KILLED
proof of input_cLk7YfP7Te.trs
# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished


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

(0) CpxTRS
(1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxTRS
(3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(4) CpxTRS
(5) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxWeightedTrs
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CpxTypedWeightedTrs
    (9) CompletionProof [UPPER BOUND(ID), 0 ms]
    (10) CpxTypedWeightedCompleteTrs
        (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (12) CpxRNTS
    (13) CompletionProof [UPPER BOUND(ID), 0 ms]
    (14) CpxTypedWeightedCompleteTrs
        (15) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (16) CpxTypedWeightedCompleteTrs
        (17) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (18) CpxRNTS
        (19) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (20) CpxRNTS
        (21) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
        (22) CpxRNTS
        (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (24) CpxRNTS
        (25) IntTrsBoundProof [UPPER BOUND(ID), 296 ms]
        (26) CpxRNTS
        (27) IntTrsBoundProof [UPPER BOUND(ID), 140 ms]
        (28) CpxRNTS
        (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (30) CpxRNTS
        (31) IntTrsBoundProof [UPPER BOUND(ID), 447 ms]
        (32) CpxRNTS
        (33) IntTrsBoundProof [UPPER BOUND(ID), 126 ms]
        (34) CpxRNTS
        (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
        (36) CpxRNTS
        (37) IntTrsBoundProof [UPPER BOUND(ID), 1287 ms]
        (38) CpxRNTS
        (39) IntTrsBoundProof [UPPER BOUND(ID), 5583 ms]
        (40) CpxRNTS
(41) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(42) CdtProblem
    (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (44) CdtProblem
    (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (46) CdtProblem
    (47) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 181 ms]
    (48) CdtProblem
    (49) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 49 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) CdtProblem
    (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) CdtProblem
    (57) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (64) CdtProblem
    (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (66) CdtProblem
    (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (70) CdtProblem
    (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
    (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (76) CdtProblem
    (77) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) CdtProblem
    (81) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtNarrowingProof [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), 170 ms]
    (92) CdtProblem
    (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (94) CdtProblem
    (95) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem
    (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (102) CdtProblem
    (103) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (104) CdtProblem
    (105) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (106) CdtProblem
    (107) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (112) CdtProblem
    (113) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (116) CdtProblem
    (117) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (118) CdtProblem
    (119) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (122) CdtProblem
    (123) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (124) CdtProblem
    (125) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (126) CdtProblem
    (127) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (128) CdtProblem
    (129) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (130) CdtProblem
    (131) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (132) CdtProblem
    (133) CdtRewritingProof [BOTH BOUNDS(ID, ID), 6 ms]
    (134) CdtProblem
    (135) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (136) CdtProblem
    (137) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms]
    (138) CdtProblem
    (139) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1 ms]
    (140) CdtProblem
    (141) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (142) CdtProblem
    (143) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (144) CdtProblem
    (145) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (146) CdtProblem
    (147) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (148) CdtProblem
    (149) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (150) CdtProblem
    (151) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (152) CdtProblem
    (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (154) CdtProblem
    (155) CdtRewritingProof [BOTH BOUNDS(ID, ID), 8 ms]
    (156) CdtProblem
    (157) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (158) CdtProblem
    (159) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (160) CdtProblem
    (161) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (162) CdtProblem
    (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (164) CdtProblem
    (165) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (166) CdtProblem
    (167) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (168) CdtProblem


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

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


The TRS R consists of the following rules:

   select(x', revprefix, Cons(x, xs)) -> mapconsapp(x', permute(revapp(revprefix, Cons(x, xs))), select(x, Cons(x', revprefix), xs))
   revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest))
   permute(Cons(x, xs)) -> select(x, Nil, xs)
   mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest))
   select(x, revprefix, Nil) -> mapconsapp(x, permute(revapp(revprefix, Nil)), Nil)
   revapp(Nil, rest) -> rest
   permute(Nil) -> Cons(Nil, Nil)
   mapconsapp(x, Nil, rest) -> rest
   goal(xs) -> permute(xs)

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

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

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


The TRS R consists of the following rules:

   select(x', revprefix, Cons(x, xs)) -> mapconsapp(x', permute(revapp(revprefix, Cons(x, xs))), select(x, Cons(x', revprefix), xs))
   revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest))
   permute(Cons(x, xs)) -> select(x, Nil, xs)
   mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest))
   select(x, revprefix, Nil) -> mapconsapp(x, permute(revapp(revprefix, Nil)), Nil)
   revapp(Nil, rest) -> rest
   permute(Nil) -> Cons(Nil, Nil)
   mapconsapp(x, Nil, rest) -> rest
   goal(xs) -> permute(xs)

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

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

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


The TRS R consists of the following rules:

   select(x', revprefix, Cons(x, xs)) -> mapconsapp(x', permute(revapp(revprefix, Cons(x, xs))), select(x, Cons(x', revprefix), xs))
   revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest))
   permute(Cons(x, xs)) -> select(x, Nil, xs)
   mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest))
   select(x, revprefix, Nil) -> mapconsapp(x, permute(revapp(revprefix, Nil)), Nil)
   revapp(Nil, rest) -> rest
   permute(Nil) -> Cons(Nil, Nil)
   mapconsapp(x, Nil, rest) -> rest
   goal(xs) -> permute(xs)

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

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

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


The TRS R consists of the following rules:

   select(x', revprefix, Cons(x, xs)) -> mapconsapp(x', permute(revapp(revprefix, Cons(x, xs))), select(x, Cons(x', revprefix), xs)) [1]
   revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) [1]
   permute(Cons(x, xs)) -> select(x, Nil, xs) [1]
   mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest)) [1]
   select(x, revprefix, Nil) -> mapconsapp(x, permute(revapp(revprefix, Nil)), Nil) [1]
   revapp(Nil, rest) -> rest [1]
   permute(Nil) -> Cons(Nil, Nil) [1]
   mapconsapp(x, Nil, rest) -> rest [1]
   goal(xs) -> permute(xs) [1]

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

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

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

   select(x', revprefix, Cons(x, xs)) -> mapconsapp(x', permute(revapp(revprefix, Cons(x, xs))), select(x, Cons(x', revprefix), xs)) [1]
   revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) [1]
   permute(Cons(x, xs)) -> select(x, Nil, xs) [1]
   mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest)) [1]
   select(x, revprefix, Nil) -> mapconsapp(x, permute(revapp(revprefix, Nil)), Nil) [1]
   revapp(Nil, rest) -> rest [1]
   permute(Nil) -> Cons(Nil, Nil) [1]
   mapconsapp(x, Nil, rest) -> rest [1]
   goal(xs) -> permute(xs) [1]

The TRS has the following type information:
select :: Cons:Nil -> Cons:Nil -> Cons:Nil -> Cons:Nil
Cons :: Cons:Nil -> Cons:Nil -> Cons:Nil
mapconsapp :: Cons:Nil -> Cons:Nil -> Cons:Nil -> Cons:Nil
permute :: Cons:Nil -> Cons:Nil
revapp :: Cons:Nil -> Cons:Nil -> Cons:Nil
Nil :: Cons:Nil
goal :: Cons:Nil -> Cons:Nil

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

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

And the following fresh constants: none

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

(10)
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:

   select(x', revprefix, Cons(x, xs)) -> mapconsapp(x', permute(revapp(revprefix, Cons(x, xs))), select(x, Cons(x', revprefix), xs)) [1]
   revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) [1]
   permute(Cons(x, xs)) -> select(x, Nil, xs) [1]
   mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest)) [1]
   select(x, revprefix, Nil) -> mapconsapp(x, permute(revapp(revprefix, Nil)), Nil) [1]
   revapp(Nil, rest) -> rest [1]
   permute(Nil) -> Cons(Nil, Nil) [1]
   mapconsapp(x, Nil, rest) -> rest [1]
   goal(xs) -> permute(xs) [1]

The TRS has the following type information:
select :: Cons:Nil -> Cons:Nil -> Cons:Nil -> Cons:Nil
Cons :: Cons:Nil -> Cons:Nil -> Cons:Nil
mapconsapp :: Cons:Nil -> Cons:Nil -> Cons:Nil -> Cons:Nil
permute :: Cons:Nil -> Cons:Nil
revapp :: Cons:Nil -> Cons:Nil -> Cons:Nil
Nil :: Cons:Nil
goal :: Cons:Nil -> Cons:Nil

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

(11) 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

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

(12)
Obligation:
Complexity RNTS consisting of the following rules:

   goal(z) -{ 1 }-> permute(xs) :|: xs >= 0, z = xs
   mapconsapp(z, z', z'') -{ 1 }-> rest :|: x >= 0, z'' = rest, rest >= 0, z = x, z' = 0
   mapconsapp(z, z', z'') -{ 1 }-> 1 + (1 + x' + x) + mapconsapp(x', xs, rest) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, x >= 0, z'' = rest, rest >= 0, z = x'
   permute(z) -{ 1 }-> select(x, 0, xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
   permute(z) -{ 1 }-> 1 + 0 + 0 :|: z = 0
   revapp(z, z') -{ 1 }-> rest :|: z' = rest, rest >= 0, z = 0
   revapp(z, z') -{ 1 }-> revapp(xs, 1 + x + rest) :|: z = 1 + x + xs, xs >= 0, z' = rest, x >= 0, rest >= 0
   select(z, z', z'') -{ 1 }-> mapconsapp(x, permute(revapp(revprefix, 0)), 0) :|: z'' = 0, z' = revprefix, x >= 0, revprefix >= 0, z = x
   select(z, z', z'') -{ 1 }-> mapconsapp(x', permute(revapp(revprefix, 1 + x + xs)), select(x, 1 + x' + revprefix, xs)) :|: xs >= 0, z' = revprefix, x' >= 0, x >= 0, z'' = 1 + x + xs, revprefix >= 0, z = x'

Only complete derivations are relevant for the runtime complexity.

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

(13) CompletionProof (UPPER BOUND(ID))
The transformation into a RNTS is sound, since:

(a) The obligation is a constructor system where every type has a constant constructor,

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:

   goal_1

(c) The following functions are completely defined:

   permute_1
   revapp_2
   select_3
   mapconsapp_3

Due to the following rules being added:
none

And the following fresh constants: none

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

(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:

   select(x', revprefix, Cons(x, xs)) -> mapconsapp(x', permute(revapp(revprefix, Cons(x, xs))), select(x, Cons(x', revprefix), xs)) [1]
   revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) [1]
   permute(Cons(x, xs)) -> select(x, Nil, xs) [1]
   mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest)) [1]
   select(x, revprefix, Nil) -> mapconsapp(x, permute(revapp(revprefix, Nil)), Nil) [1]
   revapp(Nil, rest) -> rest [1]
   permute(Nil) -> Cons(Nil, Nil) [1]
   mapconsapp(x, Nil, rest) -> rest [1]
   goal(xs) -> permute(xs) [1]

The TRS has the following type information:
select :: Cons:Nil -> Cons:Nil -> Cons:Nil -> Cons:Nil
Cons :: Cons:Nil -> Cons:Nil -> Cons:Nil
mapconsapp :: Cons:Nil -> Cons:Nil -> Cons:Nil -> Cons:Nil
permute :: Cons:Nil -> Cons:Nil
revapp :: Cons:Nil -> Cons:Nil -> Cons:Nil
Nil :: Cons:Nil
goal :: Cons:Nil -> Cons:Nil

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

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

(16)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   select(x', Cons(x'', xs'), Cons(x, Cons(x1, xs''))) -> mapconsapp(x', permute(revapp(xs', Cons(x'', Cons(x, Cons(x1, xs''))))), mapconsapp(x, permute(revapp(Cons(x', Cons(x'', xs')), Cons(x1, xs''))), select(x1, Cons(x, Cons(x', Cons(x'', xs'))), xs''))) [3]
   select(x', Cons(x'', xs'), Cons(x, Nil)) -> mapconsapp(x', permute(revapp(xs', Cons(x'', Cons(x, Nil)))), mapconsapp(x, permute(revapp(Cons(x', Cons(x'', xs')), Nil)), Nil)) [3]
   select(x', Nil, Cons(x, Cons(x2, xs1))) -> mapconsapp(x', permute(Cons(x, Cons(x2, xs1))), mapconsapp(x, permute(revapp(Cons(x', Nil), Cons(x2, xs1))), select(x2, Cons(x, Cons(x', Nil)), xs1))) [3]
   select(x', Nil, Cons(x, Nil)) -> mapconsapp(x', permute(Cons(x, Nil)), mapconsapp(x, permute(revapp(Cons(x', Nil), Nil)), Nil)) [3]
   revapp(Cons(x, xs), rest) -> revapp(xs, Cons(x, rest)) [1]
   permute(Cons(x, xs)) -> select(x, Nil, xs) [1]
   mapconsapp(x', Cons(x, xs), rest) -> Cons(Cons(x', x), mapconsapp(x', xs, rest)) [1]
   select(x, Cons(x3, xs2), Nil) -> mapconsapp(x, permute(revapp(xs2, Cons(x3, Nil))), Nil) [2]
   select(x, Nil, Nil) -> mapconsapp(x, permute(Nil), Nil) [2]
   revapp(Nil, rest) -> rest [1]
   permute(Nil) -> Cons(Nil, Nil) [1]
   mapconsapp(x, Nil, rest) -> rest [1]
   goal(xs) -> permute(xs) [1]

The TRS has the following type information:
select :: Cons:Nil -> Cons:Nil -> Cons:Nil -> Cons:Nil
Cons :: Cons:Nil -> Cons:Nil -> Cons:Nil
mapconsapp :: Cons:Nil -> Cons:Nil -> Cons:Nil -> Cons:Nil
permute :: Cons:Nil -> Cons:Nil
revapp :: Cons:Nil -> Cons:Nil -> Cons:Nil
Nil :: Cons:Nil
goal :: Cons:Nil -> Cons:Nil

