/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 56 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 3 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 0 ms]
    (10) typed CpxTrs
    (11) RewriteLemmaProof [LOWER BOUND(ID), 481 ms]
    (12) BOUNDS(1, INF)
(13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 5 ms]
(14) TRS for Loop Detection
(15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(16) CpxTRS
(17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(18) CpxRelTRS
    (19) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxRelTRS
    (21) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxWeightedTrs
        (23) 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), 0 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 0 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (52) CdtProblem
        (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (58) CdtProblem
        (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (60) CdtProblem
        (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (62) CdtProblem
        (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (64) CdtProblem
        (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (66) CdtProblem
        (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (68) CdtProblem
        (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (70) CdtProblem
        (71) 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) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (78) CdtProblem
        (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (80) CdtProblem
        (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (82) CdtProblem
        (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (84) CdtProblem
        (85) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (86) CdtProblem
        (87) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (88) CdtProblem
        (89) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (90) CdtProblem
        (91) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1 ms]
        (92) CdtProblem
        (93) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (94) CdtProblem
        (95) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 2 ms]
        (96) CdtProblem
        (97) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 3 ms]
        (98) CdtProblem
        (99) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (100) CdtProblem
        (101) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (102) 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(f(x)) -> g(f(x))
   g(g(x)) -> f(x)

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(cons_f(x_1)) -> f(encArg(x_1))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encode_f(x_1) -> f(encArg(x_1))
   encode_g(x_1) -> g(encArg(x_1))


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

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


The TRS R consists of the following rules:

   f(f(x)) -> g(f(x))
   g(g(x)) -> f(x)

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

   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encode_f(x_1) -> f(encArg(x_1))
   encode_g(x_1) -> g(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   f(f(x)) -> g(f(x))
   g(g(x)) -> f(x)

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

   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encode_f(x_1) -> f(encArg(x_1))
   encode_g(x_1) -> g(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   f(f(x)) -> g(f(x))
   g(g(x)) -> f(x)

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

   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encode_f(x_1) -> f(encArg(x_1))
   encode_g(x_1) -> g(encArg(x_1))

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

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

(8)
Obligation:
TRS:
Rules:
f(f(x)) -> g(f(x))
g(g(x)) -> f(x)
encArg(cons_f(x_1)) -> f(encArg(x_1))
encArg(cons_g(x_1)) -> g(encArg(x_1))
encode_f(x_1) -> f(encArg(x_1))
encode_g(x_1) -> g(encArg(x_1))

Types:
f :: f:g:encArg:encode_f:encode_g -> f:g:encArg:encode_f:encode_g
g :: f:g:encArg:encode_f:encode_g -> f:g:encArg:encode_f:encode_g
encArg :: cons_f:cons_g -> f:g:encArg:encode_f:encode_g
cons_f :: cons_f:cons_g -> cons_f:cons_g
cons_g :: cons_f:cons_g -> cons_f:cons_g
encode_f :: cons_f:cons_g -> f:g:encArg:encode_f:encode_g
encode_g :: cons_f:cons_g -> f:g:encArg:encode_f:encode_g
hole_f:g:encArg:encode_f:encode_g1_0 :: f:g:encArg:encode_f:encode_g
hole_cons_f:cons_g2_0 :: cons_f:cons_g
gen_cons_f:cons_g3_0 :: Nat -> cons_f:cons_g

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

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

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

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

(10)
Obligation:
TRS:
Rules:
f(f(x)) -> g(f(x))
g(g(x)) -> f(x)
encArg(cons_f(x_1)) -> f(encArg(x_1))
encArg(cons_g(x_1)) -> g(encArg(x_1))
encode_f(x_1) -> f(encArg(x_1))
encode_g(x_1) -> g(encArg(x_1))

Types:
f :: f:g:encArg:encode_f:encode_g -> f:g:encArg:encode_f:encode_g
g :: f:g:encArg:encode_f:encode_g -> f:g:encArg:encode_f:encode_g
encArg :: cons_f:cons_g -> f:g:encArg:encode_f:encode_g
cons_f :: cons_f:cons_g -> cons_f:cons_g
cons_g :: cons_f:cons_g -> cons_f:cons_g
encode_f :: cons_f:cons_g -> f:g:encArg:encode_f:encode_g
encode_g :: cons_f:cons_g -> f:g:encArg:encode_f:encode_g
hole_f:g:encArg:encode_f:encode_g1_0 :: f:g:encArg:encode_f:encode_g
hole_cons_f:cons_g2_0 :: cons_f:cons_g
gen_cons_f:cons_g3_0 :: Nat -> cons_f:cons_g


Generator Equations:
gen_cons_f:cons_g3_0(0) <=> hole_cons_f:cons_g2_0
gen_cons_f:cons_g3_0(+(x, 1)) <=> cons_f(gen_cons_f:cons_g3_0(x))


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

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

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

(11) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_cons_f:cons_g3_0(+(1, n11_0))) -> *4_0, rt in Omega(0)

Induction Base:
encArg(gen_cons_f:cons_g3_0(+(1, 0)))

Induction Step:
encArg(gen_cons_f:cons_g3_0(+(1, +(n11_0, 1)))) ->_R^Omega(0)
f(encArg(gen_cons_f:cons_g3_0(+(1, n11_0)))) ->_IH
f(*4_0)

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

(12)
BOUNDS(1, INF)

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

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

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

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


The TRS R consists of the following rules:

   f(f(x)) -> g(f(x))
   g(g(x)) -> f(x)

