/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


KILLED
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 89 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 2 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 0 ms]
    (10) typed CpxTrs
    (11) RewriteLemmaProof [LOWER BOUND(ID), 515 ms]
    (12) BOUNDS(1, INF)
(13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(14) TRS for Loop Detection
(15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(16) CpxTRS
(17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(18) CpxRelTRS
    (19) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxRelTRS
    (21) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxWeightedTrs
        (23) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxWeightedTrs
        (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (26) CpxTypedWeightedTrs
        (27) CompletionProof [UPPER BOUND(ID), 0 ms]
        (28) CpxTypedWeightedCompleteTrs
            (29) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
            (30) CpxTypedWeightedCompleteTrs
            (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (32) CpxRNTS
            (33) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
            (34) CpxRNTS
        (35) CompletionProof [UPPER BOUND(ID), 0 ms]
        (36) CpxTypedWeightedCompleteTrs
            (37) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (38) CpxRNTS
    (39) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
    (40) CdtProblem
        (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (42) CdtProblem
        (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (44) CdtProblem
        (45) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (46) CdtProblem
        (47) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (48) CdtProblem
        (49) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (54) CdtProblem
        (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [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) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (66) CdtProblem
        (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (68) CdtProblem
        (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (70) CdtProblem
        (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (72) CdtProblem
        (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (74) CdtProblem
        (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (76) CdtProblem
        (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (78) CdtProblem
        (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (80) CdtProblem
        (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (82) CdtProblem
        (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (84) CdtProblem
        (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (86) CdtProblem
        (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms]
        (88) CdtProblem
        (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms]
        (90) CdtProblem
        (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 55 ms]
        (92) CdtProblem
        (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (94) CdtProblem
        (95) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (96) CdtProblem
        (97) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (98) CdtProblem
        (99) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (100) CdtProblem
        (101) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (102) CdtProblem
        (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (104) CdtProblem
        (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 47 ms]
        (106) CdtProblem
        (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (108) CdtProblem
        (109) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (110) CdtProblem
        (111) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (112) CdtProblem
        (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (114) CdtProblem
        (115) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (116) CdtProblem
        (117) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (118) CdtProblem
        (119) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (120) CdtProblem
        (121) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (122) CdtProblem
        (123) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (124) CdtProblem
        (125) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 9 ms]
        (126) CdtProblem


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

(0)
Obligation:
The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   0(0(0(0(x1)))) -> 1(0(1(1(x1))))
   0(1(0(1(x1)))) -> 0(0(1(0(x1))))

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

(1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID))
The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem:

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))


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

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


The TRS R consists of the following rules:

   0(0(0(0(x1)))) -> 1(0(1(1(x1))))
   0(1(0(1(x1)))) -> 0(0(1(0(x1))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))

Rewrite Strategy: FULL
----------------------------------------

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

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


The TRS R consists of the following rules:

   0(0(0(0(x1)))) -> 1(0(1(1(x1))))
   0(1(0(1(x1)))) -> 0(0(1(0(x1))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))

Rewrite Strategy: FULL
----------------------------------------

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

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


The TRS R consists of the following rules:

   0(0(0(0(x1)))) -> 1(0(1(1(x1))))
   0(1(0(1(x1)))) -> 0(0(1(0(x1))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))

Rewrite Strategy: FULL
----------------------------------------

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

(8)
Obligation:
TRS:
Rules:
0(0(0(0(x1)))) -> 1(0(1(1(x1))))
0(1(0(1(x1)))) -> 0(0(1(0(x1))))
encArg(1(x_1)) -> 1(encArg(x_1))
encArg(cons_0(x_1)) -> 0(encArg(x_1))
encode_0(x_1) -> 0(encArg(x_1))
encode_1(x_1) -> 1(encArg(x_1))

Types:
0 :: 1:cons_0 -> 1:cons_0
1 :: 1:cons_0 -> 1:cons_0
encArg :: 1:cons_0 -> 1:cons_0
cons_0 :: 1:cons_0 -> 1:cons_0
encode_0 :: 1:cons_0 -> 1:cons_0
encode_1 :: 1:cons_0 -> 1:cons_0
hole_1:cons_01_2 :: 1:cons_0
gen_1:cons_02_2 :: Nat -> 1:cons_0

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

(9) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
0, encArg

They will be analysed ascendingly in the following order:
0 < encArg

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

(10)
Obligation:
TRS:
Rules:
0(0(0(0(x1)))) -> 1(0(1(1(x1))))
0(1(0(1(x1)))) -> 0(0(1(0(x1))))
encArg(1(x_1)) -> 1(encArg(x_1))
encArg(cons_0(x_1)) -> 0(encArg(x_1))
encode_0(x_1) -> 0(encArg(x_1))
encode_1(x_1) -> 1(encArg(x_1))

Types:
0 :: 1:cons_0 -> 1:cons_0
1 :: 1:cons_0 -> 1:cons_0
encArg :: 1:cons_0 -> 1:cons_0
cons_0 :: 1:cons_0 -> 1:cons_0
encode_0 :: 1:cons_0 -> 1:cons_0
encode_1 :: 1:cons_0 -> 1:cons_0
hole_1:cons_01_2 :: 1:cons_0
gen_1:cons_02_2 :: Nat -> 1:cons_0


Generator Equations:
gen_1:cons_02_2(0) <=> hole_1:cons_01_2
gen_1:cons_02_2(+(x, 1)) <=> 1(gen_1:cons_02_2(x))


The following defined symbols remain to be analysed:
0, encArg

They will be analysed ascendingly in the following order:
0 < encArg

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

(11) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_1:cons_02_2(+(1, n12_2))) -> *3_2, rt in Omega(0)

Induction Base:
encArg(gen_1:cons_02_2(+(1, 0)))

Induction Step:
encArg(gen_1:cons_02_2(+(1, +(n12_2, 1)))) ->_R^Omega(0)
1(encArg(gen_1:cons_02_2(+(1, n12_2)))) ->_IH
1(*3_2)

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

(12)
BOUNDS(1, INF)

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

(13) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
Transformed a relative TRS into a decreasing-loop problem.
----------------------------------------

(14)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

   0(0(0(0(x1)))) -> 1(0(1(1(x1))))
   0(1(0(1(x1)))) -> 0(0(1(0(x1))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))

Rewrite Strategy: FULL
----------------------------------------

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

(16)
Obligation:
The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   0(0(0(0(x1)))) -> 1(0(1(1(x1))))
   0(1(0(1(x1)))) -> 0(0(1(0(x1))))
   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))

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

(17) NonCtorToCtorProof (UPPER BOUND(ID))
transformed non-ctor to ctor-system
----------------------------------------

(18)
Obligation:
The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   0(1(c_0(1(x1)))) -> 0(0(1(0(x1))))
   0(c_0(c_0(c_0(x1)))) -> 1(0(1(1(x1))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   0(x0) -> c_0(x0)

Rewrite Strategy: FULL
----------------------------------------

(19) RcToIrcProof (BOTH BOUNDS(ID, ID))
Converted rc-obligation to irc-obligation.

As the TRS is a non-duplicating overlay system, we have rc = irc.
----------------------------------------

(20)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   0(1(c_0(1(x1)))) -> 0(0(1(0(x1))))
   0(c_0(c_0(c_0(x1)))) -> 1(0(1(1(x1))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   0(x0) -> c_0(x0)

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

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

(22)
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:

   0(1(c_0(1(x1)))) -> 0(0(1(0(x1)))) [1]
   0(c_0(c_0(c_0(x1)))) -> 1(0(1(1(x1)))) [1]
   encArg(1(x_1)) -> 1(encArg(x_1)) [0]
   encArg(cons_0(x_1)) -> 0(encArg(x_1)) [0]
   encode_0(x_1) -> 0(encArg(x_1)) [0]
   encode_1(x_1) -> 1(encArg(x_1)) [0]
   0(x0) -> c_0(x0) [0]

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

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

0 => 0'

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

(24)
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:

   0'(1(c_0(1(x1)))) -> 0'(0'(1(0'(x1)))) [1]
   0'(c_0(c_0(c_0(x1)))) -> 1(0'(1(1(x1)))) [1]
   encArg(1(x_1)) -> 1(encArg(x_1)) [0]
   encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0]
   encode_0(x_1) -> 0'(encArg(x_1)) [0]
   encode_1(x_1) -> 1(encArg(x_1)) [0]
   0'(x0) -> c_0(x0) [0]

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

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

(26)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   0'(1(c_0(1(x1)))) -> 0'(0'(1(0'(x1)))) [1]
   0'(c_0(c_0(c_0(x1)))) -> 1(0'(1(1(x1)))) [1]
   encArg(1(x_1)) -> 1(encArg(x_1)) [0]
   encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0]
   encode_0(x_1) -> 0'(encArg(x_1)) [0]
   encode_1(x_1) -> 1(encArg(x_1)) [0]
   0'(x0) -> c_0(x0) [0]