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

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

   Nil => 0

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

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

   goal(z) -{ 1 }-> permute(xs) :|: xs >= 0, z = xs
   mapconsapp(z, z', z'') -{ 1 }-> rest :|: x >= 0, z'' = rest, rest >= 0, z = x, z' = 0
   mapconsapp(z, z', z'') -{ 1 }-> 1 + (1 + x' + x) + mapconsapp(x', xs, rest) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, x >= 0, z'' = rest, rest >= 0, z = x'
   permute(z) -{ 1 }-> select(x, 0, xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
   permute(z) -{ 1 }-> 1 + 0 + 0 :|: z = 0
   revapp(z, z') -{ 1 }-> rest :|: z' = rest, rest >= 0, z = 0
   revapp(z, z') -{ 1 }-> revapp(xs, 1 + x + rest) :|: z = 1 + x + xs, xs >= 0, z' = rest, x >= 0, rest >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(x, permute(revapp(xs2, 1 + x3 + 0)), 0) :|: z'' = 0, xs2 >= 0, z' = 1 + x3 + xs2, x >= 0, z = x, x3 >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(x, permute(0), 0) :|: z'' = 0, x >= 0, z = x, z' = 0
   select(z, z', z'') -{ 3 }-> mapconsapp(x', permute(revapp(xs', 1 + x'' + (1 + x + 0))), mapconsapp(x, permute(revapp(1 + x' + (1 + x'' + xs'), 0)), 0)) :|: z'' = 1 + x + 0, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x'' + xs', x'' >= 0, z = x'
   select(z, z', z'') -{ 3 }-> mapconsapp(x', permute(revapp(xs', 1 + x'' + (1 + x + (1 + x1 + xs'')))), mapconsapp(x, permute(revapp(1 + x' + (1 + x'' + xs'), 1 + x1 + xs'')), select(x1, 1 + x + (1 + x' + (1 + x'' + xs')), xs''))) :|: x1 >= 0, x' >= 0, xs' >= 0, x >= 0, xs'' >= 0, z'' = 1 + x + (1 + x1 + xs''), z' = 1 + x'' + xs', x'' >= 0, z = x'
   select(z, z', z'') -{ 3 }-> mapconsapp(x', permute(1 + x + 0), mapconsapp(x, permute(revapp(1 + x' + 0, 0)), 0)) :|: z'' = 1 + x + 0, x' >= 0, x >= 0, z = x', z' = 0
   select(z, z', z'') -{ 3 }-> mapconsapp(x', permute(1 + x + (1 + x2 + xs1)), mapconsapp(x, permute(revapp(1 + x' + 0, 1 + x2 + xs1)), select(x2, 1 + x + (1 + x' + 0), xs1))) :|: x' >= 0, x >= 0, z'' = 1 + x + (1 + x2 + xs1), xs1 >= 0, x2 >= 0, z = x', z' = 0


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

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

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

   goal(z) -{ 1 }-> permute(z) :|: z >= 0
   mapconsapp(z, z', z'') -{ 1 }-> z'' :|: z >= 0, z'' >= 0, z' = 0
   mapconsapp(z, z', z'') -{ 1 }-> 1 + (1 + z + x) + mapconsapp(z, xs, z'') :|: xs >= 0, z' = 1 + x + xs, z >= 0, x >= 0, z'' >= 0
   permute(z) -{ 1 }-> select(x, 0, xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
   permute(z) -{ 1 }-> 1 + 0 + 0 :|: z = 0
   revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   revapp(z, z') -{ 1 }-> revapp(xs, 1 + x + z') :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(revapp(xs', 1 + x'' + (1 + x + (1 + x1 + xs'')))), mapconsapp(x, permute(revapp(1 + z + (1 + x'' + xs'), 1 + x1 + xs'')), select(x1, 1 + x + (1 + z + (1 + x'' + xs')), xs''))) :|: x1 >= 0, z >= 0, xs' >= 0, x >= 0, xs'' >= 0, z'' = 1 + x + (1 + x1 + xs''), z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(revapp(xs', 1 + x'' + (1 + (z'' - 1) + 0))), mapconsapp(z'' - 1, permute(revapp(1 + z + (1 + x'' + xs'), 0)), 0)) :|: z >= 0, xs' >= 0, z'' - 1 >= 0, z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(z, permute(revapp(xs2, 1 + x3 + 0)), 0) :|: z'' = 0, xs2 >= 0, z' = 1 + x3 + xs2, z >= 0, x3 >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(z, permute(0), 0) :|: z'' = 0, z >= 0, z' = 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(1 + x + (1 + x2 + xs1)), mapconsapp(x, permute(revapp(1 + z + 0, 1 + x2 + xs1)), select(x2, 1 + x + (1 + z + 0), xs1))) :|: z >= 0, x >= 0, z'' = 1 + x + (1 + x2 + xs1), xs1 >= 0, x2 >= 0, z' = 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(1 + (z'' - 1) + 0), mapconsapp(z'' - 1, permute(revapp(1 + z + 0, 0)), 0)) :|: z >= 0, z'' - 1 >= 0, z' = 0


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

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

   { revapp }
   { mapconsapp }
   { permute, select }
   { goal }

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

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

   goal(z) -{ 1 }-> permute(z) :|: z >= 0
   mapconsapp(z, z', z'') -{ 1 }-> z'' :|: z >= 0, z'' >= 0, z' = 0
   mapconsapp(z, z', z'') -{ 1 }-> 1 + (1 + z + x) + mapconsapp(z, xs, z'') :|: xs >= 0, z' = 1 + x + xs, z >= 0, x >= 0, z'' >= 0
   permute(z) -{ 1 }-> select(x, 0, xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
   permute(z) -{ 1 }-> 1 + 0 + 0 :|: z = 0
   revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   revapp(z, z') -{ 1 }-> revapp(xs, 1 + x + z') :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(revapp(xs', 1 + x'' + (1 + x + (1 + x1 + xs'')))), mapconsapp(x, permute(revapp(1 + z + (1 + x'' + xs'), 1 + x1 + xs'')), select(x1, 1 + x + (1 + z + (1 + x'' + xs')), xs''))) :|: x1 >= 0, z >= 0, xs' >= 0, x >= 0, xs'' >= 0, z'' = 1 + x + (1 + x1 + xs''), z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(revapp(xs', 1 + x'' + (1 + (z'' - 1) + 0))), mapconsapp(z'' - 1, permute(revapp(1 + z + (1 + x'' + xs'), 0)), 0)) :|: z >= 0, xs' >= 0, z'' - 1 >= 0, z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(z, permute(revapp(xs2, 1 + x3 + 0)), 0) :|: z'' = 0, xs2 >= 0, z' = 1 + x3 + xs2, z >= 0, x3 >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(z, permute(0), 0) :|: z'' = 0, z >= 0, z' = 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(1 + x + (1 + x2 + xs1)), mapconsapp(x, permute(revapp(1 + z + 0, 1 + x2 + xs1)), select(x2, 1 + x + (1 + z + 0), xs1))) :|: z >= 0, x >= 0, z'' = 1 + x + (1 + x2 + xs1), xs1 >= 0, x2 >= 0, z' = 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(1 + (z'' - 1) + 0), mapconsapp(z'' - 1, permute(revapp(1 + z + 0, 0)), 0)) :|: z >= 0, z'' - 1 >= 0, z' = 0

Function symbols to be analyzed: {revapp}, {mapconsapp}, {permute,select}, {goal}

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

(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:

   goal(z) -{ 1 }-> permute(z) :|: z >= 0
   mapconsapp(z, z', z'') -{ 1 }-> z'' :|: z >= 0, z'' >= 0, z' = 0
   mapconsapp(z, z', z'') -{ 1 }-> 1 + (1 + z + x) + mapconsapp(z, xs, z'') :|: xs >= 0, z' = 1 + x + xs, z >= 0, x >= 0, z'' >= 0
   permute(z) -{ 1 }-> select(x, 0, xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
   permute(z) -{ 1 }-> 1 + 0 + 0 :|: z = 0
   revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   revapp(z, z') -{ 1 }-> revapp(xs, 1 + x + z') :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(revapp(xs', 1 + x'' + (1 + x + (1 + x1 + xs'')))), mapconsapp(x, permute(revapp(1 + z + (1 + x'' + xs'), 1 + x1 + xs'')), select(x1, 1 + x + (1 + z + (1 + x'' + xs')), xs''))) :|: x1 >= 0, z >= 0, xs' >= 0, x >= 0, xs'' >= 0, z'' = 1 + x + (1 + x1 + xs''), z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(revapp(xs', 1 + x'' + (1 + (z'' - 1) + 0))), mapconsapp(z'' - 1, permute(revapp(1 + z + (1 + x'' + xs'), 0)), 0)) :|: z >= 0, xs' >= 0, z'' - 1 >= 0, z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(z, permute(revapp(xs2, 1 + x3 + 0)), 0) :|: z'' = 0, xs2 >= 0, z' = 1 + x3 + xs2, z >= 0, x3 >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(z, permute(0), 0) :|: z'' = 0, z >= 0, z' = 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(1 + x + (1 + x2 + xs1)), mapconsapp(x, permute(revapp(1 + z + 0, 1 + x2 + xs1)), select(x2, 1 + x + (1 + z + 0), xs1))) :|: z >= 0, x >= 0, z'' = 1 + x + (1 + x2 + xs1), xs1 >= 0, x2 >= 0, z' = 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(1 + (z'' - 1) + 0), mapconsapp(z'' - 1, permute(revapp(1 + z + 0, 0)), 0)) :|: z >= 0, z'' - 1 >= 0, z' = 0

Function symbols to be analyzed: {revapp}, {mapconsapp}, {permute,select}, {goal}

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

(25) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   goal(z) -{ 1 }-> permute(z) :|: z >= 0
   mapconsapp(z, z', z'') -{ 1 }-> z'' :|: z >= 0, z'' >= 0, z' = 0
   mapconsapp(z, z', z'') -{ 1 }-> 1 + (1 + z + x) + mapconsapp(z, xs, z'') :|: xs >= 0, z' = 1 + x + xs, z >= 0, x >= 0, z'' >= 0
   permute(z) -{ 1 }-> select(x, 0, xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
   permute(z) -{ 1 }-> 1 + 0 + 0 :|: z = 0
   revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   revapp(z, z') -{ 1 }-> revapp(xs, 1 + x + z') :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(revapp(xs', 1 + x'' + (1 + x + (1 + x1 + xs'')))), mapconsapp(x, permute(revapp(1 + z + (1 + x'' + xs'), 1 + x1 + xs'')), select(x1, 1 + x + (1 + z + (1 + x'' + xs')), xs''))) :|: x1 >= 0, z >= 0, xs' >= 0, x >= 0, xs'' >= 0, z'' = 1 + x + (1 + x1 + xs''), z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(revapp(xs', 1 + x'' + (1 + (z'' - 1) + 0))), mapconsapp(z'' - 1, permute(revapp(1 + z + (1 + x'' + xs'), 0)), 0)) :|: z >= 0, xs' >= 0, z'' - 1 >= 0, z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(z, permute(revapp(xs2, 1 + x3 + 0)), 0) :|: z'' = 0, xs2 >= 0, z' = 1 + x3 + xs2, z >= 0, x3 >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(z, permute(0), 0) :|: z'' = 0, z >= 0, z' = 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(1 + x + (1 + x2 + xs1)), mapconsapp(x, permute(revapp(1 + z + 0, 1 + x2 + xs1)), select(x2, 1 + x + (1 + z + 0), xs1))) :|: z >= 0, x >= 0, z'' = 1 + x + (1 + x2 + xs1), xs1 >= 0, x2 >= 0, z' = 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(1 + (z'' - 1) + 0), mapconsapp(z'' - 1, permute(revapp(1 + z + 0, 0)), 0)) :|: z >= 0, z'' - 1 >= 0, z' = 0

Function symbols to be analyzed: {revapp}, {mapconsapp}, {permute,select}, {goal}
Previous analysis results are:
  revapp: runtime: ?, size: O(n^1) [z + z']

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

(27) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: revapp
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:

   goal(z) -{ 1 }-> permute(z) :|: z >= 0
   mapconsapp(z, z', z'') -{ 1 }-> z'' :|: z >= 0, z'' >= 0, z' = 0
   mapconsapp(z, z', z'') -{ 1 }-> 1 + (1 + z + x) + mapconsapp(z, xs, z'') :|: xs >= 0, z' = 1 + x + xs, z >= 0, x >= 0, z'' >= 0
   permute(z) -{ 1 }-> select(x, 0, xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
   permute(z) -{ 1 }-> 1 + 0 + 0 :|: z = 0
   revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   revapp(z, z') -{ 1 }-> revapp(xs, 1 + x + z') :|: z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(revapp(xs', 1 + x'' + (1 + x + (1 + x1 + xs'')))), mapconsapp(x, permute(revapp(1 + z + (1 + x'' + xs'), 1 + x1 + xs'')), select(x1, 1 + x + (1 + z + (1 + x'' + xs')), xs''))) :|: x1 >= 0, z >= 0, xs' >= 0, x >= 0, xs'' >= 0, z'' = 1 + x + (1 + x1 + xs''), z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(revapp(xs', 1 + x'' + (1 + (z'' - 1) + 0))), mapconsapp(z'' - 1, permute(revapp(1 + z + (1 + x'' + xs'), 0)), 0)) :|: z >= 0, xs' >= 0, z'' - 1 >= 0, z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(z, permute(revapp(xs2, 1 + x3 + 0)), 0) :|: z'' = 0, xs2 >= 0, z' = 1 + x3 + xs2, z >= 0, x3 >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(z, permute(0), 0) :|: z'' = 0, z >= 0, z' = 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(1 + x + (1 + x2 + xs1)), mapconsapp(x, permute(revapp(1 + z + 0, 1 + x2 + xs1)), select(x2, 1 + x + (1 + z + 0), xs1))) :|: z >= 0, x >= 0, z'' = 1 + x + (1 + x2 + xs1), xs1 >= 0, x2 >= 0, z' = 0
   select(z, z', z'') -{ 3 }-> mapconsapp(z, permute(1 + (z'' - 1) + 0), mapconsapp(z'' - 1, permute(revapp(1 + z + 0, 0)), 0)) :|: z >= 0, z'' - 1 >= 0, z' = 0

