/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 157 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 0 ms]
    (12) typed CpxTrs
    (13) RewriteLemmaProof [LOWER BOUND(ID), 979 ms]
    (14) BOUNDS(1, INF)
(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) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 2 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CdtProblem
        (43) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (44) CdtProblem
        (45) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (46) CdtProblem
        (47) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (50) CdtProblem
        (51) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (56) CdtProblem
        (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (58) CdtProblem
        (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (60) CdtProblem
        (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (62) CdtProblem
        (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (64) CdtProblem
        (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (66) CdtProblem
        (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (68) CdtProblem
        (69) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (70) CdtProblem
        (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (72) CdtProblem
        (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (74) CdtProblem
        (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (76) CdtProblem
        (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (78) CdtProblem
        (79) CdtNarrowingProof [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), 3 ms]
        (86) CdtProblem
        (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (88) CdtProblem
        (89) CdtRewritingProof [BOTH BOUNDS(ID, ID), 8 ms]
        (90) CdtProblem
        (91) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (92) CdtProblem
        (93) CdtRewritingProof [BOTH BOUNDS(ID, ID), 13 ms]
        (94) CdtProblem
        (95) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (96) CdtProblem
        (97) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (98) CdtProblem
        (99) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (100) CdtProblem
        (101) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (102) CdtProblem
        (103) CdtRewritingProof [BOTH BOUNDS(ID, ID), 3 ms]
        (104) CdtProblem
        (105) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (106) CdtProblem
        (107) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (108) CdtProblem
        (109) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (110) CdtProblem
        (111) CdtRewritingProof [BOTH BOUNDS(ID, ID), 6 ms]
        (112) CdtProblem
        (113) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (114) CdtProblem
        (115) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (116) CdtProblem
        (117) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (118) CdtProblem
        (119) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (120) CdtProblem
        (121) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (122) CdtProblem
        (123) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (124) CdtProblem
        (125) CdtRewritingProof [BOTH BOUNDS(ID, ID), 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:

   f(x, f(y, a)) -> f(a, f(f(f(x, a), a), y))

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(a) -> a
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a


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

(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:

   f(x, f(y, a)) -> f(a, f(f(f(x, a), a), y))

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

   encArg(a) -> a
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a

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:

   f(x, f(y, a)) -> f(a, f(f(f(x, a), a), y))

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

   encArg(a) -> a
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a

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

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

(6)
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:

   f(x, f(y, a)) -> f(a, f(f(f(x, a), a), y))

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

   encArg(a) -> a
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a

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

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

(8)
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:

   f(x, f(y, a)) -> f(a, f(f(f(x, a), a), y))

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

   encArg(a) -> a
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a

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

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

(10)
Obligation:
TRS:
Rules:
f(x, f(y, a)) -> f(a, f(f(f(x, a), a), y))
encArg(a) -> a
encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
encode_a -> a

Types:
f :: a:cons_f -> a:cons_f -> a:cons_f
a :: a:cons_f
encArg :: a:cons_f -> a:cons_f
cons_f :: a:cons_f -> a:cons_f -> a:cons_f
encode_f :: a:cons_f -> a:cons_f -> a:cons_f
encode_a :: a:cons_f
hole_a:cons_f1_0 :: a:cons_f
gen_a:cons_f2_0 :: Nat -> a:cons_f

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

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

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

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

(12)
Obligation:
TRS:
Rules:
f(x, f(y, a)) -> f(a, f(f(f(x, a), a), y))
encArg(a) -> a
encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
encode_a -> a

Types:
f :: a:cons_f -> a:cons_f -> a:cons_f
a :: a:cons_f
encArg :: a:cons_f -> a:cons_f
cons_f :: a:cons_f -> a:cons_f -> a:cons_f
encode_f :: a:cons_f -> a:cons_f -> a:cons_f
encode_a :: a:cons_f
hole_a:cons_f1_0 :: a:cons_f
gen_a:cons_f2_0 :: Nat -> a:cons_f


Generator Equations:
gen_a:cons_f2_0(0) <=> a
gen_a:cons_f2_0(+(x, 1)) <=> cons_f(a, gen_a:cons_f2_0(x))


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

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

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

(13) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_a:cons_f2_0(n9_0)) -> *3_0, rt in Omega(0)

Induction Base:
encArg(gen_a:cons_f2_0(0))