The TRS has the following type information:
0' :: 1:c_0:cons_0 -> 1:c_0:cons_0
1 :: 1:c_0:cons_0 -> 1:c_0:cons_0
c_0 :: 1:c_0:cons_0 -> 1:c_0:cons_0
encArg :: 1:c_0:cons_0 -> 1:c_0:cons_0
cons_0 :: 1:c_0:cons_0 -> 1:c_0:cons_0
encode_0 :: 1:c_0:cons_0 -> 1:c_0:cons_0
encode_1 :: 1:c_0:cons_0 -> 1:c_0:cons_0

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

(27) 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:
none

(c) The following functions are completely defined:

   encArg_1
   encode_0_1
   encode_1_1
   0'_1

Due to the following rules being added:

   encArg(v0) -> const [0]
   encode_0(v0) -> const [0]
   encode_1(v0) -> const [0]
   0'(v0) -> const [0]

And the following fresh constants:    const

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

(28)
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:

   0'(1(c_0(1(x1)))) -> 0'(0'(1(0'(x1)))) [1]
   0'(c_0(c_0(c_0(x1)))) -> 1(0'(1(1(x1)))) [1]
   encArg(1(x_1)) -> 1(encArg(x_1)) [0]
   encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0]
   encode_0(x_1) -> 0'(encArg(x_1)) [0]
   encode_1(x_1) -> 1(encArg(x_1)) [0]
   0'(x0) -> c_0(x0) [0]
   encArg(v0) -> const [0]
   encode_0(v0) -> const [0]
   encode_1(v0) -> const [0]
   0'(v0) -> const [0]

The TRS has the following type information:
0' :: 1:c_0:cons_0:const -> 1:c_0:cons_0:const
1 :: 1:c_0:cons_0:const -> 1:c_0:cons_0:const
c_0 :: 1:c_0:cons_0:const -> 1:c_0:cons_0:const
encArg :: 1:c_0:cons_0:const -> 1:c_0:cons_0:const
cons_0 :: 1:c_0:cons_0:const -> 1:c_0:cons_0:const
encode_0 :: 1:c_0:cons_0:const -> 1:c_0:cons_0:const
encode_1 :: 1:c_0:cons_0:const -> 1:c_0:cons_0:const
const :: 1:c_0:cons_0:const

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

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

(30)
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:

   0'(1(c_0(1(1(c_0(1(x1'))))))) -> 0'(0'(1(0'(0'(1(0'(x1'))))))) [2]
   0'(1(c_0(1(c_0(c_0(c_0(x1''))))))) -> 0'(0'(1(1(0'(1(1(x1''))))))) [2]
   0'(1(c_0(1(x1)))) -> 0'(0'(1(c_0(x1)))) [1]
   0'(1(c_0(1(x1)))) -> 0'(0'(1(const))) [1]
   0'(c_0(c_0(c_0(x1)))) -> 1(0'(1(1(x1)))) [1]
   encArg(1(x_1)) -> 1(encArg(x_1)) [0]
   encArg(cons_0(1(x_1'))) -> 0'(1(encArg(x_1'))) [0]
   encArg(cons_0(cons_0(x_1''))) -> 0'(0'(encArg(x_1''))) [0]
   encArg(cons_0(x_1)) -> 0'(const) [0]
   encode_0(1(x_11)) -> 0'(1(encArg(x_11))) [0]
   encode_0(cons_0(x_12)) -> 0'(0'(encArg(x_12))) [0]
   encode_0(x_1) -> 0'(const) [0]
   encode_1(x_1) -> 1(encArg(x_1)) [0]
   0'(x0) -> c_0(x0) [0]
   encArg(v0) -> const [0]
   encode_0(v0) -> const [0]
   encode_1(v0) -> const [0]
   0'(v0) -> const [0]

The TRS has the following type information:
0' :: 1:c_0:cons_0:const -> 1:c_0:cons_0:const
1 :: 1:c_0:cons_0:const -> 1:c_0:cons_0:const
c_0 :: 1:c_0:cons_0:const -> 1:c_0:cons_0:const
encArg :: 1:c_0:cons_0:const -> 1:c_0:cons_0:const
cons_0 :: 1:c_0:cons_0:const -> 1:c_0:cons_0:const
encode_0 :: 1:c_0:cons_0:const -> 1:c_0:cons_0:const
encode_1 :: 1:c_0:cons_0:const -> 1:c_0:cons_0:const
const :: 1:c_0:cons_0:const

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

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

   const => 0

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

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

   0'(z) -{ 2 }-> 0'(0'(1 + 0'(0'(1 + 0'(x1'))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x1'))))), x1' >= 0
   0'(z) -{ 1 }-> 0'(0'(1 + 0)) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   0'(z) -{ 1 }-> 0'(0'(1 + (1 + x1))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   0'(z) -{ 2 }-> 0'(0'(1 + (1 + 0'(1 + (1 + x1''))))) :|: x1'' >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x1'')))))
   0'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   0'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   0'(z) -{ 1 }-> 1 + 0'(1 + (1 + x1)) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   encArg(z) -{ 0 }-> 0'(0'(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0
   encArg(z) -{ 0 }-> 0'(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> 0'(1 + encArg(x_1')) :|: z = 1 + (1 + x_1'), x_1' >= 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_0(z) -{ 0 }-> 0'(0'(encArg(x_12))) :|: z = 1 + x_12, x_12 >= 0
   encode_0(z) -{ 0 }-> 0'(0) :|: x_1 >= 0, z = x_1
   encode_0(z) -{ 0 }-> 0'(1 + encArg(x_11)) :|: x_11 >= 0, z = 1 + x_11
   encode_0(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_1(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1


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

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

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

   0'(z) -{ 2 }-> 0'(0'(1 + 0'(0'(1 + 0'(z - 6))))) :|: z - 6 >= 0
   0'(z) -{ 1 }-> 0'(0'(1 + 0)) :|: z - 3 >= 0
   0'(z) -{ 2 }-> 0'(0'(1 + (1 + 0'(1 + (1 + (z - 6)))))) :|: z - 6 >= 0
   0'(z) -{ 1 }-> 0'(0'(1 + (1 + (z - 3)))) :|: z - 3 >= 0
   0'(z) -{ 0 }-> 0 :|: z >= 0
   0'(z) -{ 0 }-> 1 + z :|: z >= 0
   0'(z) -{ 1 }-> 1 + 0'(1 + (1 + (z - 3))) :|: z - 3 >= 0
   encArg(z) -{ 0 }-> 0'(0'(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0'(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> 0'(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_0(z) -{ 0 }-> 0'(0'(encArg(z - 1))) :|: z - 1 >= 0
   encode_0(z) -{ 0 }-> 0'(0) :|: z >= 0
   encode_0(z) -{ 0 }-> 0'(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_0(z) -{ 0 }-> 0 :|: z >= 0
   encode_1(z) -{ 0 }-> 0 :|: z >= 0
   encode_1(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0


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

(35) 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:

   encArg(v0) -> null_encArg [0]
   encode_0(v0) -> null_encode_0 [0]
   encode_1(v0) -> null_encode_1 [0]
   0'(v0) -> null_0' [0]

And the following fresh constants:    null_encArg, null_encode_0, null_encode_1, null_0'

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

(36)
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:

   0'(1(c_0(1(x1)))) -> 0'(0'(1(0'(x1)))) [1]
   0'(c_0(c_0(c_0(x1)))) -> 1(0'(1(1(x1)))) [1]
   encArg(1(x_1)) -> 1(encArg(x_1)) [0]
   encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0]
   encode_0(x_1) -> 0'(encArg(x_1)) [0]
   encode_1(x_1) -> 1(encArg(x_1)) [0]
   0'(x0) -> c_0(x0) [0]
   encArg(v0) -> null_encArg [0]
   encode_0(v0) -> null_encode_0 [0]
   encode_1(v0) -> null_encode_1 [0]
   0'(v0) -> null_0' [0]

The TRS has the following type information:
0' :: 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0' -> 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0'
1 :: 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0' -> 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0'
c_0 :: 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0' -> 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0'
encArg :: 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0' -> 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0'
cons_0 :: 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0' -> 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0'
encode_0 :: 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0' -> 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0'
encode_1 :: 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0' -> 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0'
null_encArg :: 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0'
null_encode_0 :: 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0'
null_encode_1 :: 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0'
null_0' :: 1:c_0:cons_0:null_encArg:null_encode_0:null_encode_1:null_0'

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

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

   null_encArg => 0
   null_encode_0 => 0
   null_encode_1 => 0
   null_0' => 0

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

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

   0'(z) -{ 1 }-> 0'(0'(1 + 0'(x1))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   0'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   0'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   0'(z) -{ 1 }-> 1 + 0'(1 + (1 + x1)) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   encArg(z) -{ 0 }-> 0'(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_0(z) -{ 0 }-> 0'(encArg(x_1)) :|: x_1 >= 0, z = x_1
   encode_0(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_1(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1

Only complete derivations are relevant for the runtime complexity.

