = 0
   POL(c26(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c4(x_1)) = x_1
   POL(c6(x_1)) = x_1
   POL(c6(x_1, x_2)) = x_1 + x_2
   POL(c8(x_1, x_2)) = x_1 + x_2
   POL(c9(x_1, x_2)) = x_1 + x_2
   POL(eqList(x_1, x_2)) = 0
   POL(gt0(x_1, x_2)) = [1] + x_1 + x_2
   POL(lgth(x_1)) = 0
   POL(monus(x_1, x_2)) = [1] + x_1 + x_2
   POL(monus[Ite](x_1, x_2, x_3)) = [1] + x_3

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   GCD[FALSE][ITE](False, Cons(z0, z1), z2) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z1))), Cons(Nil, Nil)), z2, Cons(z0, z1))), MONUS(z2, Cons(z0, z1)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))), GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)), GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)), GT0(Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)), GT0(Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)), GT0(Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)), GT0(Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](True, z0, Cons(z1, z2)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), Cons(z1, z2)), MONUS(z0, Cons(z1, z2)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
S tuples:
   GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GT0_2, EQLIST_2, GCD[ITE]_3, GCD_2, MONUS_2, GCD[FALSE][ITE]_3, MONUS[ITE]_3, @'_2, LGTH_1

Compound Symbols:   c13_1, c21_1, c22_1, c6_2, c18_2, c18_1, c26_3, c_1, c26, c8_2, c4_1, c1_1, c9_2, c6_1, c10_1, c19_1


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

(141) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace GT0(Cons(z0, z1), Cons(z2, z3)) -> c13(GT0(z1, z3)) by 
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   GCD[FALSE][ITE](False, Cons(z0, z1), z2) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z1))), Cons(Nil, Nil)), z2, Cons(z0, z1))), MONUS(z2, Cons(z0, z1)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))), GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)), GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)), GT0(Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)), GT0(Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)), GT0(Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)), GT0(Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](True, z0, Cons(z1, z2)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), Cons(z1, z2)), MONUS(z0, Cons(z1, z2)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
S tuples:
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   EQLIST_2, GCD[ITE]_3, GCD_2, MONUS_2, GCD[FALSE][ITE]_3, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2

Compound Symbols:   c21_1, c22_1, c6_2, c18_2, c18_1, c26_3, c_1, c26, c8_2, c4_1, c1_1, c9_2, c6_1, c10_1, c19_1, c13_1


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

(143) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   GCD[FALSE][ITE](False, Cons(z0, z1), z2) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z1))), Cons(Nil, Nil)), z2, Cons(z0, z1))), MONUS(z2, Cons(z0, z1)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))), GT0(Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)), GT0(Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)), GT0(Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)), GT0(Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)), GT0(Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)), GT0(Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](True, z0, Cons(z1, z2)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), Cons(z1, z2)), MONUS(z0, Cons(z1, z2)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
S tuples:
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   EQLIST_2, GCD[ITE]_3, GCD_2, MONUS_2, GCD[FALSE][ITE]_3, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2

Compound Symbols:   c21_1, c22_1, c6_2, c18_2, c18_1, c26_3, c_1, c26, c8_2, c4_1, c1_1, c9_2, c6_1, c10_1, c19_1, c13_1


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

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   GCD[FALSE][ITE](False, Cons(z0, z1), z2) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z1))), Cons(Nil, Nil)), z2, Cons(z0, z1))), MONUS(z2, Cons(z0, z1)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[FALSE][ITE](True, z0, Cons(z1, z2)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), Cons(z1, z2)), MONUS(z0, Cons(z1, z2)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
S tuples:
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   EQLIST_2, GCD[ITE]_3, GCD_2, MONUS_2, GCD[FALSE][ITE]_3, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2

Compound Symbols:   c21_1, c22_1, c6_2, c18_2, c18_1, c26_3, c_1, c26, c8_2, c4_1, c1_1, c9_2, c6_1, c10_1, c19_1, c13_1


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

(147) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace GCD[FALSE][ITE](False, Cons(z0, z1), z2) -> c8(GCD(Cons(z0, z1), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z1))), Cons(Nil, Nil)), z2, Cons(z0, z1))), MONUS(z2, Cons(z0, z1))) by 
   GCD[FALSE][ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c8(GCD(Cons(x0, Cons(x1, x2)), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x1, x2)))), Cons(Nil, Nil)), Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2)))), MONUS(Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2))))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[FALSE][ITE](True, z0, Cons(z1, z2)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), Cons(z1, z2)), MONUS(z0, Cons(z1, z2)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c8(GCD(Cons(x0, Cons(x1, x2)), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x1, x2)))), Cons(Nil, Nil)), Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2)))), MONUS(Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2))))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
S tuples:
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   EQLIST_2, GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, GCD[FALSE][ITE]_3, @'_2, LGTH_1, GT0_2

Compound Symbols:   c21_1, c22_1, c6_2, c18_2, c18_1, c26_3, c_1, c26, c4_1, c1_1, c9_2, c6_1, c10_1, c19_1, c13_1, c8_2