Induction Step:
encArg(gen_a:cons_f2_0(+(n9_0, 1))) ->_R^Omega(0)
f(encArg(a), encArg(gen_a:cons_f2_0(n9_0))) ->_R^Omega(0)
f(a, encArg(gen_a:cons_f2_0(n9_0))) ->_IH
f(a, *3_0)

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

(14)
BOUNDS(1, INF)

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

(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:

   f(x, f(y, a)) -> f(a, f(f(f(x, a), a), y))
   encArg(a) -> a
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a

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:

   f(x, c_f(y, a)) -> f(a, f(f(f(x, a), a), y))

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

   encArg(a) -> a
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a
   f(x0, x1) -> c_f(x0, x1)

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:

   f(x, c_f(y, a)) -> f(a, f(f(f(x, a), a), y))

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

   encArg(a) -> a
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a
   f(x0, x1) -> c_f(x0, x1)

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:

   f(x, c_f(y, a)) -> f(a, f(f(f(x, a), a), y)) [1]
   encArg(a) -> a [0]
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_a -> a [0]
   f(x0, x1) -> c_f(x0, x1) [0]

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

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

(24)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   f(x, c_f(y, a)) -> f(a, f(f(f(x, a), a), y)) [1]
   encArg(a) -> a [0]
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_a -> a [0]
   f(x0, x1) -> c_f(x0, x1) [0]

The TRS has the following type information:
f :: a:c_f:cons_f -> a:c_f:cons_f -> a:c_f:cons_f
c_f :: a:c_f:cons_f -> a:c_f:cons_f -> a:c_f:cons_f
a :: a:c_f:cons_f
encArg :: a:c_f:cons_f -> a:c_f:cons_f
cons_f :: a:c_f:cons_f -> a:c_f:cons_f -> a:c_f:cons_f
encode_f :: a:c_f:cons_f -> a:c_f:cons_f -> a:c_f:cons_f
encode_a :: a:c_f:cons_f

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

(25) 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_f_2
   encode_a
   f_2

Due to the following rules being added:

   encArg(v0) -> a [0]
   encode_f(v0, v1) -> a [0]
   encode_a -> a [0]
   f(v0, v1) -> a [0]

And the following fresh constants: none

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

(26)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   f(x, c_f(y, a)) -> f(a, f(f(f(x, a), a), y)) [1]
   encArg(a) -> a [0]
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_a -> a [0]
   f(x0, x1) -> c_f(x0, x1) [0]
   encArg(v0) -> a [0]
   encode_f(v0, v1) -> a [0]
   encode_a -> a [0]
   f(v0, v1) -> a [0]

The TRS has the following type information:
f :: a:c_f:cons_f -> a:c_f:cons_f -> a:c_f:cons_f
c_f :: a:c_f:cons_f -> a:c_f:cons_f -> a:c_f:cons_f
a :: a:c_f:cons_f
encArg :: a:c_f:cons_f -> a:c_f:cons_f
cons_f :: a:c_f:cons_f -> a:c_f:cons_f -> a:c_f:cons_f
encode_f :: a:c_f:cons_f -> a:c_f:cons_f -> a:c_f:cons_f
encode_a :: a:c_f:cons_f

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

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

(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:

   f(x, c_f(y, a)) -> f(a, f(f(c_f(x, a), a), y)) [1]
   f(x, c_f(y, a)) -> f(a, f(f(a, a), y)) [1]
   encArg(a) -> a [0]
   encArg(cons_f(a, a)) -> f(a, a) [0]
   encArg(cons_f(a, cons_f(x_1'', x_2''))) -> f(a, f(encArg(x_1''), encArg(x_2''))) [0]
   encArg(cons_f(a, x_2)) -> f(a, a) [0]
   encArg(cons_f(cons_f(x_1', x_2'), a)) -> f(f(encArg(x_1'), encArg(x_2')), a) [0]
   encArg(cons_f(cons_f(x_1', x_2'), cons_f(x_11, x_21))) -> f(f(encArg(x_1'), encArg(x_2')), f(encArg(x_11), encArg(x_21))) [0]
   encArg(cons_f(cons_f(x_1', x_2'), x_2)) -> f(f(encArg(x_1'), encArg(x_2')), a) [0]
   encArg(cons_f(x_1, a)) -> f(a, a) [0]
   encArg(cons_f(x_1, cons_f(x_12, x_22))) -> f(a, f(encArg(x_12), encArg(x_22))) [0]
   encArg(cons_f(x_1, x_2)) -> f(a, a) [0]
   encode_f(a, a) -> f(a, a) [0]
   encode_f(a, cons_f(x_14, x_24)) -> f(a, f(encArg(x_14), encArg(x_24))) [0]
   encode_f(a, x_2) -> f(a, a) [0]
   encode_f(cons_f(x_13, x_23), a) -> f(f(encArg(x_13), encArg(x_23)), a) [0]
   encode_f(cons_f(x_13, x_23), cons_f(x_15, x_25)) -> f(f(encArg(x_13), encArg(x_23)), f(encArg(x_15), encArg(x_25))) [0]
   encode_f(cons_f(x_13, x_23), x_2) -> f(f(encArg(x_13), encArg(x_23)), a) [0]
   encode_f(x_1, a) -> f(a, a) [0]
   encode_f(x_1, cons_f(x_16, x_26)) -> f(a, f(encArg(x_16), encArg(x_26))) [0]
   encode_f(x_1, x_2) -> f(a, a) [0]
   encode_a -> a [0]
   f(x0, x1) -> c_f(x0, x1) [0]
   encArg(v0) -> a [0]
   encode_f(v0, v1) -> a [0]
   encode_a -> a [0]
   f(v0, v1) -> a [0]

The TRS has the following type information:
f :: a:c_f:cons_f -> a:c_f:cons_f -> a:c_f:cons_f
c_f :: a:c_f:cons_f -> a:c_f:cons_f -> a:c_f:cons_f
a :: a:c_f:cons_f
encArg :: a:c_f:cons_f -> a:c_f:cons_f
cons_f :: a:c_f:cons_f -> a:c_f:cons_f -> a:c_f:cons_f
encode_f :: a:c_f:cons_f -> a:c_f:cons_f -> a:c_f:cons_f
encode_a :: a:c_f:cons_f

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

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

   a => 0

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

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

   encArg(z) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), f(encArg(x_11), encArg(x_21))) :|: x_11 >= 0, x_2' >= 0, x_1' >= 0, x_21 >= 0, z = 1 + (1 + x_1' + x_2') + (1 + x_11 + x_21)
   encArg(z) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, x_1' >= 0, z = 1 + (1 + x_1' + x_2') + 0
   encArg(z) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), 0) :|: z = 1 + (1 + x_1' + x_2') + x_2, x_2' >= 0, x_1' >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(0, f(encArg(x_1''), encArg(x_2''))) :|: x_1'' >= 0, z = 1 + 0 + (1 + x_1'' + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> f(0, f(encArg(x_12), encArg(x_22))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_12 + x_22), x_12 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> f(0, 0) :|: z = 1 + 0 + 0
   encArg(z) -{ 0 }-> f(0, 0) :|: z = 1 + 0 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(0, 0) :|: z = 1 + x_1 + 0, x_1 >= 0
   encArg(z) -{ 0 }-> f(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_a -{ 0 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(f(encArg(x_13), encArg(x_23)), f(encArg(x_15), encArg(x_25))) :|: x_15 >= 0, z' = 1 + x_15 + x_25, x_25 >= 0, z = 1 + x_13 + x_23, x_13 >= 0, x_23 >= 0
   encode_f(z, z') -{ 0 }-> f(f(encArg(x_13), encArg(x_23)), 0) :|: z = 1 + x_13 + x_23, x_13 >= 0, x_23 >= 0, z' = 0
   encode_f(z, z') -{ 0 }-> f(f(encArg(x_13), encArg(x_23)), 0) :|: z = 1 + x_13 + x_23, x_13 >= 0, x_23 >= 0, x_2 >= 0, z' = x_2
   encode_f(z, z') -{ 0 }-> f(0, f(encArg(x_14), encArg(x_24))) :|: x_14 >= 0, x_24 >= 0, z = 0, z' = 1 + x_14 + x_24
   encode_f(z, z') -{ 0 }-> f(0, f(encArg(x_16), encArg(x_26))) :|: x_1 >= 0, x_16 >= 0, z' = 1 + x_16 + x_26, x_26 >= 0, z = x_1
   encode_f(z, z') -{ 0 }-> f(0, 0) :|: z = 0, z' = 0
   encode_f(z, z') -{ 0 }-> f(0, 0) :|: x_2 >= 0, z' = x_2, z = 0
   encode_f(z, z') -{ 0 }-> f(0, 0) :|: x_1 >= 0, z = x_1, z' = 0
   encode_f(z, z') -{ 0 }-> f(0, 0) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   f(z, z') -{ 1 }-> f(0, f(f(0, 0), y)) :|: x >= 0, y >= 0, z' = 1 + y + 0, z = x
   f(z, z') -{ 1 }-> f(0, f(f(1 + x + 0, 0), y)) :|: x >= 0, y >= 0, z' = 1 + y + 0, z = x
   f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   f(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1