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

   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encode_f(x_1) -> f(encArg(x_1))
   encode_g(x_1) -> g(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   f(f(x)) -> g(f(x))
   g(g(x)) -> f(x)
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encode_f(x_1) -> f(encArg(x_1))
   encode_g(x_1) -> g(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   f(c_f(x)) -> g(f(x))
   g(c_g(x)) -> f(x)

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

   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encode_f(x_1) -> f(encArg(x_1))
   encode_g(x_1) -> g(encArg(x_1))
   f(x0) -> c_f(x0)
   g(x0) -> c_g(x0)

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

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

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

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


The TRS R consists of the following rules:

   f(c_f(x)) -> g(f(x))
   g(c_g(x)) -> f(x)

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

   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encode_f(x_1) -> f(encArg(x_1))
   encode_g(x_1) -> g(encArg(x_1))
   f(x0) -> c_f(x0)
   g(x0) -> c_g(x0)

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

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

(22)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   f(c_f(x)) -> g(f(x)) [1]
   g(c_g(x)) -> f(x) [1]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   f(x0) -> c_f(x0) [0]
   g(x0) -> c_g(x0) [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(c_f(x)) -> g(f(x)) [1]
   g(c_g(x)) -> f(x) [1]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   f(x0) -> c_f(x0) [0]
   g(x0) -> c_g(x0) [0]

The TRS has the following type information:
f :: c_f:c_g -> c_f:c_g
c_f :: c_f:c_g -> c_f:c_g
g :: c_f:c_g -> c_f:c_g
c_g :: c_f:c_g -> c_f:c_g
encArg :: cons_f:cons_g -> c_f:c_g
cons_f :: cons_f:cons_g -> cons_f:cons_g
cons_g :: cons_f:cons_g -> cons_f:cons_g
encode_f :: cons_f:cons_g -> c_f:c_g
encode_g :: cons_f:cons_g -> c_f:c_g

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_1
   encode_g_1
   f_1
   g_1

Due to the following rules being added:

   encArg(v0) -> const [0]
   encode_f(v0) -> const [0]
   encode_g(v0) -> const [0]
   f(v0) -> const [0]
   g(v0) -> const [0]

And the following fresh constants:    const, const1

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

(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(c_f(x)) -> g(f(x)) [1]
   g(c_g(x)) -> f(x) [1]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   f(x0) -> c_f(x0) [0]
   g(x0) -> c_g(x0) [0]
   encArg(v0) -> const [0]
   encode_f(v0) -> const [0]
   encode_g(v0) -> const [0]
   f(v0) -> const [0]
   g(v0) -> const [0]

The TRS has the following type information:
f :: c_f:c_g:const -> c_f:c_g:const
c_f :: c_f:c_g:const -> c_f:c_g:const
g :: c_f:c_g:const -> c_f:c_g:const
c_g :: c_f:c_g:const -> c_f:c_g:const
encArg :: cons_f:cons_g -> c_f:c_g:const
cons_f :: cons_f:cons_g -> cons_f:cons_g
cons_g :: cons_f:cons_g -> cons_f:cons_g
encode_f :: cons_f:cons_g -> c_f:c_g:const
encode_g :: cons_f:cons_g -> c_f:c_g:const
const :: c_f:c_g:const
const1 :: cons_f:cons_g

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(c_f(c_f(x'))) -> g(g(f(x'))) [2]
   f(c_f(x)) -> g(c_f(x)) [1]
   f(c_f(x)) -> g(const) [1]
   g(c_g(x)) -> f(x) [1]
   encArg(cons_f(cons_f(x_1'))) -> f(f(encArg(x_1'))) [0]
   encArg(cons_f(cons_g(x_1''))) -> f(g(encArg(x_1''))) [0]
   encArg(cons_f(x_1)) -> f(const) [0]
   encArg(cons_g(cons_f(x_11))) -> g(f(encArg(x_11))) [0]
   encArg(cons_g(cons_g(x_12))) -> g(g(encArg(x_12))) [0]
   encArg(cons_g(x_1)) -> g(const) [0]
   encode_f(cons_f(x_13)) -> f(f(encArg(x_13))) [0]
   encode_f(cons_g(x_14)) -> f(g(encArg(x_14))) [0]
   encode_f(x_1) -> f(const) [0]
   encode_g(cons_f(x_15)) -> g(f(encArg(x_15))) [0]
   encode_g(cons_g(x_16)) -> g(g(encArg(x_16))) [0]
   encode_g(x_1) -> g(const) [0]
   f(x0) -> c_f(x0) [0]
   g(x0) -> c_g(x0) [0]
   encArg(v0) -> const [0]
   encode_f(v0) -> const [0]
   encode_g(v0) -> const [0]
   f(v0) -> const [0]
   g(v0) -> const [0]

The TRS has the following type information:
f :: c_f:c_g:const -> c_f:c_g:const
c_f :: c_f:c_g:const -> c_f:c_g:const
g :: c_f:c_g:const -> c_f:c_g:const
c_g :: c_f:c_g:const -> c_f:c_g:const
encArg :: cons_f:cons_g -> c_f:c_g:const
cons_f :: cons_f:cons_g -> cons_f:cons_g
cons_g :: cons_f:cons_g -> cons_f:cons_g
encode_f :: cons_f:cons_g -> c_f:c_g:const
encode_g :: cons_f:cons_g -> c_f:c_g:const
const :: c_f:c_g:const
const1 :: cons_f:cons_g