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

(149) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace GCD[FALSE][ITE](True, z0, Cons(z1, z2)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), Cons(z1, z2)), MONUS(z0, Cons(z1, z2))) by 
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c8(GCD(Cons(x0, Cons(x1, x2)), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x1, x2)))), Cons(Nil, Nil)), Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2)))), MONUS(Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2))))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
S tuples:
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1))))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   EQLIST_2, GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3

Compound Symbols:   c21_1, c22_1, c6_2, c18_2, c18_1, c26_3, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2


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

(151) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace MONUS(x0, Cons(x1, Cons(z0, z1))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z1))), Cons(Nil, Nil)), x0, Cons(x1, Cons(z0, z1))), EQLIST(lgth(Cons(x1, Cons(z0, z1))), Cons(Nil, Nil)), LGTH(Cons(x1, Cons(z0, z1)))) by MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), EQLIST(@(Cons(Nil, Nil), lgth(Cons(z2, z3))), Cons(Nil, Nil)), LGTH(Cons(z1, Cons(z2, z3))))
----------------------------------------

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c8(GCD(Cons(x0, Cons(x1, x2)), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x1, x2)))), Cons(Nil, Nil)), Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2)))), MONUS(Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2))))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), EQLIST(@(Cons(Nil, Nil), lgth(Cons(z2, z3))), Cons(Nil, Nil)), LGTH(Cons(z1, Cons(z2, z3))))
S tuples:
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2))
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), EQLIST(@(Cons(Nil, Nil), lgth(Cons(z2, z3))), Cons(Nil, Nil)), LGTH(Cons(z1, Cons(z2, z3))))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   EQLIST_2, GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3

Compound Symbols:   c21_1, c22_1, c6_2, c18_2, c18_1, c_1, c26, c4_1, c1_1, c6_1, c26_3, c10_1, c19_1, c13_1, c8_2, c9_2


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

(153) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c21(EQLIST(z0, z2)) by 
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c8(GCD(Cons(x0, Cons(x1, x2)), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x1, x2)))), Cons(Nil, Nil)), Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2)))), MONUS(Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2))))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), EQLIST(@(Cons(Nil, Nil), lgth(Cons(z2, z3))), Cons(Nil, Nil)), LGTH(Cons(z1, Cons(z2, z3))))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
S tuples:
   EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), EQLIST(@(Cons(Nil, Nil), lgth(Cons(z2, z3))), Cons(Nil, Nil)), LGTH(Cons(z1, Cons(z2, z3))))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   EQLIST_2, GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3

Compound Symbols:   c22_1, c6_2, c18_2, c18_1, c_1, c26, c4_1, c1_1, c6_1, c26_3, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1


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

(155) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace EQLIST(Cons(z0, z1), Cons(z2, z3)) -> c22(EQLIST(z1, z3)) by 
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c8(GCD(Cons(x0, Cons(x1, x2)), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x1, x2)))), Cons(Nil, Nil)), Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2)))), MONUS(Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2))))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), EQLIST(@(Cons(Nil, Nil), lgth(Cons(z2, z3))), Cons(Nil, Nil)), LGTH(Cons(z1, Cons(z2, z3))))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(EQLIST(lgth(Cons(x1, x2)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(EQLIST(lgth(Cons(x1, Nil)), Cons(Nil, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), EQLIST(@(Cons(Nil, Nil), lgth(z2)), Cons(Nil, Nil)), LGTH(Cons(z1, z2)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), EQLIST(@(Cons(Nil, Nil), lgth(Cons(z2, z3))), Cons(Nil, Nil)), LGTH(Cons(z1, Cons(z2, z3))))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c18_1, c_1, c26, c4_1, c1_1, c6_1, c26_3, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1


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

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c8(GCD(Cons(x0, Cons(x1, x2)), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x1, x2)))), Cons(Nil, Nil)), Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2)))), MONUS(Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2))))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil)))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c18_1, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2


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

(159) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace MONUS(x0, Cons(x1, Nil)) -> c1(MONUS[ITE](eqList(@(Cons(Nil, Nil), Nil), Cons(Nil, Nil)), x0, Cons(x1, Nil))) by MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
----------------------------------------

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c8(GCD(Cons(x0, Cons(x1, x2)), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x1, x2)))), Cons(Nil, Nil)), Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2)))), MONUS(Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2))))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c18_1, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2


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

(161) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace GCD[FALSE][ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c8(GCD(Cons(x0, Cons(x1, x2)), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x1, x2)))), Cons(Nil, Nil)), Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2)))), MONUS(Cons(x3, Cons(x4, x5)), Cons(x0, Cons(x1, x2)))) by GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
----------------------------------------

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c18_1, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2


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

(163) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace GCD(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)) -> c18(GCD[ITE](and(and(eqList(z0, z2), eqList(z1, z3)), eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Cons(z2, z3), x3))) by 
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c18_1, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2