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

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

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

   encArg(z) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), f(encArg(x_11), encArg(x_21))) :|: x_11 >= 0, x_2' >= 0, x_1' >= 0, x_21 >= 0, z = 1 + (1 + x_1' + x_2') + (1 + x_11 + x_21)
   encArg(z) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), 0) :|: x_2' >= 0, x_1' >= 0, z = 1 + (1 + x_1' + x_2') + 0
   encArg(z) -{ 0 }-> f(f(encArg(x_1'), encArg(x_2')), 0) :|: z = 1 + (1 + x_1' + x_2') + x_2, x_2' >= 0, x_1' >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> f(0, f(encArg(x_1''), encArg(x_2''))) :|: x_1'' >= 0, z = 1 + 0 + (1 + x_1'' + x_2''), x_2'' >= 0
   encArg(z) -{ 0 }-> f(0, f(encArg(x_12), encArg(x_22))) :|: x_1 >= 0, z = 1 + x_1 + (1 + x_12 + x_22), x_12 >= 0, x_22 >= 0
   encArg(z) -{ 0 }-> f(0, 0) :|: z = 1 + 0 + 0
   encArg(z) -{ 0 }-> f(0, 0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(0, 0) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_a -{ 0 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(f(encArg(x_13), encArg(x_23)), f(encArg(x_15), encArg(x_25))) :|: x_15 >= 0, z' = 1 + x_15 + x_25, x_25 >= 0, z = 1 + x_13 + x_23, x_13 >= 0, x_23 >= 0
   encode_f(z, z') -{ 0 }-> f(f(encArg(x_13), encArg(x_23)), 0) :|: z = 1 + x_13 + x_23, x_13 >= 0, x_23 >= 0, z' = 0
   encode_f(z, z') -{ 0 }-> f(f(encArg(x_13), encArg(x_23)), 0) :|: z = 1 + x_13 + x_23, x_13 >= 0, x_23 >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> f(0, f(encArg(x_14), encArg(x_24))) :|: x_14 >= 0, x_24 >= 0, z = 0, z' = 1 + x_14 + x_24
   encode_f(z, z') -{ 0 }-> f(0, f(encArg(x_16), encArg(x_26))) :|: z >= 0, x_16 >= 0, z' = 1 + x_16 + x_26, x_26 >= 0
   encode_f(z, z') -{ 0 }-> f(0, 0) :|: z = 0, z' = 0
   encode_f(z, z') -{ 0 }-> f(0, 0) :|: z' >= 0, z = 0
   encode_f(z, z') -{ 0 }-> f(0, 0) :|: z >= 0, z' = 0
   encode_f(z, z') -{ 0 }-> f(0, 0) :|: z >= 0, z' >= 0
   encode_f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 1 }-> f(0, f(f(0, 0), z' - 1)) :|: z >= 0, z' - 1 >= 0
   f(z, z') -{ 1 }-> f(0, f(f(1 + z + 0, 0), z' - 1)) :|: z >= 0, z' - 1 >= 0
   f(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0


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

(33) 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_f(v0, v1) -> null_encode_f [0]
   encode_a -> null_encode_a [0]
   f(v0, v1) -> null_f [0]

And the following fresh constants:    null_encArg, null_encode_f, null_encode_a, null_f

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

(34)
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:

   f(x, c_f(y, a)) -> f(a, f(f(f(x, a), a), y)) [1]
   encArg(a) -> a [0]
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_a -> a [0]
   f(x0, x1) -> c_f(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_f(v0, v1) -> null_encode_f [0]
   encode_a -> null_encode_a [0]
   f(v0, v1) -> null_f [0]