Function symbols to be analyzed: {mapconsapp}, {permute,select}, {goal}
Previous analysis results are:
  revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']

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

(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:

   goal(z) -{ 1 }-> permute(z) :|: z >= 0
   mapconsapp(z, z', z'') -{ 1 }-> z'' :|: z >= 0, z'' >= 0, z' = 0
   mapconsapp(z, z', z'') -{ 1 }-> 1 + (1 + z + x) + mapconsapp(z, xs, z'') :|: xs >= 0, z' = 1 + x + xs, z >= 0, x >= 0, z'' >= 0
   permute(z) -{ 1 }-> select(x, 0, xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
   permute(z) -{ 1 }-> 1 + 0 + 0 :|: z = 0
   revapp(z, z') -{ 2 + xs }-> s4 :|: s4 >= 0, s4 <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0
   revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   select(z, z', z'') -{ 7 + x'' + 2*xs' + z }-> mapconsapp(z, permute(s), mapconsapp(x, permute(s'), select(x1, 1 + x + (1 + z + (1 + x'' + xs')), xs''))) :|: s >= 0, s <= xs' + (1 + x'' + (1 + x + (1 + x1 + xs''))), s' >= 0, s' <= 1 + z + (1 + x'' + xs') + (1 + x1 + xs''), x1 >= 0, z >= 0, xs' >= 0, x >= 0, xs'' >= 0, z'' = 1 + x + (1 + x1 + xs''), z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 7 + x'' + 2*xs' + z }-> mapconsapp(z, permute(s''), mapconsapp(z'' - 1, permute(s1), 0)) :|: s'' >= 0, s'' <= xs' + (1 + x'' + (1 + (z'' - 1) + 0)), s1 >= 0, s1 <= 1 + z + (1 + x'' + xs') + 0, z >= 0, xs' >= 0, z'' - 1 >= 0, z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 3 + xs2 }-> mapconsapp(z, permute(s5), 0) :|: s5 >= 0, s5 <= xs2 + (1 + x3 + 0), z'' = 0, xs2 >= 0, z' = 1 + x3 + xs2, z >= 0, x3 >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(z, permute(0), 0) :|: z'' = 0, z >= 0, z' = 0
   select(z, z', z'') -{ 5 + z }-> mapconsapp(z, permute(1 + x + (1 + x2 + xs1)), mapconsapp(x, permute(s2), select(x2, 1 + x + (1 + z + 0), xs1))) :|: s2 >= 0, s2 <= 1 + z + 0 + (1 + x2 + xs1), z >= 0, x >= 0, z'' = 1 + x + (1 + x2 + xs1), xs1 >= 0, x2 >= 0, z' = 0
   select(z, z', z'') -{ 5 + z }-> mapconsapp(z, permute(1 + (z'' - 1) + 0), mapconsapp(z'' - 1, permute(s3), 0)) :|: s3 >= 0, s3 <= 1 + z + 0 + 0, z >= 0, z'' - 1 >= 0, z' = 0

Function symbols to be analyzed: {mapconsapp}, {permute,select}, {goal}
Previous analysis results are:
  revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']

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

(31) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   goal(z) -{ 1 }-> permute(z) :|: z >= 0
   mapconsapp(z, z', z'') -{ 1 }-> z'' :|: z >= 0, z'' >= 0, z' = 0
   mapconsapp(z, z', z'') -{ 1 }-> 1 + (1 + z + x) + mapconsapp(z, xs, z'') :|: xs >= 0, z' = 1 + x + xs, z >= 0, x >= 0, z'' >= 0
   permute(z) -{ 1 }-> select(x, 0, xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
   permute(z) -{ 1 }-> 1 + 0 + 0 :|: z = 0
   revapp(z, z') -{ 2 + xs }-> s4 :|: s4 >= 0, s4 <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0
   revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   select(z, z', z'') -{ 7 + x'' + 2*xs' + z }-> mapconsapp(z, permute(s), mapconsapp(x, permute(s'), select(x1, 1 + x + (1 + z + (1 + x'' + xs')), xs''))) :|: s >= 0, s <= xs' + (1 + x'' + (1 + x + (1 + x1 + xs''))), s' >= 0, s' <= 1 + z + (1 + x'' + xs') + (1 + x1 + xs''), x1 >= 0, z >= 0, xs' >= 0, x >= 0, xs'' >= 0, z'' = 1 + x + (1 + x1 + xs''), z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 7 + x'' + 2*xs' + z }-> mapconsapp(z, permute(s''), mapconsapp(z'' - 1, permute(s1), 0)) :|: s'' >= 0, s'' <= xs' + (1 + x'' + (1 + (z'' - 1) + 0)), s1 >= 0, s1 <= 1 + z + (1 + x'' + xs') + 0, z >= 0, xs' >= 0, z'' - 1 >= 0, z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 3 + xs2 }-> mapconsapp(z, permute(s5), 0) :|: s5 >= 0, s5 <= xs2 + (1 + x3 + 0), z'' = 0, xs2 >= 0, z' = 1 + x3 + xs2, z >= 0, x3 >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(z, permute(0), 0) :|: z'' = 0, z >= 0, z' = 0
   select(z, z', z'') -{ 5 + z }-> mapconsapp(z, permute(1 + x + (1 + x2 + xs1)), mapconsapp(x, permute(s2), select(x2, 1 + x + (1 + z + 0), xs1))) :|: s2 >= 0, s2 <= 1 + z + 0 + (1 + x2 + xs1), z >= 0, x >= 0, z'' = 1 + x + (1 + x2 + xs1), xs1 >= 0, x2 >= 0, z' = 0
   select(z, z', z'') -{ 5 + z }-> mapconsapp(z, permute(1 + (z'' - 1) + 0), mapconsapp(z'' - 1, permute(s3), 0)) :|: s3 >= 0, s3 <= 1 + z + 0 + 0, z >= 0, z'' - 1 >= 0, z' = 0

Function symbols to be analyzed: {mapconsapp}, {permute,select}, {goal}
Previous analysis results are:
  revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  mapconsapp: runtime: ?, size: O(n^2) [z*z' + z' + z'^2 + z'']

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

(33) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   goal(z) -{ 1 }-> permute(z) :|: z >= 0
   mapconsapp(z, z', z'') -{ 1 }-> z'' :|: z >= 0, z'' >= 0, z' = 0
   mapconsapp(z, z', z'') -{ 1 }-> 1 + (1 + z + x) + mapconsapp(z, xs, z'') :|: xs >= 0, z' = 1 + x + xs, z >= 0, x >= 0, z'' >= 0
   permute(z) -{ 1 }-> select(x, 0, xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
   permute(z) -{ 1 }-> 1 + 0 + 0 :|: z = 0
   revapp(z, z') -{ 2 + xs }-> s4 :|: s4 >= 0, s4 <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0
   revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   select(z, z', z'') -{ 7 + x'' + 2*xs' + z }-> mapconsapp(z, permute(s), mapconsapp(x, permute(s'), select(x1, 1 + x + (1 + z + (1 + x'' + xs')), xs''))) :|: s >= 0, s <= xs' + (1 + x'' + (1 + x + (1 + x1 + xs''))), s' >= 0, s' <= 1 + z + (1 + x'' + xs') + (1 + x1 + xs''), x1 >= 0, z >= 0, xs' >= 0, x >= 0, xs'' >= 0, z'' = 1 + x + (1 + x1 + xs''), z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 7 + x'' + 2*xs' + z }-> mapconsapp(z, permute(s''), mapconsapp(z'' - 1, permute(s1), 0)) :|: s'' >= 0, s'' <= xs' + (1 + x'' + (1 + (z'' - 1) + 0)), s1 >= 0, s1 <= 1 + z + (1 + x'' + xs') + 0, z >= 0, xs' >= 0, z'' - 1 >= 0, z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 3 + xs2 }-> mapconsapp(z, permute(s5), 0) :|: s5 >= 0, s5 <= xs2 + (1 + x3 + 0), z'' = 0, xs2 >= 0, z' = 1 + x3 + xs2, z >= 0, x3 >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(z, permute(0), 0) :|: z'' = 0, z >= 0, z' = 0
   select(z, z', z'') -{ 5 + z }-> mapconsapp(z, permute(1 + x + (1 + x2 + xs1)), mapconsapp(x, permute(s2), select(x2, 1 + x + (1 + z + 0), xs1))) :|: s2 >= 0, s2 <= 1 + z + 0 + (1 + x2 + xs1), z >= 0, x >= 0, z'' = 1 + x + (1 + x2 + xs1), xs1 >= 0, x2 >= 0, z' = 0
   select(z, z', z'') -{ 5 + z }-> mapconsapp(z, permute(1 + (z'' - 1) + 0), mapconsapp(z'' - 1, permute(s3), 0)) :|: s3 >= 0, s3 <= 1 + z + 0 + 0, z >= 0, z'' - 1 >= 0, z' = 0

Function symbols to be analyzed: {permute,select}, {goal}
Previous analysis results are:
  revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  mapconsapp: runtime: O(n^1) [1 + z'], size: O(n^2) [z*z' + z' + z'^2 + z'']

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

(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:

   goal(z) -{ 1 }-> permute(z) :|: z >= 0
   mapconsapp(z, z', z'') -{ 1 }-> z'' :|: z >= 0, z'' >= 0, z' = 0
   mapconsapp(z, z', z'') -{ 2 + xs }-> 1 + (1 + z + x) + s6 :|: s6 >= 0, s6 <= xs * z + xs * xs + xs + z'', xs >= 0, z' = 1 + x + xs, z >= 0, x >= 0, z'' >= 0
   permute(z) -{ 1 }-> select(x, 0, xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
   permute(z) -{ 1 }-> 1 + 0 + 0 :|: z = 0
   revapp(z, z') -{ 2 + xs }-> s4 :|: s4 >= 0, s4 <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0
   revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   select(z, z', z'') -{ 7 + x'' + 2*xs' + z }-> mapconsapp(z, permute(s), mapconsapp(x, permute(s'), select(x1, 1 + x + (1 + z + (1 + x'' + xs')), xs''))) :|: s >= 0, s <= xs' + (1 + x'' + (1 + x + (1 + x1 + xs''))), s' >= 0, s' <= 1 + z + (1 + x'' + xs') + (1 + x1 + xs''), x1 >= 0, z >= 0, xs' >= 0, x >= 0, xs'' >= 0, z'' = 1 + x + (1 + x1 + xs''), z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 7 + x'' + 2*xs' + z }-> mapconsapp(z, permute(s''), mapconsapp(z'' - 1, permute(s1), 0)) :|: s'' >= 0, s'' <= xs' + (1 + x'' + (1 + (z'' - 1) + 0)), s1 >= 0, s1 <= 1 + z + (1 + x'' + xs') + 0, z >= 0, xs' >= 0, z'' - 1 >= 0, z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 3 + xs2 }-> mapconsapp(z, permute(s5), 0) :|: s5 >= 0, s5 <= xs2 + (1 + x3 + 0), z'' = 0, xs2 >= 0, z' = 1 + x3 + xs2, z >= 0, x3 >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(z, permute(0), 0) :|: z'' = 0, z >= 0, z' = 0
   select(z, z', z'') -{ 5 + z }-> mapconsapp(z, permute(1 + x + (1 + x2 + xs1)), mapconsapp(x, permute(s2), select(x2, 1 + x + (1 + z + 0), xs1))) :|: s2 >= 0, s2 <= 1 + z + 0 + (1 + x2 + xs1), z >= 0, x >= 0, z'' = 1 + x + (1 + x2 + xs1), xs1 >= 0, x2 >= 0, z' = 0
   select(z, z', z'') -{ 5 + z }-> mapconsapp(z, permute(1 + (z'' - 1) + 0), mapconsapp(z'' - 1, permute(s3), 0)) :|: s3 >= 0, s3 <= 1 + z + 0 + 0, z >= 0, z'' - 1 >= 0, z' = 0

Function symbols to be analyzed: {permute,select}, {goal}
Previous analysis results are:
  revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  mapconsapp: runtime: O(n^1) [1 + z'], size: O(n^2) [z*z' + z' + z'^2 + z'']

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

(37) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   goal(z) -{ 1 }-> permute(z) :|: z >= 0
   mapconsapp(z, z', z'') -{ 1 }-> z'' :|: z >= 0, z'' >= 0, z' = 0
   mapconsapp(z, z', z'') -{ 2 + xs }-> 1 + (1 + z + x) + s6 :|: s6 >= 0, s6 <= xs * z + xs * xs + xs + z'', xs >= 0, z' = 1 + x + xs, z >= 0, x >= 0, z'' >= 0
   permute(z) -{ 1 }-> select(x, 0, xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
   permute(z) -{ 1 }-> 1 + 0 + 0 :|: z = 0
   revapp(z, z') -{ 2 + xs }-> s4 :|: s4 >= 0, s4 <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0
   revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   select(z, z', z'') -{ 7 + x'' + 2*xs' + z }-> mapconsapp(z, permute(s), mapconsapp(x, permute(s'), select(x1, 1 + x + (1 + z + (1 + x'' + xs')), xs''))) :|: s >= 0, s <= xs' + (1 + x'' + (1 + x + (1 + x1 + xs''))), s' >= 0, s' <= 1 + z + (1 + x'' + xs') + (1 + x1 + xs''), x1 >= 0, z >= 0, xs' >= 0, x >= 0, xs'' >= 0, z'' = 1 + x + (1 + x1 + xs''), z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 7 + x'' + 2*xs' + z }-> mapconsapp(z, permute(s''), mapconsapp(z'' - 1, permute(s1), 0)) :|: s'' >= 0, s'' <= xs' + (1 + x'' + (1 + (z'' - 1) + 0)), s1 >= 0, s1 <= 1 + z + (1 + x'' + xs') + 0, z >= 0, xs' >= 0, z'' - 1 >= 0, z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 3 + xs2 }-> mapconsapp(z, permute(s5), 0) :|: s5 >= 0, s5 <= xs2 + (1 + x3 + 0), z'' = 0, xs2 >= 0, z' = 1 + x3 + xs2, z >= 0, x3 >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(z, permute(0), 0) :|: z'' = 0, z >= 0, z' = 0
   select(z, z', z'') -{ 5 + z }-> mapconsapp(z, permute(1 + x + (1 + x2 + xs1)), mapconsapp(x, permute(s2), select(x2, 1 + x + (1 + z + 0), xs1))) :|: s2 >= 0, s2 <= 1 + z + 0 + (1 + x2 + xs1), z >= 0, x >= 0, z'' = 1 + x + (1 + x2 + xs1), xs1 >= 0, x2 >= 0, z' = 0
   select(z, z', z'') -{ 5 + z }-> mapconsapp(z, permute(1 + (z'' - 1) + 0), mapconsapp(z'' - 1, permute(s3), 0)) :|: s3 >= 0, s3 <= 1 + z + 0 + 0, z >= 0, z'' - 1 >= 0, z' = 0