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

(165) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace GCD(Cons(Nil, x1), Cons(Cons(z0, z1), x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Nil, x1), Cons(Cons(z0, z1), x3)), EQLIST(Cons(Nil, x1), Cons(Cons(z0, z1), x3))) by 
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c18_1, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2


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

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

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c18_1, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2


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

(169) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace GCD(Cons(Cons(z0, z1), x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(False, eqList(x1, x3)), Cons(Cons(z0, z1), x1), Cons(Nil, x3)), EQLIST(Cons(Cons(z0, z1), x1), Cons(Nil, x3))) by 
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))

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

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c18_1, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2


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

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c18_1, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2


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(173) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace GCD(Cons(Nil, x1), Cons(Nil, x3)) -> c18(GCD[ITE](and(True, eqList(x1, x3)), Cons(Nil, x1), Cons(Nil, x3)), EQLIST(Cons(Nil, x1), Cons(Nil, x3))) by 
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)), EQLIST(Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)), EQLIST(Cons(Nil, z0), Cons(Nil, Nil)))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))

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

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)), EQLIST(Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)), EQLIST(Cons(Nil, z0), Cons(Nil, Nil)))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)), EQLIST(Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)), EQLIST(Cons(Nil, z0), Cons(Nil, Nil)))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c18_1, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2


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

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

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c18_1, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2


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

(177) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Cons(x2, x3)), Cons(x0, Nil))), MONUS(Cons(x1, Cons(x2, x3)), Cons(x0, Nil))) by GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
----------------------------------------

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c18_1, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2


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(179) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace GCD(Cons(x0, x1), Cons(x2, x3)) -> c18(EQLIST(Cons(x0, x1), Cons(x2, x3))) by 
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(Nil, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Nil, Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))

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

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(Nil, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Nil, Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(Nil, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Nil, Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2, c18_1


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

(181) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   GCD(Cons(Nil, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Nil, Nil), Cons(z2, z3)))

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

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2, c18_1


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

(183) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c8(GCD(Cons(x0, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x1, Nil), Cons(x0, Nil))), MONUS(Cons(x1, Nil), Cons(x0, Nil))) by GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
----------------------------------------

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2, c18_1


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

(185) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Cons(x2, x3), x4), Cons(Cons(x0, x1), Nil))) by GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
----------------------------------------

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2, c18_1


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

(187) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), x5))) by 
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), Cons(x2, x3))) -> c6(GT0(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), Cons(x2, x3))))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Nil)) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), Nil)) -> c6(GT0(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c6(GT0(Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Nil)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)))

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

(188)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), Cons(x2, x3))) -> c6(GT0(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), Cons(x2, x3))))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Nil)) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), Nil)) -> c6(GT0(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c6(GT0(Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Nil)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2, c18_1


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

(189) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing nodes:
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Nil)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), Nil)) -> c6(GT0(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Nil)) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)) -> c6(GT0(Cons(Cons(x0, x1), Nil), Cons(Cons(x2, x3), x4)))
   GCD[ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), Cons(x2, x3))) -> c6(GT0(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), Cons(x2, x3))))

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

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2, c18_1


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

(191) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Cons(x0, x1), x2), Cons(Nil, Nil))), MONUS(Cons(Cons(x0, x1), x2), Cons(Nil, Nil))) by GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(z0, z1), z2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil))), MONUS(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
----------------------------------------

(192)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(z0, z1), z2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil))), MONUS(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2, c18_1


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

(193) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c8(GCD(Cons(Cons(x0, x1), Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x2), Cons(Cons(x0, x1), Nil))), MONUS(Cons(Nil, x2), Cons(Cons(x0, x1), Nil))) by GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, z2)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z2), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Nil, z2), Cons(Cons(z0, z1), Nil)))
----------------------------------------

(194)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(z0, z1), z2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil))), MONUS(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, z2)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z2), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Nil, z2), Cons(Cons(z0, z1), Nil)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c8_2, c9_2, c21_1, c22_1, c, c1, c26_2, c18_1


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

(195) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(Nil, x0), Cons(Nil, Nil))), MONUS(Cons(Nil, x0), Cons(Nil, Nil))) by GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, z0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z0), Cons(Nil, Nil))), MONUS(Cons(Nil, z0), Cons(Nil, Nil)))
----------------------------------------

(196)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(z0, z1), z2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil))), MONUS(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, z2)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z2), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Nil, z2), Cons(Cons(z0, z1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, z0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z0), Cons(Nil, Nil))), MONUS(Cons(Nil, z0), Cons(Nil, Nil)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c9_2, c21_1, c22_1, c, c1, c26_2, c8_2, c18_1


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

(197) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), x3)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), x3))) by 
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(z1, z2), Cons(x2, x3))) -> c6(GT0(Cons(Nil, Nil), Cons(Cons(z1, z2), Cons(x2, x3))))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Nil)) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Nil)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(z1, z2), Nil)) -> c6(GT0(Cons(Nil, Nil), Cons(Cons(z1, z2), Nil)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))))
   GCD[ITE](False, Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)) -> c6(GT0(Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c6(GT0(Cons(Nil, Nil), Cons(Cons(x0, x1), x2)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), Nil)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), Nil)))