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

(39) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS to CDT
----------------------------------------

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encode_0(z0) -> 0(encArg(z0))
   encode_1(z0) -> 1(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   ENCARG(cons_0(z0)) -> c1(0'(encArg(z0)), ENCARG(z0))
   ENCODE_0(z0) -> c2(0'(encArg(z0)), ENCARG(z0))
   ENCODE_1(z0) -> c3(ENCARG(z0))
   0'(z0) -> c4
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6(0'(1(1(z0))))
S tuples:
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6(0'(1(1(z0))))
K tuples:none
Defined Rule Symbols:   0_1, encArg_1, encode_0_1, encode_1_1

Defined Pair Symbols:   ENCARG_1, ENCODE_0_1, ENCODE_1_1, 0'_1

Compound Symbols:   c_1, c1_2, c2_2, c3_1, c4, c5_3, c6_1


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

(41) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   ENCODE_1(z0) -> c3(ENCARG(z0))
Removed 1 trailing nodes:
   0'(z0) -> c4

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encode_0(z0) -> 0(encArg(z0))
   encode_1(z0) -> 1(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   ENCARG(cons_0(z0)) -> c1(0'(encArg(z0)), ENCARG(z0))
   ENCODE_0(z0) -> c2(0'(encArg(z0)), ENCARG(z0))
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6(0'(1(1(z0))))
S tuples:
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6(0'(1(1(z0))))
K tuples:none
Defined Rule Symbols:   0_1, encArg_1, encode_0_1, encode_1_1

Defined Pair Symbols:   ENCARG_1, ENCODE_0_1, 0'_1

Compound Symbols:   c_1, c1_2, c2_2, c5_3, c6_1


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

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encode_0(z0) -> 0(encArg(z0))
   encode_1(z0) -> 1(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   ENCARG(cons_0(z0)) -> c1(0'(encArg(z0)), ENCARG(z0))
   ENCODE_0(z0) -> c2(0'(encArg(z0)), ENCARG(z0))
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
S tuples:
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
K tuples:none
Defined Rule Symbols:   0_1, encArg_1, encode_0_1, encode_1_1

Defined Pair Symbols:   ENCARG_1, ENCODE_0_1, 0'_1

Compound Symbols:   c_1, c1_2, c2_2, c5_3, c6


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

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encode_0(z0) -> 0(encArg(z0))
   encode_1(z0) -> 1(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   ENCARG(cons_0(z0)) -> c1(0'(encArg(z0)), ENCARG(z0))
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCODE_0(z0) -> c3(0'(encArg(z0)))
   ENCODE_0(z0) -> c3(ENCARG(z0))
S tuples:
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
K tuples:none
Defined Rule Symbols:   0_1, encArg_1, encode_0_1, encode_1_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c1_2, c5_3, c6, c3_1


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

(47) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   ENCODE_0(z0) -> c3(ENCARG(z0))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encode_0(z0) -> 0(encArg(z0))
   encode_1(z0) -> 1(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   ENCARG(cons_0(z0)) -> c1(0'(encArg(z0)), ENCARG(z0))
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCODE_0(z0) -> c3(0'(encArg(z0)))
S tuples:
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
K tuples:none
Defined Rule Symbols:   0_1, encArg_1, encode_0_1, encode_1_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c1_2, c5_3, c6, c3_1


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

(49) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   encode_0(z0) -> 0(encArg(z0))
   encode_1(z0) -> 1(encArg(z0))

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   ENCARG(cons_0(z0)) -> c1(0'(encArg(z0)), ENCARG(z0))
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCODE_0(z0) -> c3(0'(encArg(z0)))
S tuples:
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c1_2, c5_3, c6, c3_1


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_0(z0)) -> c1(0'(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_0(1(z0))) -> c1(0'(1(encArg(z0))), ENCARG(1(z0)))
   ENCARG(cons_0(cons_0(z0))) -> c1(0'(0(encArg(z0))), ENCARG(cons_0(z0)))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCODE_0(z0) -> c3(0'(encArg(z0)))
   ENCARG(cons_0(1(z0))) -> c1(0'(1(encArg(z0))), ENCARG(1(z0)))
   ENCARG(cons_0(cons_0(z0))) -> c1(0'(0(encArg(z0))), ENCARG(cons_0(z0)))
S tuples:
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c5_3, c6, c3_1, c1_2


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

(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace 0'(1(c_0(1(z0)))) -> c5(0'(0(1(0(z0)))), 0'(1(0(z0))), 0'(z0)) by 
   0'(1(c_0(1(x0)))) -> c5(0'(c_0(1(0(x0)))), 0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(c_0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCODE_0(z0) -> c3(0'(encArg(z0)))
   ENCARG(cons_0(1(z0))) -> c1(0'(1(encArg(z0))), ENCARG(1(z0)))
   ENCARG(cons_0(cons_0(z0))) -> c1(0'(0(encArg(z0))), ENCARG(cons_0(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(c_0(1(0(x0)))), 0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(c_0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(x0)))) -> c5(0'(c_0(1(0(x0)))), 0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(c_0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c3_1, c1_2, c5_3


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

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCODE_0(z0) -> c3(0'(encArg(z0)))
   ENCARG(cons_0(1(z0))) -> c1(0'(1(encArg(z0))), ENCARG(1(z0)))
   ENCARG(cons_0(cons_0(z0))) -> c1(0'(0(encArg(z0))), ENCARG(cons_0(z0)))
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(c_0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(c_0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c3_1, c1_2, c5_3, c5_2


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

(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_0(z0) -> c3(0'(encArg(z0))) by 
   ENCODE_0(1(z0)) -> c3(0'(1(encArg(z0))))
   ENCODE_0(cons_0(z0)) -> c3(0'(0(encArg(z0))))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(z0))) -> c1(0'(1(encArg(z0))), ENCARG(1(z0)))
   ENCARG(cons_0(cons_0(z0))) -> c1(0'(0(encArg(z0))), ENCARG(cons_0(z0)))
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(c_0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   ENCODE_0(1(z0)) -> c3(0'(1(encArg(z0))))
   ENCODE_0(cons_0(z0)) -> c3(0'(0(encArg(z0))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(c_0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c1_2, c5_3, c5_2, c3_1


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_0(1(z0))) -> c1(0'(1(encArg(z0))), ENCARG(1(z0))) by 
   ENCARG(cons_0(1(1(z0)))) -> c1(0'(1(1(encArg(z0)))), ENCARG(1(1(z0))))
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(cons_0(z0))) -> c1(0'(0(encArg(z0))), ENCARG(cons_0(z0)))
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(c_0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   ENCODE_0(1(z0)) -> c3(0'(1(encArg(z0))))
   ENCODE_0(cons_0(z0)) -> c3(0'(0(encArg(z0))))
   ENCARG(cons_0(1(1(z0)))) -> c1(0'(1(1(encArg(z0)))), ENCARG(1(1(z0))))
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(c_0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c1_2, c5_3, c5_2, c3_1, c1_1


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

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(cons_0(z0))) -> c1(0'(0(encArg(z0))), ENCARG(cons_0(z0)))
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(c_0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   ENCODE_0(1(z0)) -> c3(0'(1(encArg(z0))))
   ENCODE_0(cons_0(z0)) -> c3(0'(0(encArg(z0))))
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(c_0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c1_2, c5_3, c5_2, c3_1, c1_1


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_0(cons_0(z0))) -> c1(0'(0(encArg(z0))), ENCARG(cons_0(z0))) by 
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(c_0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   ENCODE_0(1(z0)) -> c3(0'(1(encArg(z0))))
   ENCODE_0(cons_0(z0)) -> c3(0'(0(encArg(z0))))
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(z0)))) -> c5(0'(0(1(c_0(z0)))), 0'(1(0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c5_3, c5_2, c3_1, c1_2, c1_1


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

(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace 0'(1(c_0(1(z0)))) -> c5(0'(0(1(c_0(z0)))), 0'(1(0(z0))), 0'(z0)) by 
   0'(1(c_0(1(x0)))) -> c5(0'(c_0(1(c_0(x0)))), 0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   ENCODE_0(1(z0)) -> c3(0'(1(encArg(z0))))
   ENCODE_0(cons_0(z0)) -> c3(0'(0(encArg(z0))))
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(x0)))) -> c5(0'(c_0(1(c_0(x0)))), 0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(x0)))) -> c5(0'(c_0(1(c_0(x0)))), 0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c5_3, c5_2, c3_1, c1_2, c1_1


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

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   ENCODE_0(1(z0)) -> c3(0'(1(encArg(z0))))
   ENCODE_0(cons_0(z0)) -> c3(0'(0(encArg(z0))))
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c5_3, c5_2, c3_1, c1_2, c1_1