Function symbols to be analyzed: {permute,select}, {goal}
Previous analysis results are:
  revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  mapconsapp: runtime: O(n^1) [1 + z'], size: O(n^2) [z*z' + z' + z'^2 + z'']
  permute: runtime: ?, size: INF
  select: runtime: ?, size: INF

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

(39) IntTrsBoundProof (UPPER BOUND(ID))

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

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

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

   goal(z) -{ 1 }-> permute(z) :|: z >= 0
   mapconsapp(z, z', z'') -{ 1 }-> z'' :|: z >= 0, z'' >= 0, z' = 0
   mapconsapp(z, z', z'') -{ 2 + xs }-> 1 + (1 + z + x) + s6 :|: s6 >= 0, s6 <= xs * z + xs * xs + xs + z'', xs >= 0, z' = 1 + x + xs, z >= 0, x >= 0, z'' >= 0
   permute(z) -{ 1 }-> select(x, 0, xs) :|: z = 1 + x + xs, xs >= 0, x >= 0
   permute(z) -{ 1 }-> 1 + 0 + 0 :|: z = 0
   revapp(z, z') -{ 2 + xs }-> s4 :|: s4 >= 0, s4 <= xs + (1 + x + z'), z = 1 + x + xs, xs >= 0, x >= 0, z' >= 0
   revapp(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0
   select(z, z', z'') -{ 7 + x'' + 2*xs' + z }-> mapconsapp(z, permute(s), mapconsapp(x, permute(s'), select(x1, 1 + x + (1 + z + (1 + x'' + xs')), xs''))) :|: s >= 0, s <= xs' + (1 + x'' + (1 + x + (1 + x1 + xs''))), s' >= 0, s' <= 1 + z + (1 + x'' + xs') + (1 + x1 + xs''), x1 >= 0, z >= 0, xs' >= 0, x >= 0, xs'' >= 0, z'' = 1 + x + (1 + x1 + xs''), z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 7 + x'' + 2*xs' + z }-> mapconsapp(z, permute(s''), mapconsapp(z'' - 1, permute(s1), 0)) :|: s'' >= 0, s'' <= xs' + (1 + x'' + (1 + (z'' - 1) + 0)), s1 >= 0, s1 <= 1 + z + (1 + x'' + xs') + 0, z >= 0, xs' >= 0, z'' - 1 >= 0, z' = 1 + x'' + xs', x'' >= 0
   select(z, z', z'') -{ 3 + xs2 }-> mapconsapp(z, permute(s5), 0) :|: s5 >= 0, s5 <= xs2 + (1 + x3 + 0), z'' = 0, xs2 >= 0, z' = 1 + x3 + xs2, z >= 0, x3 >= 0
   select(z, z', z'') -{ 2 }-> mapconsapp(z, permute(0), 0) :|: z'' = 0, z >= 0, z' = 0
   select(z, z', z'') -{ 5 + z }-> mapconsapp(z, permute(1 + x + (1 + x2 + xs1)), mapconsapp(x, permute(s2), select(x2, 1 + x + (1 + z + 0), xs1))) :|: s2 >= 0, s2 <= 1 + z + 0 + (1 + x2 + xs1), z >= 0, x >= 0, z'' = 1 + x + (1 + x2 + xs1), xs1 >= 0, x2 >= 0, z' = 0
   select(z, z', z'') -{ 5 + z }-> mapconsapp(z, permute(1 + (z'' - 1) + 0), mapconsapp(z'' - 1, permute(s3), 0)) :|: s3 >= 0, s3 <= 1 + z + 0 + 0, z >= 0, z'' - 1 >= 0, z' = 0

Function symbols to be analyzed: {permute,select}, {goal}
Previous analysis results are:
  revapp: runtime: O(n^1) [1 + z], size: O(n^1) [z + z']
  mapconsapp: runtime: O(n^1) [1 + z'], size: O(n^2) [z*z' + z' + z'^2 + z'']
  permute: runtime: INF, size: INF
  select: runtime: ?, size: INF

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

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
   goal(z0) -> permute(z0)
Tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   REVAPP(Nil, z0) -> c4
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   PERMUTE(Nil) -> c6
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   MAPCONSAPP(z0, Nil, z1) -> c8
   GOAL(z0) -> c9(PERMUTE(z0))
S tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   REVAPP(Nil, z0) -> c4
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   PERMUTE(Nil) -> c6
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   MAPCONSAPP(z0, Nil, z1) -> c8
   GOAL(z0) -> c9(PERMUTE(z0))
K tuples:none
Defined Rule Symbols:   select_3, revapp_2, permute_1, mapconsapp_3, goal_1

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3, GOAL_1

Compound Symbols:   c_3, c1_2, c2_3, c3_1, c4, c5_1, c6, c7_1, c8, c9_1


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

(43) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   GOAL(z0) -> c9(PERMUTE(z0))
Removed 3 trailing nodes:
   MAPCONSAPP(z0, Nil, z1) -> c8
   PERMUTE(Nil) -> c6
   REVAPP(Nil, z0) -> c4

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
   goal(z0) -> permute(z0)
Tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
S tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
K tuples:none
Defined Rule Symbols:   select_3, revapp_2, permute_1, mapconsapp_3, goal_1

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c_3, c1_2, c2_3, c3_1, c5_1, c7_1


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

(45) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   goal(z0) -> permute(z0)

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
S tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
K tuples:none
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c_3, c1_2, c2_3, c3_1, c5_1, c7_1


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

(47) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
We considered the (Usable) Rules:
   revapp(Nil, z0) -> z0
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
And the Tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(Cons(x_1, x_2)) = [1] + x_2
   POL(MAPCONSAPP(x_1, x_2, x_3)) = 0
   POL(Nil) = 0
   POL(PERMUTE(x_1)) = x_1
   POL(REVAPP(x_1, x_2)) = 0
   POL(SELECT(x_1, x_2, x_3)) = x_2 + x_3
   POL(c(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c1(x_1, x_2)) = x_1 + x_2
   POL(c2(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c3(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(mapconsapp(x_1, x_2, x_3)) = [1] + x_1 + x_2 + x_3
   POL(permute(x_1)) = [1]
   POL(revapp(x_1, x_2)) = x_1 + x_2
   POL(select(x_1, x_2, x_3)) = 0

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
S tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c_3, c1_2, c2_3, c3_1, c5_1, c7_1


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

(49) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
We considered the (Usable) Rules:
   revapp(Nil, z0) -> z0
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
And the Tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(Cons(x_1, x_2)) = [1] + x_2
   POL(MAPCONSAPP(x_1, x_2, x_3)) = 0
   POL(Nil) = 0
   POL(PERMUTE(x_1)) = x_1
   POL(REVAPP(x_1, x_2)) = 0
   POL(SELECT(x_1, x_2, x_3)) = [1] + x_2 + x_3
   POL(c(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c1(x_1, x_2)) = x_1 + x_2
   POL(c2(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c3(x_1)) = x_1
   POL(c5(x_1)) = x_1
   POL(c7(x_1)) = x_1
   POL(mapconsapp(x_1, x_2, x_3)) = [1] + x_1 + x_2 + x_3
   POL(permute(x_1)) = [1]
   POL(revapp(x_1, x_2)) = x_1 + x_2
   POL(select(x_1, x_2, x_3)) = 0

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
S tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c_3, c1_2, c2_3, c3_1, c5_1, c7_1


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3))) by 
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), PERMUTE(revapp(x1, Cons(z0, Cons(z2, z3)))), REVAPP(x1, Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(z0, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), PERMUTE(revapp(x1, Cons(z0, Nil))), REVAPP(x1, Cons(z0, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, x3))), REVAPP(Cons(z0, z1), Cons(x2, x3)))
   SELECT(x0, Nil, Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), PERMUTE(revapp(Nil, Cons(x2, x3))), REVAPP(Nil, Cons(x2, x3)))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), PERMUTE(revapp(x1, Cons(z0, Cons(z2, z3)))), REVAPP(x1, Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(z0, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), PERMUTE(revapp(x1, Cons(z0, Nil))), REVAPP(x1, Cons(z0, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, x3))), REVAPP(Cons(z0, z1), Cons(x2, x3)))
   SELECT(x0, Nil, Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), PERMUTE(revapp(Nil, Cons(x2, x3))), REVAPP(Nil, Cons(x2, x3)))
S tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c1_2, c2_3, c3_1, c5_1, c7_1, c_3


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

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), PERMUTE(revapp(x1, Cons(z0, Cons(z2, z3)))), REVAPP(x1, Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(z0, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), PERMUTE(revapp(x1, Cons(z0, Nil))), REVAPP(x1, Cons(z0, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, x3))), REVAPP(Cons(z0, z1), Cons(x2, x3)))
   SELECT(x0, Nil, Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), PERMUTE(revapp(Nil, Cons(x2, x3))))
S tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c1_2, c2_3, c3_1, c5_1, c7_1, c_3, c_2


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SELECT(z0, z1, Cons(z2, z3)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), SELECT(z2, Cons(z0, z1), z3)) by 
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), PERMUTE(revapp(x1, Cons(z0, Cons(z2, z3)))), REVAPP(x1, Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(z0, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), PERMUTE(revapp(x1, Cons(z0, Nil))), REVAPP(x1, Cons(z0, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, x3))), REVAPP(Cons(z0, z1), Cons(x2, x3)))
   SELECT(x0, Nil, Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), PERMUTE(revapp(Nil, Cons(x2, x3))))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c2_3, c3_1, c5_1, c7_1, c_3, c_2, c1_2, c1_1


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

(57) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), PERMUTE(revapp(x1, Cons(z0, Cons(z2, z3)))), REVAPP(x1, Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(z0, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), PERMUTE(revapp(x1, Cons(z0, Nil))), REVAPP(x1, Cons(z0, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, x3))), REVAPP(Cons(z0, z1), Cons(x2, x3)))
   SELECT(x0, Nil, Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), PERMUTE(revapp(Nil, Cons(x2, x3))))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c2_3, c3_1, c5_1, c7_1, c_3, c_2, c1_2, c1_1


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil)) by 
   SELECT(x0, Cons(z0, z1), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Nil))), Nil), PERMUTE(revapp(Cons(z0, z1), Nil)), REVAPP(Cons(z0, z1), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil)), REVAPP(Nil, Nil))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), PERMUTE(revapp(x1, Cons(z0, Cons(z2, z3)))), REVAPP(x1, Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(z0, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), PERMUTE(revapp(x1, Cons(z0, Nil))), REVAPP(x1, Cons(z0, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, x3))), REVAPP(Cons(z0, z1), Cons(x2, x3)))
   SELECT(x0, Nil, Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), PERMUTE(revapp(Nil, Cons(x2, x3))))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, Cons(z0, z1), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Nil))), Nil), PERMUTE(revapp(Cons(z0, z1), Nil)), REVAPP(Cons(z0, z1), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil)), REVAPP(Nil, Nil))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c_3, c_2, c1_2, c1_1, c2_3


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

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), PERMUTE(revapp(x1, Cons(z0, Cons(z2, z3)))), REVAPP(x1, Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(z0, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), PERMUTE(revapp(x1, Cons(z0, Nil))), REVAPP(x1, Cons(z0, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, x3))), REVAPP(Cons(z0, z1), Cons(x2, x3)))
   SELECT(x0, Nil, Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), PERMUTE(revapp(Nil, Cons(x2, x3))))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, Cons(z0, z1), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Nil))), Nil), PERMUTE(revapp(Cons(z0, z1), Nil)), REVAPP(Cons(z0, z1), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil)))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c_3, c_2, c1_2, c1_1, c2_3, c2_2


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), PERMUTE(revapp(x1, Cons(z0, Cons(z2, z3)))), REVAPP(x1, Cons(z0, Cons(z2, z3)))) by 
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))), REVAPP(Nil, Cons(x2, Cons(x3, x4))))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), PERMUTE(revapp(x1, Cons(z0, Nil))), REVAPP(x1, Cons(z0, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, x3))), REVAPP(Cons(z0, z1), Cons(x2, x3)))
   SELECT(x0, Nil, Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), PERMUTE(revapp(Nil, Cons(x2, x3))))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, Cons(z0, z1), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Nil))), Nil), PERMUTE(revapp(Cons(z0, z1), Nil)), REVAPP(Cons(z0, z1), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil)))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))), REVAPP(Nil, Cons(x2, Cons(x3, x4))))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c_3, c_2, c1_2, c1_1, c2_3, c2_2


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

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), PERMUTE(revapp(x1, Cons(z0, Nil))), REVAPP(x1, Cons(z0, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, x3))), REVAPP(Cons(z0, z1), Cons(x2, x3)))
   SELECT(x0, Nil, Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), PERMUTE(revapp(Nil, Cons(x2, x3))))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, Cons(z0, z1), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Nil))), Nil), PERMUTE(revapp(Cons(z0, z1), Nil)), REVAPP(Cons(z0, z1), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil)))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c_3, c_2, c1_2, c1_1, c2_3, c2_2