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

(198)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(z0, z1), z2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil))), MONUS(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, z2)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z2), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Nil, z2), Cons(Cons(z0, z1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, z0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z0), Cons(Nil, Nil))), MONUS(Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(z1, z2), Cons(x2, x3))) -> c6(GT0(Cons(Nil, Nil), Cons(Cons(z1, z2), Cons(x2, x3))))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Nil)) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Nil)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(z1, z2), Nil)) -> c6(GT0(Cons(Nil, Nil), Cons(Cons(z1, z2), Nil)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))))
   GCD[ITE](False, Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)) -> c6(GT0(Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c6(GT0(Cons(Nil, Nil), Cons(Cons(x0, x1), x2)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), Nil)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), Nil)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c9_2, c21_1, c22_1, c, c1, c26_2, c8_2, c18_1


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

(199) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing nodes:
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(z1, z2), Cons(x2, x3))) -> c6(GT0(Cons(Nil, Nil), Cons(Cons(z1, z2), Cons(x2, x3))))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x0, x1), x2)) -> c6(GT0(Cons(Nil, Nil), Cons(Cons(x0, x1), x2)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), Nil)) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), Nil)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(z1, z2), Nil)) -> c6(GT0(Cons(Nil, Nil), Cons(Cons(z1, z2), Nil)))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Nil)) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Nil)))

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

(200)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(z0, z1), z2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil))), MONUS(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, z2)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z2), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Nil, z2), Cons(Cons(z0, z1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, z0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z0), Cons(Nil, Nil))), MONUS(Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))))
   GCD[ITE](False, Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)) -> c6(GT0(Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c9_2, c21_1, c22_1, c, c1, c26_2, c8_2, c18_1


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

(201) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, x3)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, x3))) by 
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, Cons(x2, x3))) -> c6(GT0(Cons(Cons(z0, z1), Nil), Cons(Nil, Cons(x2, x3))))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Nil)) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, Nil)) -> c6(GT0(Cons(Cons(z0, z1), Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c6(GT0(Cons(Cons(x0, x1), Nil), Cons(Nil, x2)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, Nil)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))

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

(202)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(z0, z1), z2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil))), MONUS(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, z2)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z2), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Nil, z2), Cons(Cons(z0, z1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, z0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z0), Cons(Nil, Nil))), MONUS(Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))))
   GCD[ITE](False, Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)) -> c6(GT0(Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, Cons(x2, x3))) -> c6(GT0(Cons(Cons(z0, z1), Nil), Cons(Nil, Cons(x2, x3))))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Nil)) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, Nil)) -> c6(GT0(Cons(Cons(z0, z1), Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c6(GT0(Cons(Cons(x0, x1), Nil), Cons(Nil, x2)))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, Nil)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c9_2, c21_1, c22_1, c, c1, c26_2, c8_2, c18_1


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

(203) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing nodes:
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, Nil)) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, Nil)) -> c6(GT0(Cons(Cons(z0, z1), Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, Cons(x2, x3))) -> c6(GT0(Cons(Cons(z0, z1), Nil), Cons(Nil, Cons(x2, x3))))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x2)) -> c6(GT0(Cons(Cons(x0, x1), Nil), Cons(Nil, x2)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Nil)) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Nil)))

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

(204)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(z0, z1), z2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil))), MONUS(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, z2)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z2), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Nil, z2), Cons(Cons(z0, z1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, z0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z0), Cons(Nil, Nil))), MONUS(Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))))
   GCD[ITE](False, Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)) -> c6(GT0(Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c9_2, c21_1, c22_1, c, c1, c26_2, c8_2, c18_1


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

(205) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Cons(x4, x5)))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))), Cons(x3, Cons(x4, x5))), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5)))) by GCD[FALSE][ITE](True, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c9(GCD(monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z4, z5))), Nil)), Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))), Cons(z3, Cons(z4, z5))), MONUS(Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))))
----------------------------------------

(206)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(z0, z1), z2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil))), MONUS(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, z2)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z2), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Nil, z2), Cons(Cons(z0, z1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, z0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z0), Cons(Nil, Nil))), MONUS(Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))))
   GCD[ITE](False, Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)) -> c6(GT0(Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)))
   GCD[FALSE][ITE](True, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c9(GCD(monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z4, z5))), Nil)), Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))), Cons(z3, Cons(z4, z5))), MONUS(Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, GCD[FALSE][ITE]_3, EQLIST_2

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c9_2, c21_1, c22_1, c, c1, c26_2, c8_2, c18_1