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

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace 0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0))))) by 
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(c_0(1(0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   ENCODE_0(1(z0)) -> c3(0'(1(encArg(z0))))
   ENCODE_0(cons_0(z0)) -> c3(0'(0(encArg(z0))))
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(c_0(1(0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(c_0(1(0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c5_3, c5_2, c3_1, c1_2, c1_1, c5_1


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

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   ENCODE_0(1(z0)) -> c3(0'(1(encArg(z0))))
   ENCODE_0(cons_0(z0)) -> c3(0'(0(encArg(z0))))
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c5_3, c5_2, c3_1, c1_2, c1_1, c5_1


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

(73) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace 0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(0(1(1(0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0))))) by 
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(c_0(1(1(0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   ENCODE_0(1(z0)) -> c3(0'(1(encArg(z0))))
   ENCODE_0(cons_0(z0)) -> c3(0'(0(encArg(z0))))
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(c_0(1(1(0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(c_0(1(1(0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c5_2, c3_1, c1_2, c1_1, c5_3, c5_1


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

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   ENCODE_0(1(z0)) -> c3(0'(1(encArg(z0))))
   ENCODE_0(cons_0(z0)) -> c3(0'(0(encArg(z0))))
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c5_2, c3_1, c1_2, c1_1, c5_3, c5_1


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

(77) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace 0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0)) by 
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(1(1(0(1(1(z0)))))), 0'(c_0(c_0(c_0(z0)))))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   ENCODE_0(1(z0)) -> c3(0'(1(encArg(z0))))
   ENCODE_0(cons_0(z0)) -> c3(0'(0(encArg(z0))))
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(1(1(0(1(1(z0)))))), 0'(c_0(c_0(c_0(z0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(1(1(0(1(1(z0)))))), 0'(c_0(c_0(c_0(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c5_2, c3_1, c1_2, c1_1, c5_3, c5_1


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

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   ENCODE_0(1(z0)) -> c3(0'(1(encArg(z0))))
   ENCODE_0(cons_0(z0)) -> c3(0'(0(encArg(z0))))
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c5_2, c3_1, c1_2, c1_1, c5_3, c5_1


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

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_0(1(z0)) -> c3(0'(1(encArg(z0)))) by 
   ENCODE_0(1(1(z0))) -> c3(0'(1(1(encArg(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   ENCODE_0(cons_0(z0)) -> c3(0'(0(encArg(z0))))
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(1(z0))) -> c3(0'(1(1(encArg(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c5_2, c3_1, c1_2, c1_1, c5_3, c5_1


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

(83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   ENCODE_0(1(1(z0))) -> c3(0'(1(1(encArg(z0)))))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCODE_0(cons_0(z0)) -> c3(0'(0(encArg(z0))))
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c3_1, c1_2, c1_1, c5_3, c5_2, c5_1


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

(85) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_0(cons_0(z0)) -> c3(0'(0(encArg(z0)))) by 
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace 0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0))))) by 
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(c_0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(1(1(0(1(1(z0)))))), 0'(c_0(c_0(c_0(z0)))))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(c_0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(1(1(0(1(1(z0)))))), 0'(c_0(c_0(c_0(z0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(c_0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(1(1(0(1(1(z0)))))), 0'(c_0(c_0(c_0(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1


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

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace 0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0))))) by 
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(c_0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(1(1(0(1(1(z0)))))), 0'(c_0(c_0(c_0(z0)))))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(c_0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(1(1(0(1(1(z0)))))), 0'(c_0(c_0(c_0(z0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1


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

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1


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

(95) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0)))))))) by 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
----------------------------------------

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   ENCARG(1(z0)) -> c(ENCARG(z0))
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c_1, c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1


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

(97) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(1(z0)) -> c(ENCARG(z0)) by 
   ENCARG(1(1(y0))) -> c(ENCARG(1(y0)))
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(y0)))) -> c(ENCARG(cons_0(1(y0))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(cons_0(y0)))) -> c(ENCARG(cons_0(cons_0(y0))))
   ENCARG(1(cons_0(cons_0(1(y0))))) -> c(ENCARG(cons_0(cons_0(1(y0)))))
   ENCARG(1(cons_0(cons_0(cons_0(y0))))) -> c(ENCARG(cons_0(cons_0(cons_0(y0)))))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0)))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   ENCARG(1(1(y0))) -> c(ENCARG(1(y0)))
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(y0)))) -> c(ENCARG(cons_0(1(y0))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(cons_0(y0)))) -> c(ENCARG(cons_0(cons_0(y0))))
   ENCARG(1(cons_0(cons_0(1(y0))))) -> c(ENCARG(cons_0(cons_0(1(y0)))))
   ENCARG(1(cons_0(cons_0(cons_0(y0))))) -> c(ENCARG(cons_0(cons_0(cons_0(y0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   0'_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1, c_1


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

(99) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(cons_0(1(x0))) -> c1(ENCARG(1(x0))) by 
   ENCARG(cons_0(1(1(y0)))) -> c1(ENCARG(1(1(y0))))
   ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(cons_0(1(cons_0(1(y0))))) -> c1(ENCARG(1(cons_0(1(y0)))))
   ENCARG(cons_0(1(cons_0(1(1(y0)))))) -> c1(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(y0))))) -> c1(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(cons_0(y0))))))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   ENCARG(1(1(y0))) -> c(ENCARG(1(y0)))
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(y0)))) -> c(ENCARG(cons_0(1(y0))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(cons_0(y0)))) -> c(ENCARG(cons_0(cons_0(y0))))
   ENCARG(1(cons_0(cons_0(1(y0))))) -> c(ENCARG(cons_0(cons_0(1(y0)))))
   ENCARG(1(cons_0(cons_0(cons_0(y0))))) -> c(ENCARG(cons_0(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(cons_0(1(cons_0(1(y0))))) -> c1(ENCARG(1(cons_0(1(y0)))))
   ENCARG(cons_0(1(cons_0(1(1(y0)))))) -> c1(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(y0))))) -> c1(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   0'_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1, c_1


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

(101) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace 0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(0(1(1(c_0(1(1(x0))))))), 0'(1(0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0))))) by 0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(1(1(c_0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
----------------------------------------

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   ENCARG(1(1(y0))) -> c(ENCARG(1(y0)))
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(y0)))) -> c(ENCARG(cons_0(1(y0))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(cons_0(y0)))) -> c(ENCARG(cons_0(cons_0(y0))))
   ENCARG(1(cons_0(cons_0(1(y0))))) -> c(ENCARG(cons_0(cons_0(1(y0)))))
   ENCARG(1(cons_0(cons_0(cons_0(y0))))) -> c(ENCARG(cons_0(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(cons_0(1(cons_0(1(y0))))) -> c1(ENCARG(1(cons_0(1(y0)))))
   ENCARG(cons_0(1(cons_0(1(1(y0)))))) -> c1(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(y0))))) -> c1(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(1(1(c_0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(1(1(c_0(1(1(z0))))))), 0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   0'_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1, c_1


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

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   ENCARG(1(1(y0))) -> c(ENCARG(1(y0)))
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(y0)))) -> c(ENCARG(cons_0(1(y0))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(cons_0(y0)))) -> c(ENCARG(cons_0(cons_0(y0))))
   ENCARG(1(cons_0(cons_0(1(y0))))) -> c(ENCARG(cons_0(cons_0(1(y0)))))
   ENCARG(1(cons_0(cons_0(cons_0(y0))))) -> c(ENCARG(cons_0(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(cons_0(1(cons_0(1(y0))))) -> c1(ENCARG(1(cons_0(1(y0)))))
   ENCARG(cons_0(1(cons_0(1(1(y0)))))) -> c1(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(y0))))) -> c1(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   0'_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1, c_1


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

(105) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace 0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(1(0(c_0(c_0(c_0(z0)))))), 0'(c_0(c_0(c_0(z0))))) by 
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(c_0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(1(1(0(1(1(z0)))))), 0'(c_0(c_0(c_0(z0)))))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   ENCARG(1(1(y0))) -> c(ENCARG(1(y0)))
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(y0)))) -> c(ENCARG(cons_0(1(y0))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(cons_0(y0)))) -> c(ENCARG(cons_0(cons_0(y0))))
   ENCARG(1(cons_0(cons_0(1(y0))))) -> c(ENCARG(cons_0(cons_0(1(y0)))))
   ENCARG(1(cons_0(cons_0(cons_0(y0))))) -> c(ENCARG(cons_0(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(cons_0(1(cons_0(1(y0))))) -> c1(ENCARG(1(cons_0(1(y0)))))
   ENCARG(cons_0(1(cons_0(1(1(y0)))))) -> c1(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(y0))))) -> c1(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(c_0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(1(1(0(1(1(z0)))))), 0'(c_0(c_0(c_0(z0)))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(c_0(c_0(c_0(x0))))))) -> c5(0'(1(c_0(c_0(c_0(c_0(x0)))))), 0'(c_0(c_0(c_0(x0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(1(1(0(1(1(z0)))))), 0'(c_0(c_0(c_0(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   0'_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1, c_1