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:

   const => 0
   const1 => 0

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

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

   encArg(z) -{ 0 }-> g(g(encArg(x_12))) :|: z = 1 + (1 + x_12), x_12 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_11))) :|: x_11 >= 0, z = 1 + (1 + x_11)
   encArg(z) -{ 0 }-> g(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0
   encArg(z) -{ 0 }-> f(f(encArg(x_1'))) :|: z = 1 + (1 + x_1'), x_1' >= 0
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_f(z) -{ 0 }-> f(g(encArg(x_14))) :|: x_14 >= 0, z = 1 + x_14
   encode_f(z) -{ 0 }-> f(f(encArg(x_13))) :|: z = 1 + x_13, x_13 >= 0
   encode_f(z) -{ 0 }-> f(0) :|: x_1 >= 0, z = x_1
   encode_f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_g(z) -{ 0 }-> g(g(encArg(x_16))) :|: z = 1 + x_16, x_16 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_15))) :|: x_15 >= 0, z = 1 + x_15
   encode_g(z) -{ 0 }-> g(0) :|: x_1 >= 0, z = x_1
   encode_g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   f(z) -{ 2 }-> g(g(f(x'))) :|: x' >= 0, z = 1 + (1 + x')
   f(z) -{ 1 }-> g(0) :|: x >= 0, z = 1 + x
   f(z) -{ 1 }-> g(1 + x) :|: x >= 0, z = 1 + x
   f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   f(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   g(z) -{ 1 }-> f(x) :|: x >= 0, z = 1 + x
   g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   g(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0


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

(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 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_f(z) -{ 0 }-> f(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(0) :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 2 }-> g(g(f(z - 2))) :|: z - 2 >= 0
   f(z) -{ 1 }-> g(0) :|: z - 1 >= 0
   f(z) -{ 1 }-> g(1 + (z - 1)) :|: z - 1 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   g(z) -{ 1 }-> f(z - 1) :|: z - 1 >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: 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) -> null_encode_f [0]
   encode_g(v0) -> null_encode_g [0]
   f(v0) -> null_f [0]
   g(v0) -> null_g [0]

And the following fresh constants:    null_encArg, null_encode_f, null_encode_g, null_f, null_g, const

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

(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(c_f(x)) -> g(f(x)) [1]
   g(c_g(x)) -> f(x) [1]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   f(x0) -> c_f(x0) [0]
   g(x0) -> c_g(x0) [0]
   encArg(v0) -> null_encArg [0]
   encode_f(v0) -> null_encode_f [0]
   encode_g(v0) -> null_encode_g [0]
   f(v0) -> null_f [0]
   g(v0) -> null_g [0]

The TRS has the following type information:
f :: c_f:c_g:null_encArg:null_encode_f:null_encode_g:null_f:null_g -> c_f:c_g:null_encArg:null_encode_f:null_encode_g:null_f:null_g
c_f :: c_f:c_g:null_encArg:null_encode_f:null_encode_g:null_f:null_g -> c_f:c_g:null_encArg:null_encode_f:null_encode_g:null_f:null_g
g :: c_f:c_g:null_encArg:null_encode_f:null_encode_g:null_f:null_g -> c_f:c_g:null_encArg:null_encode_f:null_encode_g:null_f:null_g
c_g :: c_f:c_g:null_encArg:null_encode_f:null_encode_g:null_f:null_g -> c_f:c_g:null_encArg:null_encode_f:null_encode_g:null_f:null_g
encArg :: cons_f:cons_g -> c_f:c_g:null_encArg:null_encode_f:null_encode_g:null_f:null_g
cons_f :: cons_f:cons_g -> cons_f:cons_g
cons_g :: cons_f:cons_g -> cons_f:cons_g
encode_f :: cons_f:cons_g -> c_f:c_g:null_encArg:null_encode_f:null_encode_g:null_f:null_g
encode_g :: cons_f:cons_g -> c_f:c_g:null_encArg:null_encode_f:null_encode_g:null_f:null_g
null_encArg :: c_f:c_g:null_encArg:null_encode_f:null_encode_g:null_f:null_g
null_encode_f :: c_f:c_g:null_encArg:null_encode_f:null_encode_g:null_f:null_g
null_encode_g :: c_f:c_g:null_encArg:null_encode_f:null_encode_g:null_f:null_g
null_f :: c_f:c_g:null_encArg:null_encode_f:null_encode_g:null_f:null_g
null_g :: c_f:c_g:null_encArg:null_encode_f:null_encode_g:null_f:null_g
const :: cons_f:cons_g

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:

   null_encArg => 0
   null_encode_f => 0
   null_encode_g => 0
   null_f => 0
   null_g => 0
   const => 0

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

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

   encArg(z) -{ 0 }-> g(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_f(z) -{ 0 }-> f(encArg(x_1)) :|: x_1 >= 0, z = x_1
   encode_f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_g(z) -{ 0 }-> g(encArg(x_1)) :|: x_1 >= 0, z = x_1
   encode_g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   f(z) -{ 1 }-> g(f(x)) :|: x >= 0, z = 1 + x
   f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   f(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   g(z) -{ 1 }-> f(x) :|: x >= 0, z = 1 + x
   g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   g(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0