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

(207) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace GCD[FALSE][ITE](True, Cons(x0, Cons(x1, x2)), Cons(x3, Nil)) -> c9(GCD(monus[Ite](eqList(Cons(Nil, @(Nil, lgth(Nil))), Cons(Nil, Nil)), Cons(x0, Cons(x1, x2)), Cons(x3, Nil)), Cons(x3, Nil)), MONUS(Cons(x0, Cons(x1, x2)), Cons(x3, Nil))) by GCD[FALSE][ITE](True, Cons(z0, Cons(z1, z2)), Cons(z3, Nil)) -> c9(GCD(monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z0, Cons(z1, z2)), Cons(z3, Nil)), Cons(z3, Nil)), MONUS(Cons(z0, Cons(z1, z2)), Cons(z3, Nil)))
----------------------------------------

(208)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1)))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(z0, z1), z2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil))), MONUS(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, z2)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z2), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Nil, z2), Cons(Cons(z0, z1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, z0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z0), Cons(Nil, Nil))), MONUS(Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))))
   GCD[ITE](False, Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)) -> c6(GT0(Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)))
   GCD[FALSE][ITE](True, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c9(GCD(monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z4, z5))), Nil)), Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))), Cons(z3, Cons(z4, z5))), MONUS(Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))))
   GCD[FALSE][ITE](True, Cons(z0, Cons(z1, z2)), Cons(z3, Nil)) -> c9(GCD(monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z0, Cons(z1, z2)), Cons(z3, Nil)), Cons(z3, Nil)), MONUS(Cons(z0, Cons(z1, z2)), Cons(z3, Nil)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, EQLIST_2, GCD[FALSE][ITE]_3

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c21_1, c22_1, c, c1, c26_2, c8_2, c18_1, c9_2


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(209) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace GCD[ITE](False, Cons(Nil, x0), Cons(Nil, x1)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, x1))) by 
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Nil, Cons(x4, x5))) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Nil, Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, Cons(x2, x3))) -> c6(GT0(Cons(Nil, Nil), Cons(Nil, Cons(x2, x3))))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Nil, Nil)) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, Nil)) -> c6(GT0(Cons(Nil, Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, Cons(x1, x2))) -> c6(GT0(Cons(Nil, x0), Cons(Nil, Cons(x1, x2))))
   GCD[ITE](False, Cons(Nil, Cons(x0, x1)), Cons(Nil, x2)) -> c6(GT0(Cons(Nil, Cons(x0, x1)), Cons(Nil, x2)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c6(GT0(Cons(Nil, Nil), Cons(Nil, x0)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, Nil)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, Nil)))

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

(210)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(z0, z1), z2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil))), MONUS(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, z2)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z2), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Nil, z2), Cons(Cons(z0, z1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, z0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z0), Cons(Nil, Nil))), MONUS(Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))))
   GCD[ITE](False, Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)) -> c6(GT0(Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)))
   GCD[FALSE][ITE](True, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c9(GCD(monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z4, z5))), Nil)), Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))), Cons(z3, Cons(z4, z5))), MONUS(Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))))
   GCD[FALSE][ITE](True, Cons(z0, Cons(z1, z2)), Cons(z3, Nil)) -> c9(GCD(monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z0, Cons(z1, z2)), Cons(z3, Nil)), Cons(z3, Nil)), MONUS(Cons(z0, Cons(z1, z2)), Cons(z3, Nil)))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Nil, Cons(x4, x5))) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Nil, Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, Cons(x2, x3))) -> c6(GT0(Cons(Nil, Nil), Cons(Nil, Cons(x2, x3))))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Nil, Nil)) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, Nil)) -> c6(GT0(Cons(Nil, Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, Cons(x1, x2))) -> c6(GT0(Cons(Nil, x0), Cons(Nil, Cons(x1, x2))))
   GCD[ITE](False, Cons(Nil, Cons(x0, x1)), Cons(Nil, x2)) -> c6(GT0(Cons(Nil, Cons(x0, x1)), Cons(Nil, x2)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c6(GT0(Cons(Nil, Nil), Cons(Nil, x0)))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, Nil)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, Nil)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, EQLIST_2, GCD[FALSE][ITE]_3

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c21_1, c22_1, c, c1, c26_2, c8_2, c18_1, c9_2


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

(211) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing nodes:
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Nil, Nil)) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, Cons(x2, x3))) -> c6(GT0(Cons(Nil, Nil), Cons(Nil, Cons(x2, x3))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, Nil)) -> c6(GT0(Cons(Nil, x0), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, Nil)) -> c6(GT0(Cons(Nil, Nil), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x0)) -> c6(GT0(Cons(Nil, Nil), Cons(Nil, x0)))

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

(212)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(z0, z1), z2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil))), MONUS(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, z2)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z2), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Nil, z2), Cons(Cons(z0, z1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, z0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z0), Cons(Nil, Nil))), MONUS(Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))))
   GCD[ITE](False, Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)) -> c6(GT0(Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)))
   GCD[FALSE][ITE](True, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c9(GCD(monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z4, z5))), Nil)), Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))), Cons(z3, Cons(z4, z5))), MONUS(Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))))
   GCD[FALSE][ITE](True, Cons(z0, Cons(z1, z2)), Cons(z3, Nil)) -> c9(GCD(monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z0, Cons(z1, z2)), Cons(z3, Nil)), Cons(z3, Nil)), MONUS(Cons(z0, Cons(z1, z2)), Cons(z3, Nil)))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Nil, Cons(x4, x5))) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Nil, Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, Cons(x1, x2))) -> c6(GT0(Cons(Nil, x0), Cons(Nil, Cons(x1, x2))))
   GCD[ITE](False, Cons(Nil, Cons(x0, x1)), Cons(Nil, x2)) -> c6(GT0(Cons(Nil, Cons(x0, x1)), Cons(Nil, x2)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, EQLIST_2, GCD[FALSE][ITE]_3