The TRS has the following type information:
f :: a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f -> a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f -> a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f
c_f :: a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f -> a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f -> a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f
a :: a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f
encArg :: a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f -> a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f
cons_f :: a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f -> a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f -> a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f
encode_f :: a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f -> a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f -> a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f
encode_a :: a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f
null_encArg :: a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f
null_encode_f :: a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f
null_encode_a :: a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f
null_f :: a:c_f:cons_f:null_encArg:null_encode_f:null_encode_a:null_f

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

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

   a => 0
   null_encArg => 0
   null_encode_f => 0
   null_encode_a => 0
   null_f => 0

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

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

   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_a -{ 0 }-> 0 :|: 
   encode_f(z, z') -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   f(z, z') -{ 1 }-> f(0, f(f(f(x, 0), 0), y)) :|: x >= 0, y >= 0, z' = 1 + y + 0, z = x
   f(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   f(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1

Only complete derivations are relevant for the runtime complexity.

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

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   encode_f(z0, z1) -> f(encArg(z0), encArg(z1))
   encode_a -> a
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(a) -> c
   ENCARG(cons_f(z0, z1)) -> c1(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_F(z0, z1) -> c2(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_A -> c3
   F(z0, z1) -> c4
   F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1), F(f(z0, a), a), F(z0, a))
S tuples:
   F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1), F(f(z0, a), a), F(z0, a))
K tuples:none
Defined Rule Symbols:   f_2, encArg_1, encode_f_2, encode_a

Defined Pair Symbols:   ENCARG_1, ENCODE_F_2, ENCODE_A, F_2

Compound Symbols:   c, c1_3, c2_3, c3, c4, c5_4


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

(39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   ENCODE_A -> c3
   F(z0, z1) -> c4
   ENCARG(a) -> c

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   encode_f(z0, z1) -> f(encArg(z0), encArg(z1))
   encode_a -> a
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(z0, z1)) -> c1(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_F(z0, z1) -> c2(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1), F(f(z0, a), a), F(z0, a))
S tuples:
   F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1), F(f(z0, a), a), F(z0, a))
K tuples:none
Defined Rule Symbols:   f_2, encArg_1, encode_f_2, encode_a

Defined Pair Symbols:   ENCARG_1, ENCODE_F_2, F_2

Compound Symbols:   c1_3, c2_3, c5_4


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

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   encode_f(z0, z1) -> f(encArg(z0), encArg(z1))
   encode_a -> a
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(z0, z1)) -> c1(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_F(z0, z1) -> c2(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1))
S tuples:
   F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1))
K tuples:none
Defined Rule Symbols:   f_2, encArg_1, encode_f_2, encode_a

Defined Pair Symbols:   ENCARG_1, ENCODE_F_2, F_2

Compound Symbols:   c1_3, c2_3, c5_2


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

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   encode_f(z0, z1) -> f(encArg(z0), encArg(z1))
   encode_a -> a
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(z0, z1)) -> c1(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1))
   ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1)))
   ENCODE_F(z0, z1) -> c(ENCARG(z0))
   ENCODE_F(z0, z1) -> c(ENCARG(z1))
S tuples:
   F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1))
K tuples:none
Defined Rule Symbols:   f_2, encArg_1, encode_f_2, encode_a

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c5_2, c_1


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

(45) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 2 leading nodes:
   ENCODE_F(z0, z1) -> c(ENCARG(z0))
   ENCODE_F(z0, z1) -> c(ENCARG(z1))

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   encode_f(z0, z1) -> f(encArg(z0), encArg(z1))
   encode_a -> a
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(z0, z1)) -> c1(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1))
   ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1)))
S tuples:
   F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1))
K tuples:none
Defined Rule Symbols:   f_2, encArg_1, encode_f_2, encode_a

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c5_2, c_1


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

(47) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   encode_f(z0, z1) -> f(encArg(z0), encArg(z1))
   encode_a -> a

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(z0, z1)) -> c1(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1))
   ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1)))
S tuples:
   F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c5_2, c_1


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

(49) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(z0, z1)) -> c1(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by 
   ENCARG(cons_f(x0, a)) -> c1(F(encArg(x0), a), ENCARG(x0), ENCARG(a))
   ENCARG(cons_f(x0, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1)))
   ENCARG(cons_f(a, x1)) -> c1(F(a, encArg(x1)), ENCARG(a), ENCARG(x1))
   ENCARG(cons_f(cons_f(z0, z1), x1)) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1))