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

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   ENCARG(1(1(y0))) -> c(ENCARG(1(y0)))
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(y0)))) -> c(ENCARG(cons_0(1(y0))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(cons_0(y0)))) -> c(ENCARG(cons_0(cons_0(y0))))
   ENCARG(1(cons_0(cons_0(1(y0))))) -> c(ENCARG(cons_0(cons_0(1(y0)))))
   ENCARG(1(cons_0(cons_0(cons_0(y0))))) -> c(ENCARG(cons_0(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(cons_0(1(cons_0(1(y0))))) -> c1(ENCARG(1(cons_0(1(y0)))))
   ENCARG(cons_0(1(cons_0(1(1(y0)))))) -> c1(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(y0))))) -> c1(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   0'_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1, c_1


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

(109) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0)))))))) by 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
----------------------------------------

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   ENCARG(1(1(y0))) -> c(ENCARG(1(y0)))
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(y0)))) -> c(ENCARG(cons_0(1(y0))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(cons_0(y0)))) -> c(ENCARG(cons_0(cons_0(y0))))
   ENCARG(1(cons_0(cons_0(1(y0))))) -> c(ENCARG(cons_0(cons_0(1(y0)))))
   ENCARG(1(cons_0(cons_0(cons_0(y0))))) -> c(ENCARG(cons_0(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(cons_0(1(cons_0(1(y0))))) -> c1(ENCARG(1(cons_0(1(y0)))))
   ENCARG(cons_0(1(cons_0(1(1(y0)))))) -> c1(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(y0))))) -> c1(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   0'_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1, c_1


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

(111) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace 0'(1(c_0(1(z0)))) -> c5(0'(1(c_0(z0))), 0'(z0)) by 
   0'(1(c_0(1(c_0(c_0(c_0(y0))))))) -> c5(0'(1(c_0(c_0(c_0(c_0(y0)))))), 0'(c_0(c_0(c_0(y0)))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))), 0'(1(1(y0))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))), 0'(1(1(c_0(1(y0))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))), 0'(1(1(c_0(1(1(c_0(1(y0)))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))), 0'(1(c_0(c_0(c_0(y0))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))), 0'(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   ENCARG(1(1(y0))) -> c(ENCARG(1(y0)))
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(y0)))) -> c(ENCARG(cons_0(1(y0))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(cons_0(y0)))) -> c(ENCARG(cons_0(cons_0(y0))))
   ENCARG(1(cons_0(cons_0(1(y0))))) -> c(ENCARG(cons_0(cons_0(1(y0)))))
   ENCARG(1(cons_0(cons_0(cons_0(y0))))) -> c(ENCARG(cons_0(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(cons_0(1(cons_0(1(y0))))) -> c1(ENCARG(1(cons_0(1(y0)))))
   ENCARG(cons_0(1(cons_0(1(1(y0)))))) -> c1(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(y0))))) -> c1(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(c_0(c_0(c_0(y0))))))) -> c5(0'(1(c_0(c_0(c_0(c_0(y0)))))), 0'(c_0(c_0(c_0(y0)))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))), 0'(1(1(y0))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))), 0'(1(1(c_0(1(y0))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))), 0'(1(1(c_0(1(1(c_0(1(y0)))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))), 0'(1(c_0(c_0(c_0(y0))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))), 0'(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(c_0(c_0(c_0(y0))))))) -> c5(0'(1(c_0(c_0(c_0(c_0(y0)))))), 0'(c_0(c_0(c_0(y0)))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))), 0'(1(1(y0))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))), 0'(1(1(c_0(1(y0))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))), 0'(1(1(c_0(1(1(c_0(1(y0)))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))), 0'(1(c_0(c_0(c_0(y0))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))), 0'(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   0'_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1, c_1


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

(113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing tuple parts
----------------------------------------

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   ENCARG(1(1(y0))) -> c(ENCARG(1(y0)))
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(y0)))) -> c(ENCARG(cons_0(1(y0))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(cons_0(y0)))) -> c(ENCARG(cons_0(cons_0(y0))))
   ENCARG(1(cons_0(cons_0(1(y0))))) -> c(ENCARG(cons_0(cons_0(1(y0)))))
   ENCARG(1(cons_0(cons_0(cons_0(y0))))) -> c(ENCARG(cons_0(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(cons_0(1(cons_0(1(y0))))) -> c1(ENCARG(1(cons_0(1(y0)))))
   ENCARG(cons_0(1(cons_0(1(1(y0)))))) -> c1(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(y0))))) -> c1(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   0'_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1, c_1


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

(115) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(1(1(y0))) -> c(ENCARG(1(y0))) by 
   ENCARG(1(1(1(y0)))) -> c(ENCARG(1(1(y0))))
   ENCARG(1(1(cons_0(1(cons_0(y0)))))) -> c(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(1(1(cons_0(1(y0))))) -> c(ENCARG(1(cons_0(1(y0)))))
   ENCARG(1(1(cons_0(1(1(y0)))))) -> c(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(1(1(cons_0(cons_0(y0))))) -> c(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(1(1(cons_0(cons_0(1(y0)))))) -> c(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(1(1(cons_0(cons_0(cons_0(y0)))))) -> c(ENCARG(1(cons_0(cons_0(cons_0(y0))))))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(y0)))) -> c(ENCARG(cons_0(1(y0))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(cons_0(y0)))) -> c(ENCARG(cons_0(cons_0(y0))))
   ENCARG(1(cons_0(cons_0(1(y0))))) -> c(ENCARG(cons_0(cons_0(1(y0)))))
   ENCARG(1(cons_0(cons_0(cons_0(y0))))) -> c(ENCARG(cons_0(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(cons_0(1(cons_0(1(y0))))) -> c1(ENCARG(1(cons_0(1(y0)))))
   ENCARG(cons_0(1(cons_0(1(1(y0)))))) -> c1(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(y0))))) -> c1(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   ENCARG(1(1(1(y0)))) -> c(ENCARG(1(1(y0))))
   ENCARG(1(1(cons_0(1(cons_0(y0)))))) -> c(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(1(1(cons_0(1(y0))))) -> c(ENCARG(1(cons_0(1(y0)))))
   ENCARG(1(1(cons_0(1(1(y0)))))) -> c(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(1(1(cons_0(cons_0(y0))))) -> c(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(1(1(cons_0(cons_0(1(y0)))))) -> c(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(1(1(cons_0(cons_0(cons_0(y0)))))) -> c(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   0'_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1, c_1


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

(117) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0)))) by 
   ENCARG(cons_0(1(1(1(y0))))) -> c1(ENCARG(1(1(1(y0)))))
   ENCARG(cons_0(1(1(cons_0(1(cons_0(y0))))))) -> c1(ENCARG(1(1(cons_0(1(cons_0(y0)))))))
   ENCARG(cons_0(1(1(cons_0(1(y0)))))) -> c1(ENCARG(1(1(cons_0(1(y0))))))
   ENCARG(cons_0(1(1(cons_0(1(1(y0))))))) -> c1(ENCARG(1(1(cons_0(1(1(y0)))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(1(cons_0(cons_0(y0))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(1(y0))))))) -> c1(ENCARG(1(1(cons_0(cons_0(1(y0)))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(cons_0(y0))))))) -> c1(ENCARG(1(1(cons_0(cons_0(cons_0(y0)))))))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(y0)))) -> c(ENCARG(cons_0(1(y0))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(cons_0(y0)))) -> c(ENCARG(cons_0(cons_0(y0))))
   ENCARG(1(cons_0(cons_0(1(y0))))) -> c(ENCARG(cons_0(cons_0(1(y0)))))
   ENCARG(1(cons_0(cons_0(cons_0(y0))))) -> c(ENCARG(cons_0(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(cons_0(1(cons_0(1(y0))))) -> c1(ENCARG(1(cons_0(1(y0)))))
   ENCARG(cons_0(1(cons_0(1(1(y0)))))) -> c1(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(y0))))) -> c1(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   ENCARG(1(1(1(y0)))) -> c(ENCARG(1(1(y0))))
   ENCARG(1(1(cons_0(1(cons_0(y0)))))) -> c(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(1(1(cons_0(1(y0))))) -> c(ENCARG(1(cons_0(1(y0)))))
   ENCARG(1(1(cons_0(1(1(y0)))))) -> c(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(1(1(cons_0(cons_0(y0))))) -> c(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(1(1(cons_0(cons_0(1(y0)))))) -> c(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(1(1(cons_0(cons_0(cons_0(y0)))))) -> c(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   ENCARG(cons_0(1(1(1(y0))))) -> c1(ENCARG(1(1(1(y0)))))
   ENCARG(cons_0(1(1(cons_0(1(cons_0(y0))))))) -> c1(ENCARG(1(1(cons_0(1(cons_0(y0)))))))
   ENCARG(cons_0(1(1(cons_0(1(y0)))))) -> c1(ENCARG(1(1(cons_0(1(y0))))))
   ENCARG(cons_0(1(1(cons_0(1(1(y0))))))) -> c1(ENCARG(1(1(cons_0(1(1(y0)))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(1(cons_0(cons_0(y0))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(1(y0))))))) -> c1(ENCARG(1(1(cons_0(cons_0(1(y0)))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(cons_0(y0))))))) -> c1(ENCARG(1(1(cons_0(cons_0(cons_0(y0)))))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   0'_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1, c_1