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c21_1, c22_1, c, c1, c26_2, c8_2, c18_1, c9_2


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

(213) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, lgth(z2))), Cons(Nil, Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2))) by MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](and(eqList(Nil, Nil), eqList(@(Nil, lgth(z2)), Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
----------------------------------------

(214)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(z0, z1), z2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil))), MONUS(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, z2)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z2), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Nil, z2), Cons(Cons(z0, z1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, z0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z0), Cons(Nil, Nil))), MONUS(Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))))
   GCD[ITE](False, Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)) -> c6(GT0(Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)))
   GCD[FALSE][ITE](True, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c9(GCD(monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z4, z5))), Nil)), Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))), Cons(z3, Cons(z4, z5))), MONUS(Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))))
   GCD[FALSE][ITE](True, Cons(z0, Cons(z1, z2)), Cons(z3, Nil)) -> c9(GCD(monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z0, Cons(z1, z2)), Cons(z3, Nil)), Cons(z3, Nil)), MONUS(Cons(z0, Cons(z1, z2)), Cons(z3, Nil)))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Nil, Cons(x4, x5))) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Nil, Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, Cons(x1, x2))) -> c6(GT0(Cons(Nil, x0), Cons(Nil, Cons(x1, x2))))
   GCD[ITE](False, Cons(Nil, Cons(x0, x1)), Cons(Nil, x2)) -> c6(GT0(Cons(Nil, Cons(x0, x1)), Cons(Nil, x2)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](and(eqList(Nil, Nil), eqList(@(Nil, lgth(z2)), Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](and(eqList(Nil, Nil), eqList(@(Nil, lgth(z2)), Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, EQLIST_2, GCD[FALSE][ITE]_3

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c21_1, c22_1, c, c1, c26_2, c8_2, c18_1, c9_2


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

(215) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(@(Cons(Nil, Nil), @(Cons(Nil, Nil), lgth(z3))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3)))) by MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, @(Cons(Nil, Nil), lgth(z3)))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
----------------------------------------