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1))
   ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1)))
   ENCARG(cons_f(x0, a)) -> c1(F(encArg(x0), a), ENCARG(x0), ENCARG(a))
   ENCARG(cons_f(x0, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1)))
   ENCARG(cons_f(a, x1)) -> c1(F(a, encArg(x1)), ENCARG(a), ENCARG(x1))
   ENCARG(cons_f(cons_f(z0, z1), x1)) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1))
S tuples:
   F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c5_2, c_1, c1_3


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

(51) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing tuple parts
----------------------------------------

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1))
   ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1)))
   ENCARG(cons_f(x0, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1)))
   ENCARG(cons_f(cons_f(z0, z1), x1)) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1))
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c1(F(a, encArg(x1)), ENCARG(x1))
S tuples:
   F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c5_2, c_1, c1_3, c1_1, c1_2


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

(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(z0, c_f(z1, a)) -> c5(F(a, f(f(f(z0, a), a), z1)), F(f(f(z0, a), a), z1)) by 
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1)))
   ENCARG(cons_f(x0, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1)))
   ENCARG(cons_f(cons_f(z0, z1), x1)) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1))
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c1(F(a, encArg(x1)), ENCARG(x1))
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
S tuples:
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCODE_F_2, ENCARG_1, F_2

Compound Symbols:   c_1, c1_3, c1_1, c1_2, c5_2


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(z0, z1) -> c(F(encArg(z0), encArg(z1))) by 
   ENCODE_F(x0, a) -> c(F(encArg(x0), a))
   ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c(F(a, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1)))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1)))
   ENCARG(cons_f(cons_f(z0, z1), x1)) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1))
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c1(F(a, encArg(x1)), ENCARG(x1))
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, a) -> c(F(encArg(x0), a))
   ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c(F(a, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1)))
S tuples:
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_1, c1_2, c5_2, c_1


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

(57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   ENCODE_F(x0, a) -> c(F(encArg(x0), a))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1)))
   ENCARG(cons_f(cons_f(z0, z1), x1)) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1))
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c1(F(a, encArg(x1)), ENCARG(x1))
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c(F(a, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1)))
S tuples:
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_1, c1_2, c5_2, c_1


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(x0, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) by 
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(a), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(cons_f(z0, z1), x1)) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1))
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c1(F(a, encArg(x1)), ENCARG(x1))
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c(F(a, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(a), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
S tuples:
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_1, c1_2, c5_2, c_1


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

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(cons_f(z0, z1), x1)) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1))
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c1(F(a, encArg(x1)), ENCARG(x1))
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c(F(a, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
S tuples:
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_1, c1_2, c5_2, c_1


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(cons_f(z0, z1), x1)) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) by 
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)), ENCARG(a))
   ENCARG(cons_f(cons_f(x0, x1), cons_f(z0, z1))) -> c1(F(f(encArg(x0), encArg(x1)), f(encArg(z0), encArg(z1))), ENCARG(cons_f(x0, x1)), ENCARG(cons_f(z0, z1)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c1(F(a, encArg(x1)), ENCARG(x1))
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c(F(a, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)), ENCARG(a))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
S tuples:
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_1, c1_2, c5_2, c_1, c1_3


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

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c1(F(a, encArg(x1)), ENCARG(x1))
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c(F(a, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
S tuples:
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_1, c1_2, c5_2, c_1, c1_3


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

(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(a, x1)) -> c1(F(a, encArg(x1)), ENCARG(x1)) by 
   ENCARG(cons_f(a, a)) -> c1(F(a, a), ENCARG(a))
   ENCARG(cons_f(a, cons_f(z0, z1))) -> c1(F(a, f(encArg(z0), encArg(z1))), ENCARG(cons_f(z0, z1)))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c(F(a, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(a, a)) -> c1(F(a, a), ENCARG(a))
S tuples:
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_1, c5_2, c_1, c1_3, c1_2


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

(69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   ENCARG(cons_f(a, a)) -> c1(F(a, a), ENCARG(a))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c(F(a, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
S tuples:
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_1, c5_2, c_1, c1_3, c1_2


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1)) by 
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c(F(a, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
S tuples:
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_1, c5_2, c_1, c1_3, c1_2, c5_1


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

(73) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a))) by 
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c(F(a, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
S tuples:
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_1, c5_2, c_1, c1_3, c1_2, c5_1