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

(119) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(1(cons_0(1(y0)))) -> c(ENCARG(cons_0(1(y0)))) by 
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(1(cons_0(1(cons_0(y0))))))) -> c(ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))))
   ENCARG(1(cons_0(1(cons_0(1(y0)))))) -> c(ENCARG(cons_0(1(cons_0(1(y0))))))
   ENCARG(1(cons_0(1(cons_0(1(1(y0))))))) -> c(ENCARG(cons_0(1(cons_0(1(1(y0)))))))
   ENCARG(1(cons_0(1(cons_0(cons_0(y0)))))) -> c(ENCARG(cons_0(1(cons_0(cons_0(y0))))))
   ENCARG(1(cons_0(1(cons_0(cons_0(1(y0))))))) -> c(ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))))
   ENCARG(1(cons_0(1(cons_0(cons_0(cons_0(y0))))))) -> c(ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))))
   ENCARG(1(cons_0(1(1(1(y0)))))) -> c(ENCARG(cons_0(1(1(1(y0))))))
   ENCARG(1(cons_0(1(1(cons_0(1(cons_0(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(cons_0(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(1(y0))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(y0)))))))
   ENCARG(1(cons_0(1(1(cons_0(1(1(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(1(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(y0))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(y0)))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(1(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(1(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(cons_0(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(cons_0(y0))))))))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(1(1(z0)))) -> c1(ENCARG(1(1(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(cons_0(y0)))) -> c(ENCARG(cons_0(cons_0(y0))))
   ENCARG(1(cons_0(cons_0(1(y0))))) -> c(ENCARG(cons_0(cons_0(1(y0)))))
   ENCARG(1(cons_0(cons_0(cons_0(y0))))) -> c(ENCARG(cons_0(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(cons_0(1(cons_0(1(y0))))) -> c1(ENCARG(1(cons_0(1(y0)))))
   ENCARG(cons_0(1(cons_0(1(1(y0)))))) -> c1(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(y0))))) -> c1(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   ENCARG(1(1(1(y0)))) -> c(ENCARG(1(1(y0))))
   ENCARG(1(1(cons_0(1(cons_0(y0)))))) -> c(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(1(1(cons_0(1(y0))))) -> c(ENCARG(1(cons_0(1(y0)))))
   ENCARG(1(1(cons_0(1(1(y0)))))) -> c(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(1(1(cons_0(cons_0(y0))))) -> c(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(1(1(cons_0(cons_0(1(y0)))))) -> c(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(1(1(cons_0(cons_0(cons_0(y0)))))) -> c(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   ENCARG(cons_0(1(1(1(y0))))) -> c1(ENCARG(1(1(1(y0)))))
   ENCARG(cons_0(1(1(cons_0(1(cons_0(y0))))))) -> c1(ENCARG(1(1(cons_0(1(cons_0(y0)))))))
   ENCARG(cons_0(1(1(cons_0(1(y0)))))) -> c1(ENCARG(1(1(cons_0(1(y0))))))
   ENCARG(cons_0(1(1(cons_0(1(1(y0))))))) -> c1(ENCARG(1(1(cons_0(1(1(y0)))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(1(cons_0(cons_0(y0))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(1(y0))))))) -> c1(ENCARG(1(1(cons_0(cons_0(1(y0)))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(cons_0(y0))))))) -> c1(ENCARG(1(1(cons_0(cons_0(cons_0(y0)))))))
   ENCARG(1(cons_0(1(cons_0(1(cons_0(y0))))))) -> c(ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))))
   ENCARG(1(cons_0(1(cons_0(1(y0)))))) -> c(ENCARG(cons_0(1(cons_0(1(y0))))))
   ENCARG(1(cons_0(1(cons_0(1(1(y0))))))) -> c(ENCARG(cons_0(1(cons_0(1(1(y0)))))))
   ENCARG(1(cons_0(1(cons_0(cons_0(y0)))))) -> c(ENCARG(cons_0(1(cons_0(cons_0(y0))))))
   ENCARG(1(cons_0(1(cons_0(cons_0(1(y0))))))) -> c(ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))))
   ENCARG(1(cons_0(1(cons_0(cons_0(cons_0(y0))))))) -> c(ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))))
   ENCARG(1(cons_0(1(1(1(y0)))))) -> c(ENCARG(cons_0(1(1(1(y0))))))
   ENCARG(1(cons_0(1(1(cons_0(1(cons_0(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(cons_0(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(1(y0))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(y0)))))))
   ENCARG(1(cons_0(1(1(cons_0(1(1(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(1(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(y0))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(y0)))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(1(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(1(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(cons_0(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(cons_0(y0))))))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   0'_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c6, c1_2, c1_1, c5_3, c5_2, c5_1, c3_1, c_1


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

(121) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(cons_0(1(1(y0)))) -> c1(ENCARG(1(1(y0)))) by 
   ENCARG(cons_0(1(1(1(y0))))) -> c1(ENCARG(1(1(1(y0)))))
   ENCARG(cons_0(1(1(cons_0(1(cons_0(y0))))))) -> c1(ENCARG(1(1(cons_0(1(cons_0(y0)))))))
   ENCARG(cons_0(1(1(cons_0(1(y0)))))) -> c1(ENCARG(1(1(cons_0(1(y0))))))
   ENCARG(cons_0(1(1(cons_0(1(1(y0))))))) -> c1(ENCARG(1(1(cons_0(1(1(y0)))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(1(cons_0(cons_0(y0))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(1(y0))))))) -> c1(ENCARG(1(1(cons_0(cons_0(1(y0)))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(cons_0(y0))))))) -> c1(ENCARG(1(1(cons_0(cons_0(cons_0(y0)))))))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(cons_0(y0)))) -> c(ENCARG(cons_0(cons_0(y0))))
   ENCARG(1(cons_0(cons_0(1(y0))))) -> c(ENCARG(cons_0(cons_0(1(y0)))))
   ENCARG(1(cons_0(cons_0(cons_0(y0))))) -> c(ENCARG(cons_0(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(cons_0(1(cons_0(1(y0))))) -> c1(ENCARG(1(cons_0(1(y0)))))
   ENCARG(cons_0(1(cons_0(1(1(y0)))))) -> c1(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(y0))))) -> c1(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   ENCARG(1(1(1(y0)))) -> c(ENCARG(1(1(y0))))
   ENCARG(1(1(cons_0(1(cons_0(y0)))))) -> c(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(1(1(cons_0(1(y0))))) -> c(ENCARG(1(cons_0(1(y0)))))
   ENCARG(1(1(cons_0(1(1(y0)))))) -> c(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(1(1(cons_0(cons_0(y0))))) -> c(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(1(1(cons_0(cons_0(1(y0)))))) -> c(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(1(1(cons_0(cons_0(cons_0(y0)))))) -> c(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   ENCARG(cons_0(1(1(1(y0))))) -> c1(ENCARG(1(1(1(y0)))))
   ENCARG(cons_0(1(1(cons_0(1(cons_0(y0))))))) -> c1(ENCARG(1(1(cons_0(1(cons_0(y0)))))))
   ENCARG(cons_0(1(1(cons_0(1(y0)))))) -> c1(ENCARG(1(1(cons_0(1(y0))))))
   ENCARG(cons_0(1(1(cons_0(1(1(y0))))))) -> c1(ENCARG(1(1(cons_0(1(1(y0)))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(1(cons_0(cons_0(y0))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(1(y0))))))) -> c1(ENCARG(1(1(cons_0(cons_0(1(y0)))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(cons_0(y0))))))) -> c1(ENCARG(1(1(cons_0(cons_0(cons_0(y0)))))))
   ENCARG(1(cons_0(1(cons_0(1(cons_0(y0))))))) -> c(ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))))
   ENCARG(1(cons_0(1(cons_0(1(y0)))))) -> c(ENCARG(cons_0(1(cons_0(1(y0))))))
   ENCARG(1(cons_0(1(cons_0(1(1(y0))))))) -> c(ENCARG(cons_0(1(cons_0(1(1(y0)))))))
   ENCARG(1(cons_0(1(cons_0(cons_0(y0)))))) -> c(ENCARG(cons_0(1(cons_0(cons_0(y0))))))
   ENCARG(1(cons_0(1(cons_0(cons_0(1(y0))))))) -> c(ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))))
   ENCARG(1(cons_0(1(cons_0(cons_0(cons_0(y0))))))) -> c(ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))))
   ENCARG(1(cons_0(1(1(1(y0)))))) -> c(ENCARG(cons_0(1(1(1(y0))))))
   ENCARG(1(cons_0(1(1(cons_0(1(cons_0(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(cons_0(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(1(y0))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(y0)))))))
   ENCARG(1(cons_0(1(1(cons_0(1(1(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(1(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(y0))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(y0)))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(1(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(1(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(cons_0(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(cons_0(y0))))))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   0'_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c6, c1_2, c5_3, c5_2, c5_1, c3_1, c_1, c1_1