(216)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gt0(Cons(z0, z1), Nil) -> True
   gt0(Cons(z0, z1), Cons(z2, z3)) -> gt0(z1, z3)
   gt0(Nil, z0) -> False
   monus(z0, z1) -> monus[Ite](eqList(lgth(z1), Cons(Nil, Nil)), z0, z1)
   monus[Ite](False, Cons(z0, z1), Cons(z2, z3)) -> monus(z1, z3)
   monus[Ite](True, Cons(z0, z1), z2) -> z1
   eqList(Cons(z0, z1), Cons(z2, z3)) -> and(eqList(z0, z2), eqList(z1, z3))
   eqList(Nil, Cons(z0, z1)) -> False
   eqList(Cons(z0, z1), Nil) -> False
   eqList(Nil, Nil) -> True
   lgth(Cons(z0, z1)) -> @(Cons(Nil, Nil), lgth(z1))
   lgth(Nil) -> Nil
   @(Cons(z0, z1), z2) -> Cons(z0, @(z1, z2))
   @(Nil, z0) -> z0
   and(False, False) -> False
   and(True, False) -> False
   and(False, True) -> False
   and(True, True) -> True
Tuples:
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c6(GCD[FALSE][ITE](gt0(z1, z3), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), GT0(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, y2))) -> c4(MONUS(z1, Cons(y1, y2)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Cons(y2, y3)))) -> c4(MONUS(z1, Cons(y1, Cons(y2, y3))))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Cons(y1, Nil))) -> c4(MONUS(z1, Cons(y1, Nil)))
   MONUS[ITE](False, Cons(z0, z1), Cons(z2, Nil)) -> c4(MONUS(z1, Nil))
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   GCD[ITE](False, Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))) -> c6(GT0(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(x4, x5))))
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   GCD[ITE](False, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c6(GCD[FALSE][ITE](True, Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Cons(x2, x3))))
   GCD[ITE](False, Cons(x0, Nil), Cons(x1, Nil)) -> c6(GCD[FALSE][ITE](False, Cons(x0, Nil), Cons(x1, Nil)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Cons(x3, x4), x5)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(x1, x2), x3)))
   GCD[ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)) -> c6(GCD[FALSE][ITE](False, Cons(Cons(x0, x1), Nil), Cons(Nil, x3)))
   GCD[ITE](False, Cons(Nil, Nil), Cons(Nil, x1)) -> c6(GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, x1)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c8(GCD(Cons(z0, Cons(z1, z2)), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z1, z2))), Nil)), Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2)))), MONUS(Cons(z3, Cons(z4, z5)), Cons(z0, Cons(z1, z2))))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Cons(z2, z3))) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Cons(z2, z3)), Cons(z0, Nil))), MONUS(Cons(z1, Cons(z2, z3)), Cons(z0, Nil)))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   GCD[FALSE][ITE](False, Cons(z0, Nil), Cons(z1, Nil)) -> c8(GCD(Cons(z0, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z1, Nil), Cons(z0, Nil))), MONUS(Cons(z1, Nil), Cons(z0, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Cons(z2, z3), z4)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Cons(z2, z3), z4), Cons(Cons(z0, z1), Nil)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Cons(x3, x4), Cons(x5, x6))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Cons(x4, x5), x6)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Cons(z0, z1), z2)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil))), MONUS(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD[FALSE][ITE](False, Cons(Cons(z0, z1), Nil), Cons(Nil, z2)) -> c8(GCD(Cons(Cons(z0, z1), Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z2), Cons(Cons(z0, z1), Nil))), MONUS(Cons(Nil, z2), Cons(Cons(z0, z1), Nil)))
   GCD[FALSE][ITE](False, Cons(Nil, Nil), Cons(Nil, z0)) -> c8(GCD(Cons(Nil, Nil), monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(Nil, z0), Cons(Nil, Nil))), MONUS(Cons(Nil, z0), Cons(Nil, Nil)))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))) -> c6(GT0(Cons(Nil, x0), Cons(Cons(x1, x2), Cons(x3, x4))))
   GCD[ITE](False, Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)) -> c6(GT0(Cons(Nil, Cons(x0, x1)), Cons(Cons(x2, x3), x4)))
   GCD[ITE](False, Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))) -> c6(GT0(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, Cons(x4, x5))))
   GCD[ITE](False, Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))) -> c6(GT0(Cons(Cons(x0, x1), x2), Cons(Nil, Cons(x3, x4))))
   GCD[ITE](False, Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)) -> c6(GT0(Cons(Cons(x0, x1), Cons(x2, x3)), Cons(Nil, x4)))
   GCD[FALSE][ITE](True, Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))) -> c9(GCD(monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Cons(z4, z5))), Nil)), Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))), Cons(z3, Cons(z4, z5))), MONUS(Cons(z0, Cons(z1, z2)), Cons(z3, Cons(z4, z5))))
   GCD[FALSE][ITE](True, Cons(z0, Cons(z1, z2)), Cons(z3, Nil)) -> c9(GCD(monus[Ite](and(eqList(Nil, Nil), eqList(@(Nil, lgth(Nil)), Nil)), Cons(z0, Cons(z1, z2)), Cons(z3, Nil)), Cons(z3, Nil)), MONUS(Cons(z0, Cons(z1, z2)), Cons(z3, Nil)))
   GCD[ITE](False, Cons(Nil, Cons(x1, x2)), Cons(Nil, Cons(x4, x5))) -> c6(GT0(Cons(Nil, Cons(x1, x2)), Cons(Nil, Cons(x4, x5))))