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

(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SELECT(x0, x1, Cons(z0, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), PERMUTE(revapp(x1, Cons(z0, Nil))), REVAPP(x1, Cons(z0, Nil))) by 
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))), REVAPP(Nil, Cons(x2, Nil)))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, x3))), REVAPP(Cons(z0, z1), Cons(x2, x3)))
   SELECT(x0, Nil, Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), PERMUTE(revapp(Nil, Cons(x2, x3))))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, Cons(z0, z1), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Nil))), Nil), PERMUTE(revapp(Cons(z0, z1), Nil)), REVAPP(Cons(z0, z1), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil)))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))), REVAPP(Nil, Cons(x2, Nil)))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c_3, c_2, c1_2, c1_1, c2_3, c2_2


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

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, x3))), REVAPP(Cons(z0, z1), Cons(x2, x3)))
   SELECT(x0, Nil, Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), PERMUTE(revapp(Nil, Cons(x2, x3))))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, Cons(z0, z1), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Nil))), Nil), PERMUTE(revapp(Cons(z0, z1), Nil)), REVAPP(Cons(z0, z1), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil)))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c_3, c_2, c1_2, c1_1, c2_3, c2_2


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, x3))), REVAPP(Cons(z0, z1), Cons(x2, x3))) by 
   SELECT(x0, Cons(x1, x2), Cons(z0, Cons(z2, z3))) -> c(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Cons(z2, z3))))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Cons(x1, x2))), z3))), PERMUTE(revapp(Cons(x1, x2), Cons(z0, Cons(z2, z3)))), REVAPP(Cons(x1, x2), Cons(z0, Cons(z2, z3))))
   SELECT(x0, Cons(x1, x2), Cons(z0, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Nil)))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Nil)), Nil)), PERMUTE(revapp(Cons(x1, x2), Cons(z0, Nil))), REVAPP(Cons(x1, x2), Cons(z0, Nil)))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))), REVAPP(Cons(x1, Nil), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), PERMUTE(revapp(Nil, Cons(x2, x3))))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, Cons(z0, z1), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Nil))), Nil), PERMUTE(revapp(Cons(z0, z1), Nil)), REVAPP(Cons(z0, z1), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil)))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))), REVAPP(Cons(x1, Nil), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c_2, c1_2, c1_1, c2_3, c2_2, c_3


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

(73) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SELECT(x0, Nil, Cons(x2, x3)) -> c(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), PERMUTE(revapp(Nil, Cons(x2, x3)))) by 
   SELECT(x0, Nil, Cons(z0, Cons(z2, z3))) -> c(MAPCONSAPP(x0, permute(Cons(z0, Cons(z2, z3))), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Nil)), z3))), PERMUTE(revapp(Nil, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, Nil, Cons(z0, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(z0, Nil)), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(z0, Nil))))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, Cons(z0, z1), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Nil))), Nil), PERMUTE(revapp(Cons(z0, z1), Nil)), REVAPP(Cons(z0, z1), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil)))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))), REVAPP(Cons(x1, Nil), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3)))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c1_2, c1_1, c2_3, c2_2, c_3, c_2, c_1


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SELECT(x0, x1, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, x1)), z3))), SELECT(z0, Cons(x0, x1), Cons(z2, z3))) by 
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, Cons(z0, z1), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Nil))), Nil), PERMUTE(revapp(Cons(z0, z1), Nil)), REVAPP(Cons(z0, z1), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil)))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))), REVAPP(Cons(x1, Nil), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c1_2, c1_1, c2_3, c2_2, c_3, c_2, c_1


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

(77) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, Cons(z0, z1), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Nil))), Nil), PERMUTE(revapp(Cons(z0, z1), Nil)), REVAPP(Cons(z0, z1), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil)))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))), REVAPP(Cons(x1, Nil), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c1_2, c1_1, c2_3, c2_2, c_3, c_2, c_1


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SELECT(x0, x1, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x0, x1), Nil)), Nil)), SELECT(z0, Cons(x0, x1), Nil)) by 
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, Cons(z0, z1), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Nil))), Nil), PERMUTE(revapp(Cons(z0, z1), Nil)), REVAPP(Cons(z0, z1), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil)))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))), REVAPP(Cons(x1, Nil), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c1_2, c1_1, c2_3, c2_2, c_3, c_2, c_1


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

(81) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, Cons(z0, z1), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Nil))), Nil), PERMUTE(revapp(Cons(z0, z1), Nil)), REVAPP(Cons(z0, z1), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil)))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))), REVAPP(Cons(x1, Nil), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c1_2, c1_1, c2_3, c2_2, c_3, c_2, c_1


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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SELECT(x0, Cons(z0, z1), Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, x3)))), select(x2, Cons(x0, Cons(z0, z1)), x3)), SELECT(x2, Cons(x0, Cons(z0, z1)), x3)) by 
   SELECT(x0, Cons(x1, x2), Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Cons(z2, z3))))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Cons(x1, x2))), z3))), SELECT(z0, Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   SELECT(x0, Cons(x1, x2), Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Nil)))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Nil)), Nil)), SELECT(z0, Cons(x0, Cons(x1, x2)), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, Cons(z0, z1), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Nil))), Nil), PERMUTE(revapp(Cons(z0, z1), Nil)), REVAPP(Cons(z0, z1), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil)))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))), REVAPP(Cons(x1, Nil), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c1_2, c1_1, c2_3, c2_2, c_3, c_2, c_1


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

(85) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3)) by 
   SELECT(x0, Nil, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(Cons(z0, Cons(z2, z3))), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Nil)), z3))), SELECT(z0, Cons(x0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(z0, Nil)), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(z0, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, Cons(z0, z1), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Nil))), Nil), PERMUTE(revapp(Cons(z0, z1), Nil)), REVAPP(Cons(z0, z1), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil)))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))), REVAPP(Cons(x1, Nil), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c1_1, c2_3, c2_2, c_3, c_2, c_1, c1_2


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SELECT(x0, Cons(z0, z1), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Nil))), Nil), PERMUTE(revapp(Cons(z0, z1), Nil)), REVAPP(Cons(z0, z1), Nil)) by 
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)), REVAPP(Cons(x1, Nil), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil)))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))), REVAPP(Cons(x1, Nil), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)), REVAPP(Cons(x1, Nil), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c1_1, c2_2, c_3, c_2, c_1, c1_2, c2_3


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

(89) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, permute(Nil), Nil), PERMUTE(revapp(Nil, Nil))) by 
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil), PERMUTE(revapp(Nil, Nil)))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))), REVAPP(Cons(x1, Nil), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)), REVAPP(Cons(x1, Nil), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil), PERMUTE(revapp(Nil, Nil)))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil), PERMUTE(revapp(Nil, Nil))) by 
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil), PERMUTE(Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))), REVAPP(Cons(x1, Nil), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)), REVAPP(Cons(x1, Nil), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil), PERMUTE(Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2, c2_1


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

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3)))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))), REVAPP(Cons(x1, Nil), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)), REVAPP(Cons(x1, Nil), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2, c2_1


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

(95) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), REVAPP(x1, Cons(x2, Cons(z0, Cons(z2, z3))))) by SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
----------------------------------------

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil))))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))), REVAPP(Cons(x1, Nil), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)), REVAPP(Cons(x1, Nil), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2, c2_1


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

(97) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), PERMUTE(revapp(x1, Cons(x2, Cons(z0, Nil)))), REVAPP(x1, Cons(x2, Cons(z0, Nil)))) by SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
----------------------------------------

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))), REVAPP(Cons(x1, Nil), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)), REVAPP(Cons(x1, Nil), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
S tuples:
   REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2)))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   REVAPP_2, PERMUTE_1, MAPCONSAPP_3, SELECT_3

Compound Symbols:   c3_1, c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2, c2_1


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

(99) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace REVAPP(Cons(z0, z1), z2) -> c3(REVAPP(z1, Cons(z0, z2))) by 
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))), REVAPP(Cons(x1, Nil), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)), REVAPP(Cons(x1, Nil), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2, c2_1, c3_1


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

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2, c2_1, c3_1


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

(103) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4)))) by SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
----------------------------------------

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2, c2_1, c3_1


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

(105) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4))))) by SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
----------------------------------------

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2, c2_1, c3_1


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

(107) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil))) by SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
----------------------------------------

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2, c2_1, c3_1


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

(109) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil)))) by SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
----------------------------------------

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Cons(x3, x4)))), REVAPP(Cons(z0, z1), Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2, c2_1, c3_1


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

(111) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Cons(x1, x2), Cons(z0, Cons(z2, z3))) -> c(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Cons(z2, z3))))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Cons(x1, x2))), z3))), PERMUTE(revapp(Cons(x1, x2), Cons(z0, Cons(z2, z3)))), REVAPP(Cons(x1, x2), Cons(z0, Cons(z2, z3)))) by SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
----------------------------------------

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), PERMUTE(revapp(Cons(z0, z1), Cons(x2, Nil))), REVAPP(Cons(z0, z1), Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2, c2_1, c3_1


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

(113) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Cons(x1, x2), Cons(z0, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Nil)))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Nil)), Nil)), PERMUTE(revapp(Cons(x1, x2), Cons(z0, Nil))), REVAPP(Cons(x1, x2), Cons(z0, Nil))) by SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
----------------------------------------

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2, c2_1, c3_1


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

(115) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Cons(x3, x4))), REVAPP(Cons(x1, Cons(z0, z1)), Cons(x3, x4))) by SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
----------------------------------------

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2, c2_1, c3_1


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

(117) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c(PERMUTE(revapp(Cons(x1, x2), Cons(x3, x4))), REVAPP(Cons(x1, x2), Cons(x3, x4))) by SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
----------------------------------------

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), PERMUTE(revapp(Nil, Cons(x2, Cons(x3, x4)))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2, c2_1, c3_1


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

(119) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Nil, Cons(z0, Cons(z2, z3))) -> c(MAPCONSAPP(x0, permute(Cons(z0, Cons(z2, z3))), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Nil)), z3))), PERMUTE(revapp(Nil, Cons(z0, Cons(z2, z3))))) by SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
----------------------------------------

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(x2, Nil))))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2, c2_1, c3_1


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

(121) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Nil, Cons(z0, Nil)) -> c(MAPCONSAPP(x0, permute(Cons(z0, Nil)), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Nil)), Nil)), PERMUTE(revapp(Nil, Cons(z0, Nil)))) by SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
----------------------------------------

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1))))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c_2, c_1, c1_2, c2_3, c2_2, c2_1, c3_1


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

(123) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Nil, Cons(z0, z1)) -> c(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), PERMUTE(revapp(Nil, Cons(z0, z1)))) by SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
----------------------------------------

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c_1, c1_2, c2_3, c2_2, c2_1, c3_1, c_2


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

(125) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Nil, Cons(x1, x2)) -> c(PERMUTE(revapp(Nil, Cons(x1, x2)))) by SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
----------------------------------------

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3))))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c1_2, c2_3, c2_2, c2_1, c3_1, c_2, c_1


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

(127) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, x1, Cons(x2, Cons(z0, Cons(z2, z3)))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Cons(z2, z3))))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Cons(z2, z3)))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x2, Cons(x0, x1))), z3)))), SELECT(x2, Cons(x0, x1), Cons(z0, Cons(z2, z3)))) by SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
----------------------------------------

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c1_2, c2_3, c2_2, c2_1, c3_1, c_2, c_1


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

(129) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, x1, Cons(x2, Cons(z0, Nil))) -> c1(MAPCONSAPP(x0, permute(revapp(x1, Cons(x2, Cons(z0, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, x1), Cons(z0, Nil))), mapconsapp(z0, permute(revapp(Cons(x2, Cons(x0, x1)), Nil)), Nil))), SELECT(x2, Cons(x0, x1), Cons(z0, Nil))) by SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
----------------------------------------

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c1_2, c2_3, c2_2, c2_1, c3_1, c_2, c_1


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

(131) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4))) by SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
----------------------------------------

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c1_2, c2_3, c2_2, c2_1, c3_1, c_2, c_1


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

(133) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4))) by SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
----------------------------------------

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c1_1, c_3, c1_2, c2_3, c2_2, c2_1, c3_1, c_2, c_1


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

(135) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace SELECT(x0, x1, Cons(x2, x3)) -> c1(SELECT(x2, Cons(x0, x1), x3)) by 
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x2, Cons(x0, x1), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, x1)), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c_3, c1_2, c1_1, c2_3, c2_2, c2_1, c3_1, c_2, c_1


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

(137) CdtKnowledgeProof (BOTH BOUNDS(ID, ID))
The following tuples could be moved from S to K by knowledge propagation:
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
K tuples:
   PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1))
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   PERMUTE_1, MAPCONSAPP_3, SELECT_3, REVAPP_2

Compound Symbols:   c5_1, c7_1, c_3, c1_2, c1_1, c2_3, c2_2, c2_1, c3_1, c_2, c_1


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

(139) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace PERMUTE(Cons(z0, z1)) -> c5(SELECT(z0, Nil, z1)) by 
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Nil)) -> c5(SELECT(z0, Nil, Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)), PERMUTE(Cons(z1, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Nil)) -> c5(SELECT(z0, Nil, Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
K tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Nil)) -> c5(SELECT(z0, Nil, Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   MAPCONSAPP_3, SELECT_3, REVAPP_2, PERMUTE_1

Compound Symbols:   c7_1, c_3, c1_2, c1_1, c2_3, c2_2, c2_1, c3_1, c_2, c_1, c5_1


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

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Nil)) -> c5(SELECT(z0, Nil, Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(PERMUTE(Cons(z1, Nil)))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
K tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Nil)) -> c5(SELECT(z0, Nil, Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   MAPCONSAPP_3, SELECT_3, REVAPP_2, PERMUTE_1

Compound Symbols:   c7_1, c_3, c1_2, c1_1, c2_3, c2_2, c2_1, c3_1, c_2, c_1, c5_1, c4_1


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

(143) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil)) by SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
----------------------------------------

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Nil)) -> c5(SELECT(z0, Nil, Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(PERMUTE(Cons(z1, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
S tuples:
   MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
K tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Nil)) -> c5(SELECT(z0, Nil, Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   MAPCONSAPP_3, SELECT_3, REVAPP_2, PERMUTE_1

Compound Symbols:   c7_1, c_3, c1_2, c1_1, c2_3, c2_2, c2_1, c3_1, c_2, c_1, c5_1, c4_1