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

(123) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0))))) by 
   ENCARG(1(cons_0(1(1(1(y0)))))) -> c(ENCARG(cons_0(1(1(1(y0))))))
   ENCARG(1(cons_0(1(1(cons_0(1(cons_0(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(cons_0(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(1(y0))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(y0)))))))
   ENCARG(1(cons_0(1(1(cons_0(1(1(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(1(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(y0))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(y0)))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(1(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(1(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(cons_0(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(cons_0(y0))))))))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(cons_0(y0)))) -> c(ENCARG(cons_0(cons_0(y0))))
   ENCARG(1(cons_0(cons_0(1(y0))))) -> c(ENCARG(cons_0(cons_0(1(y0)))))
   ENCARG(1(cons_0(cons_0(cons_0(y0))))) -> c(ENCARG(cons_0(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(cons_0(1(cons_0(1(y0))))) -> c1(ENCARG(1(cons_0(1(y0)))))
   ENCARG(cons_0(1(cons_0(1(1(y0)))))) -> c1(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(y0))))) -> c1(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   ENCARG(1(1(1(y0)))) -> c(ENCARG(1(1(y0))))
   ENCARG(1(1(cons_0(1(cons_0(y0)))))) -> c(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(1(1(cons_0(1(y0))))) -> c(ENCARG(1(cons_0(1(y0)))))
   ENCARG(1(1(cons_0(1(1(y0)))))) -> c(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(1(1(cons_0(cons_0(y0))))) -> c(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(1(1(cons_0(cons_0(1(y0)))))) -> c(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(1(1(cons_0(cons_0(cons_0(y0)))))) -> c(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   ENCARG(cons_0(1(1(1(y0))))) -> c1(ENCARG(1(1(1(y0)))))
   ENCARG(cons_0(1(1(cons_0(1(cons_0(y0))))))) -> c1(ENCARG(1(1(cons_0(1(cons_0(y0)))))))
   ENCARG(cons_0(1(1(cons_0(1(y0)))))) -> c1(ENCARG(1(1(cons_0(1(y0))))))
   ENCARG(cons_0(1(1(cons_0(1(1(y0))))))) -> c1(ENCARG(1(1(cons_0(1(1(y0)))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(1(cons_0(cons_0(y0))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(1(y0))))))) -> c1(ENCARG(1(1(cons_0(cons_0(1(y0)))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(cons_0(y0))))))) -> c1(ENCARG(1(1(cons_0(cons_0(cons_0(y0)))))))
   ENCARG(1(cons_0(1(cons_0(1(cons_0(y0))))))) -> c(ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))))
   ENCARG(1(cons_0(1(cons_0(1(y0)))))) -> c(ENCARG(cons_0(1(cons_0(1(y0))))))
   ENCARG(1(cons_0(1(cons_0(1(1(y0))))))) -> c(ENCARG(cons_0(1(cons_0(1(1(y0)))))))
   ENCARG(1(cons_0(1(cons_0(cons_0(y0)))))) -> c(ENCARG(cons_0(1(cons_0(cons_0(y0))))))
   ENCARG(1(cons_0(1(cons_0(cons_0(1(y0))))))) -> c(ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))))
   ENCARG(1(cons_0(1(cons_0(cons_0(cons_0(y0))))))) -> c(ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))))
   ENCARG(1(cons_0(1(1(1(y0)))))) -> c(ENCARG(cons_0(1(1(1(y0))))))
   ENCARG(1(cons_0(1(1(cons_0(1(cons_0(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(cons_0(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(1(y0))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(y0)))))))
   ENCARG(1(cons_0(1(1(cons_0(1(1(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(1(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(y0))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(y0)))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(1(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(1(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(cons_0(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(cons_0(y0))))))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   0'_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c6, c1_2, c5_3, c5_2, c5_1, c3_1, c_1, c1_1