   GCD[ITE](False, Cons(Nil, x0), Cons(Nil, Cons(x1, x2))) -> c6(GT0(Cons(Nil, x0), Cons(Nil, Cons(x1, x2))))
   GCD[ITE](False, Cons(Nil, Cons(x0, x1)), Cons(Nil, x2)) -> c6(GT0(Cons(Nil, Cons(x0, x1)), Cons(Nil, x2)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](and(eqList(Nil, Nil), eqList(@(Nil, lgth(z2)), Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, @(Cons(Nil, Nil), lgth(z3)))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
S tuples:
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))) -> c18(GCD[ITE](and(eqList(x0, x2), and(eqList(z0, z2), eqList(z1, z3))), Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Cons(z2, z3))))
   GCD(Cons(x0, Nil), Cons(x2, Cons(z0, z1))) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Nil), Cons(x2, Cons(z0, z1))), EQLIST(Cons(x0, Nil), Cons(x2, Cons(z0, z1))))
   GCD(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), False), Cons(x0, Cons(z0, z1)), Cons(x2, Nil)), EQLIST(Cons(x0, Cons(z0, z1)), Cons(x2, Nil)))
   GCD(Cons(x0, Nil), Cons(x2, Nil)) -> c18(GCD[ITE](and(eqList(x0, x2), True), Cons(x0, Nil), Cons(x2, Nil)), EQLIST(Cons(x0, Nil), Cons(x2, Nil)))
   MONUS(x0, Cons(x1, x2)) -> c(LGTH(Cons(x1, x2)))
   MONUS(x0, Nil) -> c26
   MONUS(x0, Cons(x1, Nil)) -> c1(LGTH(Cons(x1, Nil)))
   LGTH(Cons(z0, z1)) -> c19(LGTH(z1))
   GT0(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c13(GT0(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(Cons(y0, y1), z1), Cons(Cons(y2, y3), z3)) -> c21(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(y0, y1)), Cons(z2, Cons(y2, y3))) -> c22(EQLIST(Cons(y0, y1), Cons(y2, y3)))
   EQLIST(Cons(z0, Cons(Cons(y0, y1), y2)), Cons(z2, Cons(Cons(y3, y4), y5))) -> c22(EQLIST(Cons(Cons(y0, y1), y2), Cons(Cons(y3, y4), y5)))
   MONUS(x0, Cons(x1, x2)) -> c
   MONUS(x0, Cons(x1, Nil)) -> c1
   MONUS(z0, Cons(z1, Nil)) -> c1(MONUS[ITE](eqList(Cons(Nil, @(Nil, Nil)), Cons(Nil, Nil)), z0, Cons(z1, Nil)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Nil, z5)), Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Nil), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)), EQLIST(Cons(Cons(z0, z1), z2), Cons(Cons(z3, z4), Nil)))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)) -> c18(GCD[ITE](and(and(eqList(z0, z3), eqList(z1, z4)), eqList(Cons(x1, x2), z5)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Cons(z3, z4), z5)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Cons(z1, z2), Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, Nil), Cons(Cons(z1, z2), z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Nil, Nil), Cons(Cons(z1, z2), z3)))
   GCD(Cons(Nil, z0), Cons(Cons(z1, z2), Nil)) -> c18(GCD[ITE](and(False, eqList(z0, Nil)), Cons(Nil, z0), Cons(Cons(z1, z2), Nil)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(False, eqList(z2, Cons(x4, x5))), Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Cons(z0, z1), z2), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Cons(x1, x2), z3)), Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)), EQLIST(Cons(Cons(z0, z1), Cons(x1, x2)), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), Nil), Cons(Nil, z3)) -> c18(GCD[ITE](and(False, eqList(Nil, z3)), Cons(Cons(z0, z1), Nil), Cons(Nil, z3)))
   GCD(Cons(Cons(z0, z1), z2), Cons(Nil, Nil)) -> c18(GCD[ITE](and(False, eqList(z2, Nil)), Cons(Cons(z0, z1), z2), Cons(Nil, Nil)))
   GCD(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))) -> c18(GCD[ITE](and(True, eqList(z0, Cons(x4, x5))), Cons(Nil, z0), Cons(Nil, Cons(x4, x5))), EQLIST(Cons(Nil, z0), Cons(Nil, Cons(x4, x5))))
   GCD(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Cons(x1, x2), z1)), Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)), EQLIST(Cons(Nil, Cons(x1, x2)), Cons(Nil, z1)))
   GCD(Cons(Nil, Nil), Cons(Nil, z1)) -> c18(GCD[ITE](and(True, eqList(Nil, z1)), Cons(Nil, Nil), Cons(Nil, z1)))
   GCD(Cons(Nil, z0), Cons(Nil, Nil)) -> c18(GCD[ITE](and(True, eqList(z0, Nil)), Cons(Nil, z0), Cons(Nil, Nil)))
   MONUS(z0, Cons(z1, z2)) -> c26(MONUS[ITE](and(eqList(Nil, Nil), eqList(@(Nil, lgth(z2)), Nil)), z0, Cons(z1, z2)), LGTH(Cons(z1, z2)))
   MONUS(z0, Cons(z1, Cons(z2, z3))) -> c26(MONUS[ITE](eqList(Cons(Nil, @(Nil, @(Cons(Nil, Nil), lgth(z3)))), Cons(Nil, Nil)), z0, Cons(z1, Cons(z2, z3))), LGTH(Cons(z1, Cons(z2, z3))))
K tuples:
   @'(Cons(z0, Cons(y0, y1)), z2) -> c10(@'(Cons(y0, y1), z2))
   GCD(Cons(x0, Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Nil), Cons(z2, z3)))
   GCD(Cons(Cons(x0, x1), Nil), Cons(z2, z3)) -> c18(EQLIST(Cons(Cons(x0, x1), Nil), Cons(z2, z3)))
   GCD(Cons(z0, z1), Cons(x3, Cons(x4, x5))) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Cons(x4, x5))))
   GCD(Cons(z0, z1), Cons(x3, Nil)) -> c18(EQLIST(Cons(z0, z1), Cons(x3, Nil)))
   GCD(Cons(x0, Cons(x1, x2)), Cons(z2, z3)) -> c18(EQLIST(Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
Defined Rule Symbols:   gt0_2, monus_2, monus[Ite]_3, eqList_2, lgth_1, @_2, and_2

Defined Pair Symbols:   GCD[ITE]_3, GCD_2, MONUS_2, MONUS[ITE]_3, @'_2, LGTH_1, GT0_2, EQLIST_2, GCD[FALSE][ITE]_3

Compound Symbols:   c6_2, c18_2, c_1, c26, c4_1, c1_1, c6_1, c10_1, c19_1, c13_1, c21_1, c22_1, c, c1, c8_2, c18_1, c9_2, c26_2