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(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encode_f(z0) -> f(encArg(z0))
   encode_g(z0) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   ENCARG(cons_f(z0)) -> c(F(encArg(z0)), ENCARG(z0))
   ENCARG(cons_g(z0)) -> c1(G(encArg(z0)), ENCARG(z0))
   ENCODE_F(z0) -> c2(F(encArg(z0)), ENCARG(z0))
   ENCODE_G(z0) -> c3(G(encArg(z0)), ENCARG(z0))
   F(z0) -> c4
   F(c_f(z0)) -> c5(G(f(z0)), F(z0))
   G(z0) -> c6
   G(c_g(z0)) -> c7(F(z0))
S tuples:
   F(c_f(z0)) -> c5(G(f(z0)), F(z0))
   G(c_g(z0)) -> c7(F(z0))
K tuples:none
Defined Rule Symbols:   f_1, g_1, encArg_1, encode_f_1, encode_g_1

Defined Pair Symbols:   ENCARG_1, ENCODE_F_1, ENCODE_G_1, F_1, G_1

Compound Symbols:   c_2, c1_2, c2_2, c3_2, c4, c5_2, c6, c7_1


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

(39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 2 trailing nodes:
   G(z0) -> c6
   F(z0) -> c4

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encode_f(z0) -> f(encArg(z0))
   encode_g(z0) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   ENCARG(cons_f(z0)) -> c(F(encArg(z0)), ENCARG(z0))
   ENCARG(cons_g(z0)) -> c1(G(encArg(z0)), ENCARG(z0))
   ENCODE_F(z0) -> c2(F(encArg(z0)), ENCARG(z0))
   ENCODE_G(z0) -> c3(G(encArg(z0)), ENCARG(z0))
   F(c_f(z0)) -> c5(G(f(z0)), F(z0))
   G(c_g(z0)) -> c7(F(z0))
S tuples:
   F(c_f(z0)) -> c5(G(f(z0)), F(z0))
   G(c_g(z0)) -> c7(F(z0))
K tuples:none
Defined Rule Symbols:   f_1, g_1, encArg_1, encode_f_1, encode_g_1

Defined Pair Symbols:   ENCARG_1, ENCODE_F_1, ENCODE_G_1, F_1, G_1

Compound Symbols:   c_2, c1_2, c2_2, c3_2, c5_2, c7_1


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

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encode_f(z0) -> f(encArg(z0))
   encode_g(z0) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   ENCARG(cons_f(z0)) -> c(F(encArg(z0)), ENCARG(z0))
   ENCARG(cons_g(z0)) -> c1(G(encArg(z0)), ENCARG(z0))
   F(c_f(z0)) -> c5(G(f(z0)), F(z0))
   G(c_g(z0)) -> c7(F(z0))
   ENCODE_F(z0) -> c4(F(encArg(z0)))
   ENCODE_F(z0) -> c4(ENCARG(z0))
   ENCODE_G(z0) -> c4(G(encArg(z0)))
   ENCODE_G(z0) -> c4(ENCARG(z0))
S tuples:
   F(c_f(z0)) -> c5(G(f(z0)), F(z0))
   G(c_g(z0)) -> c7(F(z0))
K tuples:none
Defined Rule Symbols:   f_1, g_1, encArg_1, encode_f_1, encode_g_1

Defined Pair Symbols:   ENCARG_1, F_1, G_1, ENCODE_F_1, ENCODE_G_1

Compound Symbols:   c_2, c1_2, c5_2, c7_1, c4_1


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

(43) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 2 leading nodes:
   ENCODE_F(z0) -> c4(ENCARG(z0))
   ENCODE_G(z0) -> c4(ENCARG(z0))

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encode_f(z0) -> f(encArg(z0))
   encode_g(z0) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   ENCARG(cons_f(z0)) -> c(F(encArg(z0)), ENCARG(z0))
   ENCARG(cons_g(z0)) -> c1(G(encArg(z0)), ENCARG(z0))
   F(c_f(z0)) -> c5(G(f(z0)), F(z0))
   G(c_g(z0)) -> c7(F(z0))
   ENCODE_F(z0) -> c4(F(encArg(z0)))
   ENCODE_G(z0) -> c4(G(encArg(z0)))
S tuples:
   F(c_f(z0)) -> c5(G(f(z0)), F(z0))
   G(c_g(z0)) -> c7(F(z0))
K tuples:none
Defined Rule Symbols:   f_1, g_1, encArg_1, encode_f_1, encode_g_1

Defined Pair Symbols:   ENCARG_1, F_1, G_1, ENCODE_F_1, ENCODE_G_1

Compound Symbols:   c_2, c1_2, c5_2, c7_1, c4_1


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

(45) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   encode_f(z0) -> f(encArg(z0))
   encode_g(z0) -> g(encArg(z0))

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   ENCARG(cons_f(z0)) -> c(F(encArg(z0)), ENCARG(z0))
   ENCARG(cons_g(z0)) -> c1(G(encArg(z0)), ENCARG(z0))
   F(c_f(z0)) -> c5(G(f(z0)), F(z0))
   G(c_g(z0)) -> c7(F(z0))
   ENCODE_F(z0) -> c4(F(encArg(z0)))
   ENCODE_G(z0) -> c4(G(encArg(z0)))
S tuples:
   F(c_f(z0)) -> c5(G(f(z0)), F(z0))
   G(c_g(z0)) -> c7(F(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   ENCARG_1, F_1, G_1, ENCODE_F_1, ENCODE_G_1