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

(125) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(cons_0(1(cons_0(1(y0))))) -> c1(ENCARG(1(cons_0(1(y0))))) by 
   ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(cons_0(1(cons_0(1(1(y0)))))) -> c1(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(cons_0(1(cons_0(1(cons_0(1(cons_0(y0)))))))) -> c1(ENCARG(1(cons_0(1(cons_0(1(cons_0(y0))))))))
   ENCARG(cons_0(1(cons_0(1(cons_0(1(y0))))))) -> c1(ENCARG(1(cons_0(1(cons_0(1(y0)))))))
   ENCARG(cons_0(1(cons_0(1(cons_0(1(1(y0)))))))) -> c1(ENCARG(1(cons_0(1(cons_0(1(1(y0))))))))
   ENCARG(cons_0(1(cons_0(1(cons_0(cons_0(y0))))))) -> c1(ENCARG(1(cons_0(1(cons_0(cons_0(y0)))))))
   ENCARG(cons_0(1(cons_0(1(cons_0(cons_0(1(y0)))))))) -> c1(ENCARG(1(cons_0(1(cons_0(cons_0(1(y0))))))))
   ENCARG(cons_0(1(cons_0(1(cons_0(cons_0(cons_0(y0)))))))) -> c1(ENCARG(1(cons_0(1(cons_0(cons_0(cons_0(y0))))))))
   ENCARG(cons_0(1(cons_0(1(1(1(y0))))))) -> c1(ENCARG(1(cons_0(1(1(1(y0)))))))
   ENCARG(cons_0(1(cons_0(1(1(cons_0(1(cons_0(y0))))))))) -> c1(ENCARG(1(cons_0(1(1(cons_0(1(cons_0(y0)))))))))
   ENCARG(cons_0(1(cons_0(1(1(cons_0(1(y0)))))))) -> c1(ENCARG(1(cons_0(1(1(cons_0(1(y0))))))))
   ENCARG(cons_0(1(cons_0(1(1(cons_0(1(1(y0))))))))) -> c1(ENCARG(1(cons_0(1(1(cons_0(1(1(y0)))))))))
   ENCARG(cons_0(1(cons_0(1(1(cons_0(cons_0(y0)))))))) -> c1(ENCARG(1(cons_0(1(1(cons_0(cons_0(y0))))))))
   ENCARG(cons_0(1(cons_0(1(1(cons_0(cons_0(1(y0))))))))) -> c1(ENCARG(1(cons_0(1(1(cons_0(cons_0(1(y0)))))))))
   ENCARG(cons_0(1(cons_0(1(1(cons_0(cons_0(cons_0(y0))))))))) -> c1(ENCARG(1(cons_0(1(1(cons_0(cons_0(cons_0(y0)))))))))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(1(z0)) -> 1(encArg(z0))
   encArg(cons_0(z0)) -> 0(encArg(z0))
   0(z0) -> c_0(z0)
   0(1(c_0(1(z0)))) -> 0(0(1(0(z0))))
   0(c_0(c_0(c_0(z0)))) -> 1(0(1(1(z0))))
Tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   ENCARG(cons_0(1(cons_0(z0)))) -> c1(0'(1(0(encArg(z0)))), ENCARG(1(cons_0(z0))))
   ENCARG(cons_0(cons_0(x0))) -> c1(0'(c_0(encArg(x0))), ENCARG(cons_0(x0)))
   ENCARG(cons_0(cons_0(1(z0)))) -> c1(0'(0(1(encArg(z0)))), ENCARG(cons_0(1(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c1(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(x0)))) -> c5(0'(1(0(x0))), 0'(x0))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   ENCODE_0(1(cons_0(z0))) -> c3(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_0(x0)) -> c3(0'(c_0(encArg(x0))))
   ENCODE_0(cons_0(1(z0))) -> c3(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_0(cons_0(z0))) -> c3(0'(0(0(encArg(z0)))))
   ENCARG(1(cons_0(1(cons_0(y0))))) -> c(ENCARG(cons_0(1(cons_0(y0)))))
   ENCARG(1(cons_0(1(1(y0))))) -> c(ENCARG(cons_0(1(1(y0)))))
   ENCARG(1(cons_0(cons_0(y0)))) -> c(ENCARG(cons_0(cons_0(y0))))
   ENCARG(1(cons_0(cons_0(1(y0))))) -> c(ENCARG(cons_0(cons_0(1(y0)))))
   ENCARG(1(cons_0(cons_0(cons_0(y0))))) -> c(ENCARG(cons_0(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(cons_0(1(cons_0(1(1(y0)))))) -> c1(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(y0))))) -> c1(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   ENCARG(1(1(1(y0)))) -> c(ENCARG(1(1(y0))))
   ENCARG(1(1(cons_0(1(cons_0(y0)))))) -> c(ENCARG(1(cons_0(1(cons_0(y0))))))
   ENCARG(1(1(cons_0(1(y0))))) -> c(ENCARG(1(cons_0(1(y0)))))
   ENCARG(1(1(cons_0(1(1(y0)))))) -> c(ENCARG(1(cons_0(1(1(y0))))))
   ENCARG(1(1(cons_0(cons_0(y0))))) -> c(ENCARG(1(cons_0(cons_0(y0)))))
   ENCARG(1(1(cons_0(cons_0(1(y0)))))) -> c(ENCARG(1(cons_0(cons_0(1(y0))))))
   ENCARG(1(1(cons_0(cons_0(cons_0(y0)))))) -> c(ENCARG(1(cons_0(cons_0(cons_0(y0))))))
   ENCARG(cons_0(1(1(1(y0))))) -> c1(ENCARG(1(1(1(y0)))))
   ENCARG(cons_0(1(1(cons_0(1(cons_0(y0))))))) -> c1(ENCARG(1(1(cons_0(1(cons_0(y0)))))))
   ENCARG(cons_0(1(1(cons_0(1(y0)))))) -> c1(ENCARG(1(1(cons_0(1(y0))))))
   ENCARG(cons_0(1(1(cons_0(1(1(y0))))))) -> c1(ENCARG(1(1(cons_0(1(1(y0)))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(y0)))))) -> c1(ENCARG(1(1(cons_0(cons_0(y0))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(1(y0))))))) -> c1(ENCARG(1(1(cons_0(cons_0(1(y0)))))))
   ENCARG(cons_0(1(1(cons_0(cons_0(cons_0(y0))))))) -> c1(ENCARG(1(1(cons_0(cons_0(cons_0(y0)))))))
   ENCARG(1(cons_0(1(cons_0(1(cons_0(y0))))))) -> c(ENCARG(cons_0(1(cons_0(1(cons_0(y0)))))))
   ENCARG(1(cons_0(1(cons_0(1(y0)))))) -> c(ENCARG(cons_0(1(cons_0(1(y0))))))
   ENCARG(1(cons_0(1(cons_0(1(1(y0))))))) -> c(ENCARG(cons_0(1(cons_0(1(1(y0)))))))
   ENCARG(1(cons_0(1(cons_0(cons_0(y0)))))) -> c(ENCARG(cons_0(1(cons_0(cons_0(y0))))))
   ENCARG(1(cons_0(1(cons_0(cons_0(1(y0))))))) -> c(ENCARG(cons_0(1(cons_0(cons_0(1(y0)))))))
   ENCARG(1(cons_0(1(cons_0(cons_0(cons_0(y0))))))) -> c(ENCARG(cons_0(1(cons_0(cons_0(cons_0(y0)))))))
   ENCARG(1(cons_0(1(1(1(y0)))))) -> c(ENCARG(cons_0(1(1(1(y0))))))
   ENCARG(1(cons_0(1(1(cons_0(1(cons_0(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(cons_0(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(1(y0))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(y0)))))))
   ENCARG(1(cons_0(1(1(cons_0(1(1(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(1(1(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(y0))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(y0)))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(1(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(1(y0))))))))
   ENCARG(1(cons_0(1(1(cons_0(cons_0(cons_0(y0)))))))) -> c(ENCARG(cons_0(1(1(cons_0(cons_0(cons_0(y0))))))))
   ENCARG(cons_0(1(cons_0(1(cons_0(1(cons_0(y0)))))))) -> c1(ENCARG(1(cons_0(1(cons_0(1(cons_0(y0))))))))
   ENCARG(cons_0(1(cons_0(1(cons_0(1(y0))))))) -> c1(ENCARG(1(cons_0(1(cons_0(1(y0)))))))
   ENCARG(cons_0(1(cons_0(1(cons_0(1(1(y0)))))))) -> c1(ENCARG(1(cons_0(1(cons_0(1(1(y0))))))))
   ENCARG(cons_0(1(cons_0(1(cons_0(cons_0(y0))))))) -> c1(ENCARG(1(cons_0(1(cons_0(cons_0(y0)))))))
   ENCARG(cons_0(1(cons_0(1(cons_0(cons_0(1(y0)))))))) -> c1(ENCARG(1(cons_0(1(cons_0(cons_0(1(y0))))))))
   ENCARG(cons_0(1(cons_0(1(cons_0(cons_0(cons_0(y0)))))))) -> c1(ENCARG(1(cons_0(1(cons_0(cons_0(cons_0(y0))))))))
   ENCARG(cons_0(1(cons_0(1(1(1(y0))))))) -> c1(ENCARG(1(cons_0(1(1(1(y0)))))))
   ENCARG(cons_0(1(cons_0(1(1(cons_0(1(cons_0(y0))))))))) -> c1(ENCARG(1(cons_0(1(1(cons_0(1(cons_0(y0)))))))))
   ENCARG(cons_0(1(cons_0(1(1(cons_0(1(y0)))))))) -> c1(ENCARG(1(cons_0(1(1(cons_0(1(y0))))))))
   ENCARG(cons_0(1(cons_0(1(1(cons_0(1(1(y0))))))))) -> c1(ENCARG(1(cons_0(1(1(cons_0(1(1(y0)))))))))
   ENCARG(cons_0(1(cons_0(1(1(cons_0(cons_0(y0)))))))) -> c1(ENCARG(1(cons_0(1(1(cons_0(cons_0(y0))))))))
   ENCARG(cons_0(1(cons_0(1(1(cons_0(cons_0(1(y0))))))))) -> c1(ENCARG(1(cons_0(1(1(cons_0(cons_0(1(y0)))))))))
   ENCARG(cons_0(1(cons_0(1(1(cons_0(cons_0(cons_0(y0))))))))) -> c1(ENCARG(1(cons_0(1(1(cons_0(cons_0(cons_0(y0)))))))))
S tuples:
   0'(c_0(c_0(c_0(z0)))) -> c6
   0'(1(c_0(1(1(z0))))) -> c5(0'(0(0(1(0(z0))))), 0'(1(0(1(z0)))), 0'(1(z0)))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(c_0(0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(0(1(0(c_0(1(0(x0))))))), 0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(0(1(0(0(1(c_0(z0))))))), 0'(1(0(1(c_0(1(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(z0)))))))))) -> c5(0'(0(1(0(0(1(0(0(1(0(z0)))))))))), 0'(1(0(1(c_0(1(1(c_0(1(z0))))))))), 0'(1(c_0(1(1(c_0(1(z0))))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))))
   0'(1(c_0(1(1(c_0(1(x0))))))) -> c5(0'(1(0(1(c_0(1(x0)))))), 0'(1(c_0(1(x0)))))
   0'(1(c_0(1(1(c_0(1(z0))))))) -> c5(0'(1(0(0(1(0(z0)))))), 0'(1(c_0(1(z0)))))
   0'(1(c_0(1(c_0(c_0(c_0(z0))))))) -> c5(0'(c_0(c_0(c_0(z0)))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(z0)))))))))) -> c5(0'(0(1(c_0(c_0(1(1(0(1(1(z0)))))))))), 0'(1(0(1(c_0(1(c_0(c_0(c_0(z0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(z0))))))))
   0'(1(c_0(1(1(c_0(1(1(y0)))))))) -> c5(0'(1(c_0(1(c_0(1(1(y0))))))), 0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(y0))))) -> c5(0'(1(c_0(1(y0)))), 0'(1(y0)))
   0'(1(c_0(1(1(c_0(1(y0))))))) -> c5(0'(1(c_0(1(c_0(1(y0)))))), 0'(1(c_0(1(y0)))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(y0))))))))), 0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(1(c_0(1(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))) -> c5(0'(1(c_0(1(c_0(1(c_0(c_0(c_0(y0))))))))), 0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))))) -> c5(0'(1(c_0(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))), 0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
   0'(1(c_0(1(1(1(y0)))))) -> c5(0'(1(c_0(1(1(y0))))))
   0'(1(c_0(1(1(1(c_0(1(y0)))))))) -> c5(0'(1(c_0(1(1(c_0(1(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(1(c_0(1(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(1(c_0(1(y0)))))))))))
   0'(1(c_0(1(1(c_0(c_0(c_0(y0)))))))) -> c5(0'(1(c_0(1(c_0(c_0(c_0(y0))))))))
   0'(1(c_0(1(1(1(c_0(1(c_0(c_0(c_0(y0))))))))))) -> c5(0'(1(c_0(1(1(c_0(1(c_0(c_0(c_0(y0)))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1

Defined Pair Symbols:   0'_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c6, c1_2, c5_3, c5_2, c5_1, c3_1, c_1, c1_1