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

(145) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace MAPCONSAPP(z0, Cons(z1, z2), z3) -> c7(MAPCONSAPP(z0, z2, z3)) by 
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, Cons(z0, z1), Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Cons(x3, x4))))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Cons(z0, z1))), x4))), SELECT(x2, Cons(x0, Cons(z0, z1)), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Cons(z0, z1), Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x2, Nil)))), mapconsapp(x2, permute(revapp(Cons(x0, Cons(z0, z1)), Nil)), Nil)), SELECT(x2, Cons(x0, Cons(z0, z1)), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Nil)) -> c5(SELECT(z0, Nil, Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(PERMUTE(Cons(z1, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
S tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
K tuples:
   SELECT(z0, z1, Cons(z2, z3)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3)), PERMUTE(revapp(z1, Cons(z2, z3))), REVAPP(z1, Cons(z2, z3)))
   SELECT(z0, z1, Nil) -> c2(MAPCONSAPP(z0, permute(revapp(z1, Nil)), Nil), PERMUTE(revapp(z1, Nil)), REVAPP(z1, Nil))
   SELECT(x0, Nil, Cons(x2, x3)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, x3)), select(x2, Cons(x0, Nil), x3)), SELECT(x2, Cons(x0, Nil), x3))
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Nil)) -> c5(SELECT(z0, Nil, Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c_3, c1_2, c1_1, c2_3, c2_2, c2_1, c3_1, c_2, c_1, c5_1, c4_1, c7_1


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

(147) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   SELECT(x0, Nil, Nil) -> c2(MAPCONSAPP(x0, Cons(Nil, Nil), Nil))
   PERMUTE(Cons(z0, Nil)) -> c5(SELECT(z0, Nil, Nil))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(PERMUTE(Cons(z1, Nil)))

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, x2), Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Cons(z2, z3))))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Cons(x1, x2))), z3))), SELECT(z0, Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   SELECT(x0, Cons(x1, x2), Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Nil)))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Nil)), Nil)), SELECT(z0, Cons(x0, Cons(x1, x2)), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(Cons(z0, Cons(z2, z3))), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Nil)), z3))), SELECT(z0, Cons(x0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
S tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
K tuples:
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c_3, c1_2, c1_1, c2_3, c2_2, c3_1, c_2, c_1, c5_1, c4_1, c7_1


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

(149) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil)) by SELECT(z0, Nil, Cons(z1, Nil)) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Nil))), Nil)), SELECT(z1, Cons(z0, Nil), Nil))
----------------------------------------

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4))))
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, x2), Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Cons(z2, z3))))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Cons(x1, x2))), z3))), SELECT(z0, Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   SELECT(x0, Cons(x1, x2), Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Nil)))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Nil)), Nil)), SELECT(z0, Cons(x0, Cons(x1, x2)), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(Cons(z0, Cons(z2, z3))), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Nil)), z3))), SELECT(z0, Cons(x0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Nil))), Nil)), SELECT(z1, Cons(z0, Nil), Nil))
S tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
K tuples:
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c_3, c1_2, c1_1, c2_3, c2_2, c3_1, c_2, c_1, c5_1, c4_1, c7_1


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

(151) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), PERMUTE(revapp(z1, Cons(x2, Cons(x3, x4)))), REVAPP(z1, Cons(x2, Cons(x3, x4)))) by 
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), mapconsapp(x3, permute(revapp(Cons(x0, x1), Cons(x2, Cons(z3, z4)))), select(z3, Cons(x3, Cons(x2, Cons(x0, x1))), z4))), PERMUTE(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), REVAPP(Cons(x0, x1), Cons(x3, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), mapconsapp(x4, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(z3, z4)))), select(z3, Cons(x4, Cons(x3, Cons(x0, Cons(x1, x2)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x4, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(x4, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(x2, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x2, Cons(x0, Cons(x1, Nil)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))))
   SELECT(x1, Cons(x0, Nil), Cons(x2, Cons(z3, z4))) -> c(MAPCONSAPP(x1, permute(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x1, Cons(z3, z4)))), select(z3, Cons(x2, Cons(x1, Cons(x0, Nil))), z4))), PERMUTE(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))), REVAPP(Cons(x0, Nil), Cons(x2, Cons(z3, z4))))
   SELECT(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x5, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(x5, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(x3, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x3, Cons(x0, Cons(x1, Cons(x2, Nil))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, x3))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, x3)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, x3)))), select(x2, Cons(x1, Cons(x0, Nil)), x3))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, x3)))), REVAPP(Nil, Cons(x1, Cons(x2, x3))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Cons(x3, x4)))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Cons(x3, x4))))), select(x2, Cons(x1, Cons(x0, Nil)), Cons(x3, x4)))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))), REVAPP(Nil, Cons(x1, Cons(x2, Cons(x3, x4)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Nil)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Nil)))), select(x2, Cons(x1, Cons(x0, Nil)), Nil))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Nil)))), REVAPP(Nil, Cons(x1, Cons(x2, Nil))))

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, x2), Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Cons(z2, z3))))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Cons(x1, x2))), z3))), SELECT(z0, Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   SELECT(x0, Cons(x1, x2), Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Nil)))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Nil)), Nil)), SELECT(z0, Cons(x0, Cons(x1, x2)), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(Cons(z0, Cons(z2, z3))), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Nil)), z3))), SELECT(z0, Cons(x0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Nil))), Nil)), SELECT(z1, Cons(z0, Nil), Nil))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), mapconsapp(x3, permute(revapp(Cons(x0, x1), Cons(x2, Cons(z3, z4)))), select(z3, Cons(x3, Cons(x2, Cons(x0, x1))), z4))), PERMUTE(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), REVAPP(Cons(x0, x1), Cons(x3, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), mapconsapp(x4, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(z3, z4)))), select(z3, Cons(x4, Cons(x3, Cons(x0, Cons(x1, x2)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x4, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(x4, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(x2, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x2, Cons(x0, Cons(x1, Nil)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))))
   SELECT(x1, Cons(x0, Nil), Cons(x2, Cons(z3, z4))) -> c(MAPCONSAPP(x1, permute(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x1, Cons(z3, z4)))), select(z3, Cons(x2, Cons(x1, Cons(x0, Nil))), z4))), PERMUTE(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))), REVAPP(Cons(x0, Nil), Cons(x2, Cons(z3, z4))))
   SELECT(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x5, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(x5, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(x3, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x3, Cons(x0, Cons(x1, Cons(x2, Nil))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, x3))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, x3)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, x3)))), select(x2, Cons(x1, Cons(x0, Nil)), x3))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, x3)))), REVAPP(Nil, Cons(x1, Cons(x2, x3))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Cons(x3, x4)))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Cons(x3, x4))))), select(x2, Cons(x1, Cons(x0, Nil)), Cons(x3, x4)))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))), REVAPP(Nil, Cons(x1, Cons(x2, Cons(x3, x4)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Nil)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Nil)))), select(x2, Cons(x1, Cons(x0, Nil)), Nil))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Nil)))), REVAPP(Nil, Cons(x1, Cons(x2, Nil))))
S tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
K tuples:
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c_3, c1_2, c1_1, c2_3, c2_2, c3_1, c_2, c_1, c5_1, c4_1, c7_1


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

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, x2), Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Cons(z2, z3))))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Cons(x1, x2))), z3))), SELECT(z0, Cons(x0, Cons(x1, x2)), Cons(z2, z3)))
   SELECT(x0, Cons(x1, x2), Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Nil)))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Nil)), Nil)), SELECT(z0, Cons(x0, Cons(x1, x2)), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(Cons(z0, Cons(z2, z3))), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Nil)), z3))), SELECT(z0, Cons(x0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Nil))), Nil)), SELECT(z1, Cons(z0, Nil), Nil))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), mapconsapp(x3, permute(revapp(Cons(x0, x1), Cons(x2, Cons(z3, z4)))), select(z3, Cons(x3, Cons(x2, Cons(x0, x1))), z4))), PERMUTE(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), REVAPP(Cons(x0, x1), Cons(x3, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), mapconsapp(x4, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(z3, z4)))), select(z3, Cons(x4, Cons(x3, Cons(x0, Cons(x1, x2)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x4, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(x4, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(x2, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x2, Cons(x0, Cons(x1, Nil)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))))
   SELECT(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x5, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(x5, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(x3, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x3, Cons(x0, Cons(x1, Cons(x2, Nil))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))))
   SELECT(x1, Cons(x0, Nil), Cons(x2, Cons(z3, z4))) -> c(MAPCONSAPP(x1, permute(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x1, Cons(z3, z4)))), select(z3, Cons(x2, Cons(x1, Cons(x0, Nil))), z4))), PERMUTE(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, x3))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, x3)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, x3)))), select(x2, Cons(x1, Cons(x0, Nil)), x3))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, x3)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Cons(x3, x4)))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Cons(x3, x4))))), select(x2, Cons(x1, Cons(x0, Nil)), Cons(x3, x4)))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Nil)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Nil)))), select(x2, Cons(x1, Cons(x0, Nil)), Nil))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Nil)))))
S tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
K tuples:
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c_3, c1_2, c1_1, c2_3, c2_2, c3_1, c_2, c_1, c5_1, c4_1, c7_1


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

(155) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Cons(x1, x2), Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Cons(z2, z3))))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Cons(x1, x2))), z3))), SELECT(z0, Cons(x0, Cons(x1, x2)), Cons(z2, z3))) by SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
----------------------------------------

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, x2), Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Nil)))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Nil)), Nil)), SELECT(z0, Cons(x0, Cons(x1, x2)), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(Cons(z0, Cons(z2, z3))), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Nil)), z3))), SELECT(z0, Cons(x0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Nil))), Nil)), SELECT(z1, Cons(z0, Nil), Nil))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), mapconsapp(x3, permute(revapp(Cons(x0, x1), Cons(x2, Cons(z3, z4)))), select(z3, Cons(x3, Cons(x2, Cons(x0, x1))), z4))), PERMUTE(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), REVAPP(Cons(x0, x1), Cons(x3, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), mapconsapp(x4, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(z3, z4)))), select(z3, Cons(x4, Cons(x3, Cons(x0, Cons(x1, x2)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x4, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(x4, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(x2, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x2, Cons(x0, Cons(x1, Nil)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))))
   SELECT(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x5, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(x5, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(x3, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x3, Cons(x0, Cons(x1, Cons(x2, Nil))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))))
   SELECT(x1, Cons(x0, Nil), Cons(x2, Cons(z3, z4))) -> c(MAPCONSAPP(x1, permute(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x1, Cons(z3, z4)))), select(z3, Cons(x2, Cons(x1, Cons(x0, Nil))), z4))), PERMUTE(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, x3))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, x3)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, x3)))), select(x2, Cons(x1, Cons(x0, Nil)), x3))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, x3)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Cons(x3, x4)))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Cons(x3, x4))))), select(x2, Cons(x1, Cons(x0, Nil)), Cons(x3, x4)))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Nil)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Nil)))), select(x2, Cons(x1, Cons(x0, Nil)), Nil))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Nil)))))
S tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
K tuples:
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c_3, c1_2, c1_1, c2_3, c2_2, c3_1, c_2, c_1, c5_1, c4_1, c7_1


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

(157) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Cons(x1, x2), Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(revapp(x2, Cons(x1, Cons(z0, Nil)))), mapconsapp(z0, permute(revapp(Cons(x0, Cons(x1, x2)), Nil)), Nil)), SELECT(z0, Cons(x0, Cons(x1, x2)), Nil)) by SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
----------------------------------------

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(Cons(z0, Cons(z2, z3))), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Nil)), z3))), SELECT(z0, Cons(x0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Nil))), Nil)), SELECT(z1, Cons(z0, Nil), Nil))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), mapconsapp(x3, permute(revapp(Cons(x0, x1), Cons(x2, Cons(z3, z4)))), select(z3, Cons(x3, Cons(x2, Cons(x0, x1))), z4))), PERMUTE(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), REVAPP(Cons(x0, x1), Cons(x3, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), mapconsapp(x4, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(z3, z4)))), select(z3, Cons(x4, Cons(x3, Cons(x0, Cons(x1, x2)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x4, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(x4, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(x2, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x2, Cons(x0, Cons(x1, Nil)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))))
   SELECT(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x5, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(x5, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(x3, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x3, Cons(x0, Cons(x1, Cons(x2, Nil))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))))
   SELECT(x1, Cons(x0, Nil), Cons(x2, Cons(z3, z4))) -> c(MAPCONSAPP(x1, permute(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x1, Cons(z3, z4)))), select(z3, Cons(x2, Cons(x1, Cons(x0, Nil))), z4))), PERMUTE(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, x3))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, x3)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, x3)))), select(x2, Cons(x1, Cons(x0, Nil)), x3))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, x3)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Cons(x3, x4)))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Cons(x3, x4))))), select(x2, Cons(x1, Cons(x0, Nil)), Cons(x3, x4)))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Nil)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Nil)))), select(x2, Cons(x1, Cons(x0, Nil)), Nil))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Nil)))))
S tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
K tuples:
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c_3, c1_2, c1_1, c2_3, c2_2, c3_1, c_2, c_1, c5_1, c4_1, c7_1


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

(159) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), SELECT(x3, Cons(x0, Cons(x1, Nil)), x4)) by SELECT(z0, Cons(z1, Nil), Cons(z2, z3)) -> c1(MAPCONSAPP(z0, select(z1, Nil, Cons(z2, z3)), select(z2, Cons(z0, Cons(z1, Nil)), z3)), SELECT(z2, Cons(z0, Cons(z1, Nil)), z3))
----------------------------------------