Compound Symbols:   c_2, c1_2, c5_2, c7_1, c4_1


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

(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(z0)) -> c(F(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_f(cons_f(z0))) -> c(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c(F(g(encArg(z0))), ENCARG(cons_g(z0)))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   ENCARG(cons_g(z0)) -> c1(G(encArg(z0)), ENCARG(z0))
   F(c_f(z0)) -> c5(G(f(z0)), F(z0))
   G(c_g(z0)) -> c7(F(z0))
   ENCODE_F(z0) -> c4(F(encArg(z0)))
   ENCODE_G(z0) -> c4(G(encArg(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c(F(g(encArg(z0))), ENCARG(cons_g(z0)))
S tuples:
   F(c_f(z0)) -> c5(G(f(z0)), F(z0))
   G(c_g(z0)) -> c7(F(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   ENCARG_1, F_1, G_1, ENCODE_F_1, ENCODE_G_1

Compound Symbols:   c1_2, c5_2, c7_1, c4_1, c_2


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

(49) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_g(z0)) -> c1(G(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_g(cons_f(z0))) -> c1(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c1(G(g(encArg(z0))), ENCARG(cons_g(z0)))

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   F(c_f(z0)) -> c5(G(f(z0)), F(z0))
   G(c_g(z0)) -> c7(F(z0))
   ENCODE_F(z0) -> c4(F(encArg(z0)))
   ENCODE_G(z0) -> c4(G(encArg(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c1(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c1(G(g(encArg(z0))), ENCARG(cons_g(z0)))
S tuples:
   F(c_f(z0)) -> c5(G(f(z0)), F(z0))
   G(c_g(z0)) -> c7(F(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   F_1, G_1, ENCODE_F_1, ENCODE_G_1, ENCARG_1

Compound Symbols:   c5_2, c7_1, c4_1, c_2, c1_2


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(c_f(z0)) -> c5(G(f(z0)), F(z0)) by 
   F(c_f(z0)) -> c5(G(c_f(z0)), F(z0))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   ENCODE_F(z0) -> c4(F(encArg(z0)))
   ENCODE_G(z0) -> c4(G(encArg(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c1(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c1(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   F(c_f(z0)) -> c5(G(c_f(z0)), F(z0))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(z0)) -> c5(G(c_f(z0)), F(z0))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, ENCODE_F_1, ENCODE_G_1, ENCARG_1, F_1

Compound Symbols:   c7_1, c4_1, c_2, c1_2, c5_2


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

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   ENCODE_F(z0) -> c4(F(encArg(z0)))
   ENCODE_G(z0) -> c4(G(encArg(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c1(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c1(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, ENCODE_F_1, ENCODE_G_1, ENCARG_1, F_1

Compound Symbols:   c7_1, c4_1, c_2, c1_2, c5_2, c5_1


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(z0) -> c4(F(encArg(z0))) by 
   ENCODE_F(cons_f(z0)) -> c4(F(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c4(F(g(encArg(z0))))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   ENCODE_G(z0) -> c4(G(encArg(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c1(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c1(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
   ENCODE_F(cons_f(z0)) -> c4(F(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c4(F(g(encArg(z0))))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, ENCODE_G_1, ENCARG_1, F_1, ENCODE_F_1

Compound Symbols:   c7_1, c4_1, c_2, c1_2, c5_2, c5_1


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

(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_G(z0) -> c4(G(encArg(z0))) by 
   ENCODE_G(cons_f(z0)) -> c4(G(f(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c4(G(g(encArg(z0))))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   ENCARG(cons_f(cons_f(z0))) -> c(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c1(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c1(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
   ENCODE_F(cons_f(z0)) -> c4(F(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c4(F(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c4(G(f(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c4(G(g(encArg(z0))))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, ENCARG_1, F_1, ENCODE_F_1, ENCODE_G_1

Compound Symbols:   c7_1, c_2, c1_2, c5_2, c5_1, c4_1


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(cons_f(z0))) -> c(F(f(encArg(z0))), ENCARG(cons_f(z0))) by 
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   ENCARG(cons_f(cons_g(z0))) -> c(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c1(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c1(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
   ENCODE_F(cons_f(z0)) -> c4(F(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c4(F(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c4(G(f(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c4(G(g(encArg(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, ENCARG_1, F_1, ENCODE_F_1, ENCODE_G_1

Compound Symbols:   c7_1, c_2, c1_2, c5_2, c5_1, c4_1


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

(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(cons_g(z0))) -> c(F(g(encArg(z0))), ENCARG(cons_g(z0))) by 
   ENCARG(cons_f(cons_g(x0))) -> c(F(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   ENCARG(cons_g(cons_f(z0))) -> c1(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c1(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
   ENCODE_F(cons_f(z0)) -> c4(F(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c4(F(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c4(G(f(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c4(G(g(encArg(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c(F(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, ENCARG_1, F_1, ENCODE_F_1, ENCODE_G_1

Compound Symbols:   c7_1, c1_2, c5_2, c5_1, c4_1, c_2


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

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   ENCARG(cons_g(cons_f(z0))) -> c1(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c1(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
   ENCODE_F(cons_f(z0)) -> c4(F(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c4(F(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c4(G(f(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c4(G(g(encArg(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c(ENCARG(cons_g(x0)))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, ENCARG_1, F_1, ENCODE_F_1, ENCODE_G_1

Compound Symbols:   c7_1, c1_2, c5_2, c5_1, c4_1, c_2, c_1


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

(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_g(cons_f(z0))) -> c1(G(f(encArg(z0))), ENCARG(cons_f(z0))) by 
   ENCARG(cons_g(cons_f(x0))) -> c1(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   ENCARG(cons_g(cons_g(z0))) -> c1(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
   ENCODE_F(cons_f(z0)) -> c4(F(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c4(F(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c4(G(f(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c4(G(g(encArg(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c(ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_f(x0))) -> c1(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, ENCARG_1, F_1, ENCODE_F_1, ENCODE_G_1