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1)) by 
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c(F(a, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
S tuples:
   F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_1, c5_2, c_1, c1_3, c1_2, c5_1


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

(77) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(z0, c_f(x1, a)) -> c5(F(a, f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1)) by 
   F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(x0, a), a), z1)), F(f(f(x0, a), a), z1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c(F(a, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
S tuples:
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, ENCODE_F_2, F_2

Compound Symbols:   c1_1, c_1, c1_3, c1_2, c5_2, c5_1


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(x0, cons_f(z0, z1)) -> c(F(encArg(x0), f(encArg(z0), encArg(z1)))) by 
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   ENCODE_F(a, x1) -> c(F(a, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
S tuples:
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, ENCODE_F_2, F_2

Compound Symbols:   c1_1, c_1, c1_3, c1_2, c5_2, c5_1


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

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(a, x1) -> c(F(a, encArg(x1))) by 
   ENCODE_F(a, a) -> c(F(a, a))
   ENCODE_F(a, cons_f(z0, z1)) -> c(F(a, f(encArg(z0), encArg(z1))))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(a, a) -> c(F(a, a))
S tuples:
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, ENCODE_F_2, F_2

Compound Symbols:   c1_1, c_1, c1_3, c1_2, c5_2, c5_1


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

(83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   ENCODE_F(a, a) -> c(F(a, a))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
S tuples:
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, ENCODE_F_2, F_2

Compound Symbols:   c1_1, c_1, c1_3, c1_2, c5_2, c5_1


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

(85) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(cons_f(z0, z1), x1) -> c(F(f(encArg(z0), encArg(z1)), encArg(x1))) by 
   ENCODE_F(cons_f(x0, x1), a) -> c(F(f(encArg(x0), encArg(x1)), a))
   ENCODE_F(cons_f(x0, x1), cons_f(z0, z1)) -> c(F(f(encArg(x0), encArg(x1)), f(encArg(z0), encArg(z1))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), a) -> c(F(f(encArg(x0), encArg(x1)), a))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
S tuples:
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_1, c1_3, c1_2, c5_2, c5_1, c_1


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

(87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   ENCODE_F(cons_f(x0, x1), a) -> c(F(f(encArg(x0), encArg(x1)), a))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
S tuples:
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_1, c1_3, c1_2, c5_2, c5_1, c_1


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

(89) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1)) by F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
----------------------------------------

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
S tuples:
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_1, c1_3, c1_2, c5_2, c5_1, c_1


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

(91) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(cons_f(x0, a)) -> c1(ENCARG(x0)) by 
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
S tuples:
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_2, c5_1, c_1


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

(93) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1)) by F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
----------------------------------------

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
S tuples:
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_2, c5_1, c_1


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

(95) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1)) by F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
----------------------------------------

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
S tuples:
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_2, c5_1, c_1


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

(97) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a))) by F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
----------------------------------------

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
S tuples:
   F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a)))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_2, c5_1, c_1


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

(99) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a))) by F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
----------------------------------------

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
S tuples:
   F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_2, c5_1, c_1


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

(101) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(x0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(x0, a), a), a), a), a), a), z1)))), F(f(f(x0, a), a), c_f(c_f(z1, a), a))) by F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
----------------------------------------

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
S tuples:
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_2, c5_1, c_1


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

(103) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a))) by F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
----------------------------------------

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
S tuples:
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_2, c5_1, c_1


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

(105) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a))) by F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
----------------------------------------

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
S tuples:
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_2, c5_1, c_1


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

(107) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a))) by F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
----------------------------------------

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
S tuples:
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_2, c5_1, c_1


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

(109) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a))) by F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
----------------------------------------

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
S tuples:
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_2, c5_1, c_1


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

(111) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(x0, c_f(c_f(x1, a), a)) -> c5(F(f(f(x0, a), a), c_f(x1, a))) by F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
----------------------------------------

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), x1)), F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
S tuples:
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_2, c5_1, c_1


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

(113) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(x0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(x0, a), a), z1)), F(f(f(x0, a), a), z1)) by F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
----------------------------------------

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(x0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), x1))), F(f(f(x0, a), a), c_f(x1, a)))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
S tuples:
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_2, c5_1, c_1


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

(115) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a))) by F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
----------------------------------------