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil)))
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(Cons(z0, Cons(z2, z3))), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Nil)), z3))), SELECT(z0, Cons(x0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Nil))), Nil)), SELECT(z1, Cons(z0, Nil), Nil))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), mapconsapp(x3, permute(revapp(Cons(x0, x1), Cons(x2, Cons(z3, z4)))), select(z3, Cons(x3, Cons(x2, Cons(x0, x1))), z4))), PERMUTE(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), REVAPP(Cons(x0, x1), Cons(x3, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), mapconsapp(x4, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(z3, z4)))), select(z3, Cons(x4, Cons(x3, Cons(x0, Cons(x1, x2)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x4, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(x4, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(x2, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x2, Cons(x0, Cons(x1, Nil)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))))
   SELECT(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x5, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(x5, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(x3, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x3, Cons(x0, Cons(x1, Cons(x2, Nil))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))))
   SELECT(x1, Cons(x0, Nil), Cons(x2, Cons(z3, z4))) -> c(MAPCONSAPP(x1, permute(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x1, Cons(z3, z4)))), select(z3, Cons(x2, Cons(x1, Cons(x0, Nil))), z4))), PERMUTE(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, x3))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, x3)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, x3)))), select(x2, Cons(x1, Cons(x0, Nil)), x3))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, x3)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Cons(x3, x4)))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Cons(x3, x4))))), select(x2, Cons(x1, Cons(x0, Nil)), Cons(x3, x4)))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Nil)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Nil)))), select(x2, Cons(x1, Cons(x0, Nil)), Nil))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Nil)))))
   SELECT(z0, Cons(z1, Nil), Cons(z2, z3)) -> c1(MAPCONSAPP(z0, select(z1, Nil, Cons(z2, z3)), select(z2, Cons(z0, Cons(z1, Nil)), z3)), SELECT(z2, Cons(z0, Cons(z1, Nil)), z3))
S tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
   SELECT(z0, Cons(z1, Nil), Cons(z2, z3)) -> c1(MAPCONSAPP(z0, select(z1, Nil, Cons(z2, z3)), select(z2, Cons(z0, Cons(z1, Nil)), z3)), SELECT(z2, Cons(z0, Cons(z1, Nil)), z3))
K tuples:
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c_3, c1_2, c1_1, c2_3, c2_2, c3_1, c_2, c_1, c5_1, c4_1, c7_1


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

(161) CdtInstantiationProof (BOTH BOUNDS(ID, ID))
Use instantiation to replace SELECT(z0, z1, Cons(x2, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), PERMUTE(revapp(z1, Cons(x2, Nil))), REVAPP(z1, Cons(x2, Nil))) by 
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, x1), Cons(x3, Nil))), mapconsapp(x3, permute(revapp(Cons(x0, x1), Cons(x2, Nil))), Nil)), PERMUTE(revapp(Cons(x0, x1), Cons(x3, Nil))), REVAPP(Cons(x0, x1), Cons(x3, Nil)))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil)) -> c(MAPCONSAPP(x4, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(x4, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(z2, Nil)) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x3, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, x2)), Cons(z2, Nil)))
   SELECT(x1, Cons(x0, Nil), Cons(x2, Nil)) -> c(MAPCONSAPP(x1, permute(revapp(Cons(x0, Nil), Cons(x2, Nil))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x1, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Nil), Cons(x2, Nil))), REVAPP(Cons(x0, Nil), Cons(x2, Nil)))
   SELECT(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil)) -> c(MAPCONSAPP(x5, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(x5, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil)))
   SELECT(x3, Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil)) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(x3, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil)))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, Nil)) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(x2, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Nil)), Cons(z2, Nil)))
   SELECT(x0, Nil, Cons(x1, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Nil))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Nil))), Nil)), PERMUTE(revapp(Nil, Cons(x1, Nil))), REVAPP(Nil, Cons(x1, Nil)))

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(Cons(z0, Cons(z2, z3))), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Nil)), z3))), SELECT(z0, Cons(x0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Nil))), Nil)), SELECT(z1, Cons(z0, Nil), Nil))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), mapconsapp(x3, permute(revapp(Cons(x0, x1), Cons(x2, Cons(z3, z4)))), select(z3, Cons(x3, Cons(x2, Cons(x0, x1))), z4))), PERMUTE(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), REVAPP(Cons(x0, x1), Cons(x3, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), mapconsapp(x4, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(z3, z4)))), select(z3, Cons(x4, Cons(x3, Cons(x0, Cons(x1, x2)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x4, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(x4, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(x2, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x2, Cons(x0, Cons(x1, Nil)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))))
   SELECT(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x5, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(x5, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(x3, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x3, Cons(x0, Cons(x1, Cons(x2, Nil))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))))
   SELECT(x1, Cons(x0, Nil), Cons(x2, Cons(z3, z4))) -> c(MAPCONSAPP(x1, permute(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x1, Cons(z3, z4)))), select(z3, Cons(x2, Cons(x1, Cons(x0, Nil))), z4))), PERMUTE(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, x3))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, x3)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, x3)))), select(x2, Cons(x1, Cons(x0, Nil)), x3))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, x3)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Cons(x3, x4)))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Cons(x3, x4))))), select(x2, Cons(x1, Cons(x0, Nil)), Cons(x3, x4)))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Nil)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Nil)))), select(x2, Cons(x1, Cons(x0, Nil)), Nil))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Nil)))))
   SELECT(z0, Cons(z1, Nil), Cons(z2, z3)) -> c1(MAPCONSAPP(z0, select(z1, Nil, Cons(z2, z3)), select(z2, Cons(z0, Cons(z1, Nil)), z3)), SELECT(z2, Cons(z0, Cons(z1, Nil)), z3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, x1), Cons(x3, Nil))), mapconsapp(x3, permute(revapp(Cons(x0, x1), Cons(x2, Nil))), Nil)), PERMUTE(revapp(Cons(x0, x1), Cons(x3, Nil))), REVAPP(Cons(x0, x1), Cons(x3, Nil)))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil)) -> c(MAPCONSAPP(x4, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(x4, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(z2, Nil)) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x3, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, x2)), Cons(z2, Nil)))
   SELECT(x1, Cons(x0, Nil), Cons(x2, Nil)) -> c(MAPCONSAPP(x1, permute(revapp(Cons(x0, Nil), Cons(x2, Nil))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x1, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Nil), Cons(x2, Nil))), REVAPP(Cons(x0, Nil), Cons(x2, Nil)))
   SELECT(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil)) -> c(MAPCONSAPP(x5, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(x5, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil)))
   SELECT(x3, Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil)) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(x3, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil)))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, Nil)) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(x2, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Nil)), Cons(z2, Nil)))
   SELECT(x0, Nil, Cons(x1, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Nil))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Nil))), Nil)), PERMUTE(revapp(Nil, Cons(x1, Nil))), REVAPP(Nil, Cons(x1, Nil)))
S tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
   SELECT(z0, Cons(z1, Nil), Cons(z2, z3)) -> c1(MAPCONSAPP(z0, select(z1, Nil, Cons(z2, z3)), select(z2, Cons(z0, Cons(z1, Nil)), z3)), SELECT(z2, Cons(z0, Cons(z1, Nil)), z3))
K tuples:
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c1_2, c1_1, c2_3, c2_2, c_3, c3_1, c_2, c_1, c5_1, c4_1, c7_1


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

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(Cons(z0, Cons(z2, z3))), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Nil)), z3))), SELECT(z0, Cons(x0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Nil))), Nil)), SELECT(z1, Cons(z0, Nil), Nil))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), mapconsapp(x3, permute(revapp(Cons(x0, x1), Cons(x2, Cons(z3, z4)))), select(z3, Cons(x3, Cons(x2, Cons(x0, x1))), z4))), PERMUTE(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), REVAPP(Cons(x0, x1), Cons(x3, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), mapconsapp(x4, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(z3, z4)))), select(z3, Cons(x4, Cons(x3, Cons(x0, Cons(x1, x2)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x4, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(x4, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(x2, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x2, Cons(x0, Cons(x1, Nil)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))))
   SELECT(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x5, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(x5, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(x3, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x3, Cons(x0, Cons(x1, Cons(x2, Nil))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))))
   SELECT(x1, Cons(x0, Nil), Cons(x2, Cons(z3, z4))) -> c(MAPCONSAPP(x1, permute(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x1, Cons(z3, z4)))), select(z3, Cons(x2, Cons(x1, Cons(x0, Nil))), z4))), PERMUTE(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, x3))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, x3)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, x3)))), select(x2, Cons(x1, Cons(x0, Nil)), x3))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, x3)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Cons(x3, x4)))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Cons(x3, x4))))), select(x2, Cons(x1, Cons(x0, Nil)), Cons(x3, x4)))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Nil)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Nil)))), select(x2, Cons(x1, Cons(x0, Nil)), Nil))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Nil)))))
   SELECT(z0, Cons(z1, Nil), Cons(z2, z3)) -> c1(MAPCONSAPP(z0, select(z1, Nil, Cons(z2, z3)), select(z2, Cons(z0, Cons(z1, Nil)), z3)), SELECT(z2, Cons(z0, Cons(z1, Nil)), z3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, x1), Cons(x3, Nil))), mapconsapp(x3, permute(revapp(Cons(x0, x1), Cons(x2, Nil))), Nil)), PERMUTE(revapp(Cons(x0, x1), Cons(x3, Nil))), REVAPP(Cons(x0, x1), Cons(x3, Nil)))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil)) -> c(MAPCONSAPP(x4, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(x4, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(z2, Nil)) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x3, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, x2)), Cons(z2, Nil)))
   SELECT(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil)) -> c(MAPCONSAPP(x5, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(x5, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil)))
   SELECT(x3, Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil)) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(x3, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil)))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, Nil)) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(x2, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Nil)), Cons(z2, Nil)))
   SELECT(x1, Cons(x0, Nil), Cons(x2, Nil)) -> c(MAPCONSAPP(x1, permute(revapp(Cons(x0, Nil), Cons(x2, Nil))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x1, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Nil), Cons(x2, Nil))))
   SELECT(x0, Nil, Cons(x1, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Nil))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Nil))), Nil)), PERMUTE(revapp(Nil, Cons(x1, Nil))))
S tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
   SELECT(z0, Cons(z1, Nil), Cons(z2, z3)) -> c1(MAPCONSAPP(z0, select(z1, Nil, Cons(z2, z3)), select(z2, Cons(z0, Cons(z1, Nil)), z3)), SELECT(z2, Cons(z0, Cons(z1, Nil)), z3))
K tuples:
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c1_2, c1_1, c2_3, c2_2, c_3, c3_1, c_2, c_1, c5_1, c4_1, c7_1


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

(165) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Nil, Cons(z0, Cons(z2, z3))) -> c1(MAPCONSAPP(x0, permute(Cons(z0, Cons(z2, z3))), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Cons(z2, z3))), select(z2, Cons(z0, Cons(x0, Nil)), z3))), SELECT(z0, Cons(x0, Nil), Cons(z2, z3))) by SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
----------------------------------------

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Nil))), Nil)), SELECT(z1, Cons(z0, Nil), Nil))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), mapconsapp(x3, permute(revapp(Cons(x0, x1), Cons(x2, Cons(z3, z4)))), select(z3, Cons(x3, Cons(x2, Cons(x0, x1))), z4))), PERMUTE(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), REVAPP(Cons(x0, x1), Cons(x3, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), mapconsapp(x4, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(z3, z4)))), select(z3, Cons(x4, Cons(x3, Cons(x0, Cons(x1, x2)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x4, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(x4, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(x2, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x2, Cons(x0, Cons(x1, Nil)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))))
   SELECT(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x5, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(x5, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(x3, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x3, Cons(x0, Cons(x1, Cons(x2, Nil))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))))
   SELECT(x1, Cons(x0, Nil), Cons(x2, Cons(z3, z4))) -> c(MAPCONSAPP(x1, permute(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x1, Cons(z3, z4)))), select(z3, Cons(x2, Cons(x1, Cons(x0, Nil))), z4))), PERMUTE(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, x3))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, x3)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, x3)))), select(x2, Cons(x1, Cons(x0, Nil)), x3))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, x3)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Cons(x3, x4)))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Cons(x3, x4))))), select(x2, Cons(x1, Cons(x0, Nil)), Cons(x3, x4)))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Nil)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Nil)))), select(x2, Cons(x1, Cons(x0, Nil)), Nil))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Nil)))))
   SELECT(z0, Cons(z1, Nil), Cons(z2, z3)) -> c1(MAPCONSAPP(z0, select(z1, Nil, Cons(z2, z3)), select(z2, Cons(z0, Cons(z1, Nil)), z3)), SELECT(z2, Cons(z0, Cons(z1, Nil)), z3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, x1), Cons(x3, Nil))), mapconsapp(x3, permute(revapp(Cons(x0, x1), Cons(x2, Nil))), Nil)), PERMUTE(revapp(Cons(x0, x1), Cons(x3, Nil))), REVAPP(Cons(x0, x1), Cons(x3, Nil)))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil)) -> c(MAPCONSAPP(x4, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(x4, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(z2, Nil)) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x3, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, x2)), Cons(z2, Nil)))
   SELECT(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil)) -> c(MAPCONSAPP(x5, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(x5, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil)))
   SELECT(x3, Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil)) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(x3, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil)))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, Nil)) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(x2, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Nil)), Cons(z2, Nil)))
   SELECT(x1, Cons(x0, Nil), Cons(x2, Nil)) -> c(MAPCONSAPP(x1, permute(revapp(Cons(x0, Nil), Cons(x2, Nil))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x1, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Nil), Cons(x2, Nil))))
   SELECT(x0, Nil, Cons(x1, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Nil))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Nil))), Nil)), PERMUTE(revapp(Nil, Cons(x1, Nil))))
S tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
   SELECT(z0, Cons(z1, Nil), Cons(z2, z3)) -> c1(MAPCONSAPP(z0, select(z1, Nil, Cons(z2, z3)), select(z2, Cons(z0, Cons(z1, Nil)), z3)), SELECT(z2, Cons(z0, Cons(z1, Nil)), z3))
K tuples:
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c1_2, c1_1, c2_3, c2_2, c_3, c3_1, c_2, c_1, c5_1, c4_1, c7_1


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

(167) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace SELECT(x0, Nil, Cons(z0, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(z0, Nil)), mapconsapp(z0, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(z0, Cons(x0, Nil), Nil)) by SELECT(z0, Nil, Cons(z1, Nil)) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Nil))), Nil)), SELECT(z1, Cons(z0, Nil), Nil))
----------------------------------------