Compound Symbols:   c7_1, c1_2, c5_2, c5_1, c4_1, c_2, c_1


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

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   ENCARG(cons_g(cons_g(z0))) -> c1(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
   ENCODE_F(cons_f(z0)) -> c4(F(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c4(F(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c4(G(f(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c4(G(g(encArg(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c(ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c1(ENCARG(cons_f(x0)))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, ENCARG_1, F_1, ENCODE_F_1, ENCODE_G_1

Compound Symbols:   c7_1, c1_2, c5_2, c5_1, c4_1, c_2, c_1, c1_1


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

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_g(cons_g(z0))) -> c1(G(g(encArg(z0))), ENCARG(cons_g(z0))) by 
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
   ENCODE_F(cons_f(z0)) -> c4(F(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c4(F(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c4(G(f(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c4(G(g(encArg(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c(ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c1(ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0)))
   F(c_f(z0)) -> c5(F(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, F_1, ENCODE_F_1, ENCODE_G_1, ENCARG_1

Compound Symbols:   c7_1, c5_2, c5_1, c4_1, c_2, c_1, c1_2, c1_1


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(c_f(c_f(z0))) -> c5(G(g(f(z0))), F(c_f(z0))) by 
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(z0)) -> c5(F(z0))
   ENCODE_F(cons_f(z0)) -> c4(F(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c4(F(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c4(G(f(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c4(G(g(encArg(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c(ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c1(ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(z0)) -> c5(F(z0))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, F_1, ENCODE_F_1, ENCODE_G_1, ENCARG_1

Compound Symbols:   c7_1, c5_1, c4_1, c_2, c_1, c1_2, c1_1, c5_2


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

(73) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(cons_f(z0)) -> c4(F(f(encArg(z0)))) by 
   ENCODE_F(cons_f(x0)) -> c4(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(cons_f(z0))) -> c4(F(f(f(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c4(F(f(g(encArg(z0)))))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(z0)) -> c5(F(z0))
   ENCODE_F(cons_g(z0)) -> c4(F(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c4(G(f(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c4(G(g(encArg(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c(ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c1(ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   ENCODE_F(cons_f(x0)) -> c4(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(cons_f(z0))) -> c4(F(f(f(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c4(F(f(g(encArg(z0)))))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(z0)) -> c5(F(z0))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, F_1, ENCODE_F_1, ENCODE_G_1, ENCARG_1

Compound Symbols:   c7_1, c5_1, c4_1, c_2, c_1, c1_2, c1_1, c5_2


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(cons_g(z0)) -> c4(F(g(encArg(z0)))) by 
   ENCODE_F(cons_g(x0)) -> c4(F(c_g(encArg(x0))))
   ENCODE_F(cons_g(cons_f(z0))) -> c4(F(g(f(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c4(F(g(g(encArg(z0)))))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(z0)) -> c5(F(z0))
   ENCODE_G(cons_f(z0)) -> c4(G(f(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c4(G(g(encArg(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c(ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c1(ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   ENCODE_F(cons_f(x0)) -> c4(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(cons_f(z0))) -> c4(F(f(f(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c4(F(f(g(encArg(z0)))))
   ENCODE_F(cons_g(x0)) -> c4(F(c_g(encArg(x0))))
   ENCODE_F(cons_g(cons_f(z0))) -> c4(F(g(f(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c4(F(g(g(encArg(z0)))))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(z0)) -> c5(F(z0))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, F_1, ENCODE_G_1, ENCARG_1, ENCODE_F_1

Compound Symbols:   c7_1, c5_1, c4_1, c_2, c_1, c1_2, c1_1, c5_2


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

(77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   ENCODE_F(cons_g(x0)) -> c4(F(c_g(encArg(x0))))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(z0)) -> c5(F(z0))
   ENCODE_G(cons_f(z0)) -> c4(G(f(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c4(G(g(encArg(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c(ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c1(ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   ENCODE_F(cons_f(x0)) -> c4(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(cons_f(z0))) -> c4(F(f(f(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c4(F(f(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c4(F(g(f(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c4(F(g(g(encArg(z0)))))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(z0)) -> c5(F(z0))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, F_1, ENCODE_G_1, ENCARG_1, ENCODE_F_1

Compound Symbols:   c7_1, c5_1, c4_1, c_2, c_1, c1_2, c1_1, c5_2


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_G(cons_f(z0)) -> c4(G(f(encArg(z0)))) by 
   ENCODE_G(cons_f(x0)) -> c4(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(cons_f(z0))) -> c4(G(f(f(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c4(G(f(g(encArg(z0)))))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(z0)) -> c5(F(z0))
   ENCODE_G(cons_g(z0)) -> c4(G(g(encArg(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c(ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c1(ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   ENCODE_F(cons_f(x0)) -> c4(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(cons_f(z0))) -> c4(F(f(f(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c4(F(f(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c4(F(g(f(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c4(F(g(g(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c4(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(cons_f(z0))) -> c4(G(f(f(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c4(G(f(g(encArg(z0)))))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(z0)) -> c5(F(z0))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, F_1, ENCODE_G_1, ENCARG_1, ENCODE_F_1