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
S tuples:
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_2, c5_1, c_1


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

(117) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1)) by F(z0, c_f(z1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
----------------------------------------

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(z1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
S tuples:
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(z1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_2, c5_1, c_1


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

(119) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1)) by F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
----------------------------------------

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(z0, c_f(x1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(z1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
S tuples:
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(z1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_2, c5_1, c_1


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

(121) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(x0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(x0, a), a), z1)), F(f(f(x0, a), a), z1)) by F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
----------------------------------------

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(z0, c_f(c_f(x1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), x1))), F(f(f(z0, a), a), c_f(x1, a)))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(z1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
S tuples:
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(z1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_1, c5_2, c_1


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

(123) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(x0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(x0, a), a), a), a), z1))), F(f(f(x0, a), a), c_f(z1, a))) by F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
----------------------------------------

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   F(z0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), x1)), F(f(f(z0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(z1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
S tuples:
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(z1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_1, c5_2, c_1


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

(125) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(x0, c_f(x1, a)) -> c5(F(a, f(c_f(c_f(x0, a), a), x1)), F(f(f(x0, a), a), x1)) by F(z0, c_f(z1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
----------------------------------------

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, a)) -> f(a, f(f(f(z0, a), a), z1))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c1(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c1(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c1(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c1(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c1(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c1(ENCARG(cons_f(x0, x1)))
   F(x0, c_f(x1, a)) -> c5(F(f(f(x0, a), a), x1))
   ENCODE_F(x0, cons_f(x1, x2)) -> c(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   ENCARG(cons_f(cons_f(y0, a), a)) -> c1(ENCARG(cons_f(y0, a)))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, y2))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, a)), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, a))))
   ENCARG(cons_f(cons_f(y0, cons_f(y1, cons_f(y2, y3))), a)) -> c1(ENCARG(cons_f(y0, cons_f(y1, cons_f(y2, y3)))))
   ENCARG(cons_f(cons_f(y0, cons_f(a, y1)), a)) -> c1(ENCARG(cons_f(y0, cons_f(a, y1))))
   ENCARG(cons_f(cons_f(y0, cons_f(cons_f(y1, y2), y3)), a)) -> c1(ENCARG(cons_f(y0, cons_f(cons_f(y1, y2), y3))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), cons_f(y2, y3)), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), cons_f(y2, y3))))
   ENCARG(cons_f(cons_f(a, cons_f(y0, y1)), a)) -> c1(ENCARG(cons_f(a, cons_f(y0, y1))))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), y2)))
   ENCARG(cons_f(cons_f(cons_f(y0, a), y1), a)) -> c1(ENCARG(cons_f(cons_f(y0, a), y1)))
   ENCARG(cons_f(cons_f(cons_f(y0, cons_f(y1, y2)), y3), a)) -> c1(ENCARG(cons_f(cons_f(y0, cons_f(y1, y2)), y3)))
   ENCARG(cons_f(cons_f(cons_f(a, y0), y1), a)) -> c1(ENCARG(cons_f(cons_f(a, y0), y1)))
   ENCARG(cons_f(cons_f(cons_f(cons_f(y0, y1), y2), y3), a)) -> c1(ENCARG(cons_f(cons_f(cons_f(y0, y1), y2), y3)))
   ENCARG(cons_f(cons_f(cons_f(y0, y1), a), a)) -> c1(ENCARG(cons_f(cons_f(y0, y1), a)))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(z1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
S tuples:
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(c_f(f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(a, c_f(f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
   F(z0, c_f(z1, a)) -> c5(F(c_f(f(z0, a), a), z1))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, c_f(a, f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, c_f(f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(c_f(z1, a), a), a)) -> c5(F(a, f(a, f(a, f(f(f(f(f(f(f(z0, a), a), a), a), a), a), z1)))), F(c_f(f(z0, a), a), c_f(c_f(z1, a), a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(c_f(f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(c_f(f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(c_f(f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(a, f(a, f(f(f(f(c_f(z0, a), a), a), a), z1))), F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(c_f(z1, a), a)) -> c5(F(c_f(f(z0, a), a), c_f(z1, a)))
   F(z0, c_f(z1, a)) -> c5(F(a, f(c_f(c_f(z0, a), a), z1)), F(c_f(f(z0, a), a), z1))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c1_3, c1_2, c1_1, c5_1, c_1, c5_2