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   permute(Cons(z0, z1)) -> select(z0, Nil, z1)
   permute(Nil) -> Cons(Nil, Nil)
   revapp(Cons(z0, z1), z2) -> revapp(z1, Cons(z0, z2))
   revapp(Nil, z0) -> z0
   select(z0, z1, Cons(z2, z3)) -> mapconsapp(z0, permute(revapp(z1, Cons(z2, z3))), select(z2, Cons(z0, z1), z3))
   select(z0, z1, Nil) -> mapconsapp(z0, permute(revapp(z1, Nil)), Nil)
   mapconsapp(z0, Cons(z1, z2), z3) -> Cons(Cons(z0, z1), mapconsapp(z0, z2, z3))
   mapconsapp(z0, Nil, z1) -> z1
Tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   SELECT(x0, Nil, Cons(z0, z1)) -> c1(MAPCONSAPP(x0, select(z0, Nil, z1), select(z0, Cons(x0, Nil), z1)), SELECT(z0, Cons(x0, Nil), z1))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Nil) -> c2(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Nil)))), Nil), PERMUTE(revapp(Cons(x1, Cons(z0, z1)), Nil)), REVAPP(Cons(x1, Cons(z0, z1)), Nil))
   SELECT(x0, Cons(x1, x2), Nil) -> c2(PERMUTE(revapp(Cons(x1, x2), Nil)), REVAPP(Cons(x1, x2), Nil))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), REVAPP(z1, Cons(z2, Cons(z3, Cons(z4, z5)))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), PERMUTE(revapp(z1, Cons(z2, Cons(z3, Nil)))), REVAPP(z1, Cons(z2, Cons(z3, Nil))))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(x0, Cons(x1, Nil), Cons(x3, x4)) -> c(MAPCONSAPP(x0, permute(Cons(x1, Cons(x3, x4))), select(x3, Cons(x0, Cons(x1, Nil)), x4)), PERMUTE(revapp(Cons(x1, Nil), Cons(x3, x4))))
   SELECT(x0, Cons(x1, Nil), Nil) -> c2(MAPCONSAPP(x0, permute(Cons(x1, Nil)), Nil), PERMUTE(revapp(Cons(x1, Nil), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Cons(z4, z5))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), REVAPP(Cons(z1, z2), Cons(z3, Cons(z4, z5))))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Cons(z2, z3))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), PERMUTE(Cons(z1, Cons(z2, z3))))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z0, Cons(z1, z2)), Nil)), Nil)), PERMUTE(revapp(z2, Cons(z1, Cons(z3, Nil)))), REVAPP(Cons(z1, z2), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, Cons(z2, z3)), Cons(z4, z5)) -> c(MAPCONSAPP(z0, permute(revapp(z3, Cons(z2, Cons(z1, Cons(z4, z5))))), select(z4, Cons(z0, Cons(z1, Cons(z2, z3))), z5)), PERMUTE(revapp(Cons(z2, z3), Cons(z1, Cons(z4, z5)))), REVAPP(Cons(z1, Cons(z2, z3)), Cons(z4, z5)))
   SELECT(z0, Cons(z1, z2), Cons(z3, z4)) -> c(PERMUTE(revapp(z2, Cons(z1, Cons(z3, z4)))), REVAPP(Cons(z1, z2), Cons(z3, z4)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(MAPCONSAPP(z0, select(z1, Nil, z2), select(z1, Cons(z0, Nil), z2)), PERMUTE(Cons(z1, z2)))
   SELECT(z0, Nil, Cons(z1, z2)) -> c(PERMUTE(Cons(z1, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(z0, Nil, Cons(z1, Cons(z2, z3))) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Cons(z2, z3))), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Cons(z2, z3)))), select(z2, Cons(z1, Cons(z0, Nil)), z3))), SELECT(z1, Cons(z0, Nil), Cons(z2, z3)))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c4(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Cons(z0, Nil), Nil)), Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
   SELECT(z0, Nil, Cons(z1, Nil)) -> c1(MAPCONSAPP(z0, permute(Cons(z1, Nil)), mapconsapp(z1, permute(revapp(Nil, Cons(z0, Nil))), Nil)), SELECT(z1, Cons(z0, Nil), Nil))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), mapconsapp(x3, permute(revapp(Cons(x0, x1), Cons(x2, Cons(z3, z4)))), select(z3, Cons(x3, Cons(x2, Cons(x0, x1))), z4))), PERMUTE(revapp(Cons(x0, x1), Cons(x3, Cons(z3, z4)))), REVAPP(Cons(x0, x1), Cons(x3, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), mapconsapp(x4, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x3, Cons(z3, z4)))), select(z3, Cons(x4, Cons(x3, Cons(x0, Cons(x1, x2)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, x2)), Cons(x4, Cons(z3, z4))))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x4, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(x4, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Cons(z3, z4))))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(x2, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x2, Cons(x0, Cons(x1, Nil)))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Nil)), Cons(z2, Cons(z3, z4))))
   SELECT(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x5, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(x5, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Cons(z3, z4))))
   SELECT(x3, Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(x3, Cons(z3, z4)))), select(z3, Cons(z2, Cons(x3, Cons(x0, Cons(x1, Cons(x2, Nil))))), z4))), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4)))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Cons(z3, z4))))
   SELECT(x1, Cons(x0, Nil), Cons(x2, Cons(z3, z4))) -> c(MAPCONSAPP(x1, permute(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x1, Cons(z3, z4)))), select(z3, Cons(x2, Cons(x1, Cons(x0, Nil))), z4))), PERMUTE(revapp(Cons(x0, Nil), Cons(x2, Cons(z3, z4)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, x3))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, x3)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, x3)))), select(x2, Cons(x1, Cons(x0, Nil)), x3))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, x3)))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Cons(x3, x4)))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Cons(x3, x4))))), select(x2, Cons(x1, Cons(x0, Nil)), Cons(x3, x4)))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Cons(x3, x4))))))
   SELECT(x0, Nil, Cons(x1, Cons(x2, Nil))) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Cons(x2, Nil)))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Cons(x2, Nil)))), select(x2, Cons(x1, Cons(x0, Nil)), Nil))), PERMUTE(revapp(Nil, Cons(x1, Cons(x2, Nil)))))
   SELECT(z0, Cons(z1, Nil), Cons(z2, z3)) -> c1(MAPCONSAPP(z0, select(z1, Nil, Cons(z2, z3)), select(z2, Cons(z0, Cons(z1, Nil)), z3)), SELECT(z2, Cons(z0, Cons(z1, Nil)), z3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, x1), Cons(x3, Nil))), mapconsapp(x3, permute(revapp(Cons(x0, x1), Cons(x2, Nil))), Nil)), PERMUTE(revapp(Cons(x0, x1), Cons(x3, Nil))), REVAPP(Cons(x0, x1), Cons(x3, Nil)))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil)) -> c(MAPCONSAPP(x4, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(x4, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, Nil)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(z2, Nil)) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, x2)), Cons(x3, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, x2)), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, x2)), Cons(z2, Nil)))
   SELECT(x5, Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil)) -> c(MAPCONSAPP(x5, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(x5, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Cons(x3, x4)))), Cons(z2, Nil)))
   SELECT(x3, Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil)) -> c(MAPCONSAPP(x3, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(x3, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Cons(x2, Nil))), Cons(z2, Nil)))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, Nil)) -> c(MAPCONSAPP(x2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Nil))), mapconsapp(z2, permute(revapp(Cons(x0, Cons(x1, Nil)), Cons(x2, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Cons(x1, Nil)), Cons(z2, Nil))), REVAPP(Cons(x0, Cons(x1, Nil)), Cons(z2, Nil)))
   SELECT(x1, Cons(x0, Nil), Cons(x2, Nil)) -> c(MAPCONSAPP(x1, permute(revapp(Cons(x0, Nil), Cons(x2, Nil))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x1, Nil))), Nil)), PERMUTE(revapp(Cons(x0, Nil), Cons(x2, Nil))))
   SELECT(x0, Nil, Cons(x1, Nil)) -> c(MAPCONSAPP(x0, permute(revapp(Nil, Cons(x1, Nil))), mapconsapp(x1, permute(revapp(Nil, Cons(x0, Nil))), Nil)), PERMUTE(revapp(Nil, Cons(x1, Nil))))
S tuples:
   SELECT(z0, z1, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Cons(x3, x4)))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Cons(x3, x4)))), select(x3, Cons(x2, Cons(z0, z1)), x4))), SELECT(x2, Cons(z0, z1), Cons(x3, x4)))
   SELECT(x0, x1, Cons(x2, Cons(x3, x4))) -> c1(SELECT(x2, Cons(x0, x1), Cons(x3, x4)))
   SELECT(z0, z1, Cons(x2, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(x2, Nil))), mapconsapp(x2, permute(revapp(z1, Cons(z0, Nil))), Nil)), SELECT(x2, Cons(z0, z1), Nil))
   SELECT(x0, x1, Cons(x2, Nil)) -> c1(SELECT(x2, Cons(x0, x1), Nil))
   SELECT(x0, Cons(x1, Cons(z0, z1)), Cons(x3, x4)) -> c1(MAPCONSAPP(x0, permute(revapp(z1, Cons(z0, Cons(x1, Cons(x3, x4))))), select(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4)), SELECT(x3, Cons(x0, Cons(x1, Cons(z0, z1))), x4))
   SELECT(x0, Cons(x1, x2), Cons(x3, x4)) -> c1(SELECT(x3, Cons(x0, Cons(x1, x2)), x4))
   REVAPP(Cons(z0, Cons(y0, y1)), z2) -> c3(REVAPP(Cons(y0, y1), Cons(z0, z2)))
   SELECT(z0, z1, Cons(z2, Cons(z3, Cons(z4, z5)))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Cons(z4, z5))))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Cons(z4, z5)))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z2, Cons(z0, z1))), z5)))), SELECT(z2, Cons(z0, z1), Cons(z3, Cons(z4, z5))))
   SELECT(z0, z1, Cons(z2, Cons(z3, Nil))) -> c1(MAPCONSAPP(z0, permute(revapp(z1, Cons(z2, Cons(z3, Nil)))), mapconsapp(z2, permute(revapp(Cons(z0, z1), Cons(z3, Nil))), mapconsapp(z3, permute(revapp(Cons(z0, z1), Cons(z2, Nil))), Nil))), SELECT(z2, Cons(z0, z1), Cons(z3, Nil)))
   SELECT(z0, Cons(z1, z2), Cons(z3, Cons(z4, z5))) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Cons(z4, z5))))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Cons(z4, z5)))), select(z4, Cons(z3, Cons(z0, Cons(z1, z2))), z5))), SELECT(z3, Cons(z0, Cons(z1, z2)), Cons(z4, z5)))
   SELECT(x3, Cons(x0, Cons(x1, x2)), Cons(x4, x5)) -> c1(SELECT(x4, Cons(x3, Cons(x0, Cons(x1, x2))), x5))
   SELECT(x4, Cons(x0, Cons(x1, Cons(x2, x3))), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x4, Cons(x0, Cons(x1, Cons(x2, x3)))), z3))
   SELECT(x2, Cons(x0, Cons(x1, Nil)), Cons(z2, z3)) -> c1(SELECT(z2, Cons(x2, Cons(x0, Cons(x1, Nil))), z3))
   SELECT(x1, Cons(x0, Nil), Cons(x2, x3)) -> c1(SELECT(x2, Cons(x1, Cons(x0, Nil)), x3))
   SELECT(x2, Cons(x0, x1), Cons(x3, Cons(x4, x5))) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Cons(x4, x5)))
   SELECT(x2, Cons(x0, x1), Cons(x3, Nil)) -> c1(SELECT(x3, Cons(x2, Cons(x0, x1)), Nil))
   SELECT(z0, Cons(z1, z2), Cons(z3, Nil)) -> c1(MAPCONSAPP(z0, permute(revapp(z2, Cons(z1, Cons(z3, Nil)))), mapconsapp(z3, permute(revapp(Cons(z1, z2), Cons(z0, Nil))), Nil)), SELECT(z3, Cons(z0, Cons(z1, z2)), Nil))
   MAPCONSAPP(z0, Cons(z1, Cons(y1, y2)), z3) -> c7(MAPCONSAPP(z0, Cons(y1, y2), z3))
   SELECT(z0, Cons(z1, Nil), Cons(z2, z3)) -> c1(MAPCONSAPP(z0, select(z1, Nil, Cons(z2, z3)), select(z2, Cons(z0, Cons(z1, Nil)), z3)), SELECT(z2, Cons(z0, Cons(z1, Nil)), z3))
K tuples:
   SELECT(x0, Nil, Cons(x2, Cons(x3, x4))) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Cons(x3, x4))), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Cons(x3, x4))), select(x3, Cons(x2, Cons(x0, Nil)), x4))), SELECT(x2, Cons(x0, Nil), Cons(x3, x4)))
   SELECT(x0, Nil, Cons(x2, Nil)) -> c1(MAPCONSAPP(x0, permute(Cons(x2, Nil)), mapconsapp(x2, permute(revapp(Cons(x0, Nil), Nil)), Nil)), SELECT(x2, Cons(x0, Nil), Nil))
   SELECT(x0, Nil, Cons(z2, z3)) -> c1(SELECT(z2, Cons(x0, Nil), z3))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, y4)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, y4))))
   PERMUTE(Cons(z0, Cons(y2, Nil))) -> c5(SELECT(z0, Nil, Cons(y2, Nil)))
   PERMUTE(Cons(z0, Cons(y1, y2))) -> c5(SELECT(z0, Nil, Cons(y1, y2)))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Cons(y4, y5))))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Cons(y4, y5)))))
   PERMUTE(Cons(z0, Cons(y2, Cons(y3, Nil)))) -> c5(SELECT(z0, Nil, Cons(y2, Cons(y3, Nil))))
Defined Rule Symbols:   permute_1, revapp_2, select_3, mapconsapp_3

Defined Pair Symbols:   SELECT_3, REVAPP_2, PERMUTE_1, MAPCONSAPP_3

Compound Symbols:   c1_2, c1_1, c2_3, c2_2, c_3, c3_1, c_2, c_1, c5_1, c4_1, c7_1