Compound Symbols:   c7_1, c5_1, c4_1, c_2, c_1, c1_2, c1_1, c5_2


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

(81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   ENCODE_G(cons_f(x0)) -> c4(G(c_f(encArg(x0))))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(z0)) -> c5(F(z0))
   ENCODE_G(cons_g(z0)) -> c4(G(g(encArg(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c(ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c1(ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   ENCODE_F(cons_f(x0)) -> c4(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(cons_f(z0))) -> c4(F(f(f(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c4(F(f(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c4(F(g(f(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c4(F(g(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c4(G(f(f(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c4(G(f(g(encArg(z0)))))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(z0)) -> c5(F(z0))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, F_1, ENCODE_G_1, ENCARG_1, ENCODE_F_1

Compound Symbols:   c7_1, c5_1, c4_1, c_2, c_1, c1_2, c1_1, c5_2


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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_G(cons_g(z0)) -> c4(G(g(encArg(z0)))) by 
   ENCODE_G(cons_g(x0)) -> c4(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(cons_f(z0))) -> c4(G(g(f(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c4(G(g(g(encArg(z0)))))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(z0)) -> c5(F(z0))
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c(ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c1(ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   ENCODE_F(cons_f(x0)) -> c4(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(cons_f(z0))) -> c4(F(f(f(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c4(F(f(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c4(F(g(f(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c4(F(g(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c4(G(f(f(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c4(G(f(g(encArg(z0)))))
   ENCODE_G(cons_g(x0)) -> c4(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(cons_f(z0))) -> c4(G(g(f(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c4(G(g(g(encArg(z0)))))
S tuples:
   G(c_g(z0)) -> c7(F(z0))
   F(c_f(z0)) -> c5(F(z0))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   G_1, F_1, ENCARG_1, ENCODE_F_1, ENCODE_G_1

Compound Symbols:   c7_1, c5_1, c_2, c_1, c1_2, c1_1, c5_2, c4_1


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

(85) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace G(c_g(z0)) -> c7(F(z0)) by 
   G(c_g(c_f(y0))) -> c7(F(c_f(y0)))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   F(c_f(z0)) -> c5(F(z0))
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c(ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c1(ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   ENCODE_F(cons_f(x0)) -> c4(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(cons_f(z0))) -> c4(F(f(f(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c4(F(f(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c4(F(g(f(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c4(F(g(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c4(G(f(f(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c4(G(f(g(encArg(z0)))))
   ENCODE_G(cons_g(x0)) -> c4(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(cons_f(z0))) -> c4(G(g(f(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c4(G(g(g(encArg(z0)))))
   G(c_g(c_f(y0))) -> c7(F(c_f(y0)))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
S tuples:
   F(c_f(z0)) -> c5(F(z0))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   G(c_g(c_f(y0))) -> c7(F(c_f(y0)))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   F_1, ENCARG_1, ENCODE_F_1, ENCODE_G_1, G_1

Compound Symbols:   c5_1, c_2, c_1, c1_2, c1_1, c5_2, c4_1, c7_1


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

(87) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(c_f(c_f(z0))) -> c5(G(g(c_f(z0))), F(c_f(z0))) by F(c_f(c_f(z0))) -> c5(G(c_g(c_f(z0))), F(c_f(z0)))
----------------------------------------

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   F(c_f(z0)) -> c5(F(z0))
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c(ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c1(ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   ENCODE_F(cons_f(x0)) -> c4(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(cons_f(z0))) -> c4(F(f(f(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c4(F(f(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c4(F(g(f(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c4(F(g(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c4(G(f(f(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c4(G(f(g(encArg(z0)))))
   ENCODE_G(cons_g(x0)) -> c4(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(cons_f(z0))) -> c4(G(g(f(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c4(G(g(g(encArg(z0)))))
   G(c_g(c_f(y0))) -> c7(F(c_f(y0)))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(z0))) -> c5(G(c_g(c_f(z0))), F(c_f(z0)))
S tuples:
   F(c_f(z0)) -> c5(F(z0))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   G(c_g(c_f(y0))) -> c7(F(c_f(y0)))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(z0))) -> c5(G(c_g(c_f(z0))), F(c_f(z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   F_1, ENCARG_1, ENCODE_F_1, ENCODE_G_1, G_1

Compound Symbols:   c5_1, c_2, c_1, c1_2, c1_1, c5_2, c4_1, c7_1


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

(89) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(c_f(z0)) -> c5(F(z0)) by 
   F(c_f(c_f(y0))) -> c5(F(c_f(y0)))
   F(c_f(c_f(c_f(y0)))) -> c5(F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(F(c_f(c_f(c_f(y0)))))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c(ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c1(ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   ENCODE_F(cons_f(x0)) -> c4(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(cons_f(z0))) -> c4(F(f(f(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c4(F(f(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c4(F(g(f(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c4(F(g(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c4(G(f(f(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c4(G(f(g(encArg(z0)))))
   ENCODE_G(cons_g(x0)) -> c4(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(cons_f(z0))) -> c4(G(g(f(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c4(G(g(g(encArg(z0)))))
   G(c_g(c_f(y0))) -> c7(F(c_f(y0)))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(z0))) -> c5(G(c_g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(y0))) -> c5(F(c_f(y0)))
   F(c_f(c_f(c_f(y0)))) -> c5(F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(F(c_f(c_f(c_f(y0)))))
S tuples:
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   G(c_g(c_f(y0))) -> c7(F(c_f(y0)))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(z0))) -> c5(G(c_g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(y0))) -> c5(F(c_f(y0)))
   F(c_f(c_f(c_f(y0)))) -> c5(F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(F(c_f(c_f(c_f(y0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   ENCARG_1, F_1, ENCODE_F_1, ENCODE_G_1, G_1

Compound Symbols:   c_2, c_1, c1_2, c1_1, c5_2, c4_1, c7_1, c5_1


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

(91) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(cons_f(cons_g(x0))) -> c(ENCARG(cons_g(x0))) by 
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c(ENCARG(cons_g(cons_g(cons_g(y0)))))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c1(ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   ENCODE_F(cons_f(x0)) -> c4(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(cons_f(z0))) -> c4(F(f(f(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c4(F(f(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c4(F(g(f(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c4(F(g(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c4(G(f(f(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c4(G(f(g(encArg(z0)))))
   ENCODE_G(cons_g(x0)) -> c4(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(cons_f(z0))) -> c4(G(g(f(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c4(G(g(g(encArg(z0)))))
   G(c_g(c_f(y0))) -> c7(F(c_f(y0)))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(z0))) -> c5(G(c_g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(y0))) -> c5(F(c_f(y0)))
   F(c_f(c_f(c_f(y0)))) -> c5(F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(F(c_f(c_f(c_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c(ENCARG(cons_g(cons_g(cons_g(y0)))))
S tuples:
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   G(c_g(c_f(y0))) -> c7(F(c_f(y0)))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(z0))) -> c5(G(c_g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(y0))) -> c5(F(c_f(y0)))
   F(c_f(c_f(c_f(y0)))) -> c5(F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(F(c_f(c_f(c_f(y0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   ENCARG_1, F_1, ENCODE_F_1, ENCODE_G_1, G_1

Compound Symbols:   c_2, c1_2, c1_1, c5_2, c4_1, c7_1, c5_1, c_1


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

(93) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(cons_g(cons_f(x0))) -> c1(ENCARG(cons_f(x0))) by 
   ENCARG(cons_g(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(cons_g(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_g(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(cons_f(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(cons_g(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(cons_f(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(cons_g(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   ENCODE_F(cons_f(x0)) -> c4(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(cons_f(z0))) -> c4(F(f(f(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c4(F(f(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c4(F(g(f(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c4(F(g(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c4(G(f(f(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c4(G(f(g(encArg(z0)))))
   ENCODE_G(cons_g(x0)) -> c4(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(cons_f(z0))) -> c4(G(g(f(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c4(G(g(g(encArg(z0)))))
   G(c_g(c_f(y0))) -> c7(F(c_f(y0)))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(z0))) -> c5(G(c_g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(y0))) -> c5(F(c_f(y0)))
   F(c_f(c_f(c_f(y0)))) -> c5(F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(F(c_f(c_f(c_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(cons_g(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_g(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(cons_f(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(cons_g(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(cons_f(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(cons_g(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))))
S tuples:
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   G(c_g(c_f(y0))) -> c7(F(c_f(y0)))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(z0))) -> c5(G(c_g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(y0))) -> c5(F(c_f(y0)))
   F(c_f(c_f(c_f(y0)))) -> c5(F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(F(c_f(c_f(c_f(y0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   ENCARG_1, F_1, ENCODE_F_1, ENCODE_G_1, G_1

Compound Symbols:   c_2, c1_2, c5_2, c4_1, c7_1, c5_1, c_1, c1_1


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

(95) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace G(c_g(c_f(y0))) -> c7(F(c_f(y0))) by 
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   G(c_g(c_f(c_f(c_f(c_f(y0)))))) -> c7(F(c_f(c_f(c_f(c_f(y0))))))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   ENCODE_F(cons_f(x0)) -> c4(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(cons_f(z0))) -> c4(F(f(f(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c4(F(f(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c4(F(g(f(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c4(F(g(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c4(G(f(f(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c4(G(f(g(encArg(z0)))))
   ENCODE_G(cons_g(x0)) -> c4(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(cons_f(z0))) -> c4(G(g(f(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c4(G(g(g(encArg(z0)))))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(z0))) -> c5(G(c_g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(y0))) -> c5(F(c_f(y0)))
   F(c_f(c_f(c_f(y0)))) -> c5(F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(F(c_f(c_f(c_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(cons_g(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_g(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(cons_f(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(cons_g(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(cons_f(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(cons_g(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))))
   G(c_g(c_f(c_f(c_f(c_f(y0)))))) -> c7(F(c_f(c_f(c_f(c_f(y0))))))
S tuples:
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(z0))) -> c5(G(c_g(c_f(z0))), F(c_f(z0)))
   F(c_f(c_f(y0))) -> c5(F(c_f(y0)))
   F(c_f(c_f(c_f(y0)))) -> c5(F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(F(c_f(c_f(c_f(y0)))))
   G(c_g(c_f(c_f(c_f(c_f(y0)))))) -> c7(F(c_f(c_f(c_f(c_f(y0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   ENCARG_1, F_1, ENCODE_F_1, ENCODE_G_1, G_1

Compound Symbols:   c_2, c1_2, c5_2, c4_1, c7_1, c5_1, c_1, c1_1


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

(97) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(c_f(c_f(z0))) -> c5(G(c_g(c_f(z0))), F(c_f(z0))) by 
   F(c_f(c_f(c_f(y0)))) -> c5(G(c_g(c_f(c_f(y0)))), F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(G(c_g(c_f(c_f(c_f(y0))))), F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(c_f(c_f(c_f(y0)))))) -> c5(G(c_g(c_f(c_f(c_f(c_f(y0)))))), F(c_f(c_f(c_f(c_f(y0))))))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   ENCODE_F(cons_f(x0)) -> c4(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(cons_f(z0))) -> c4(F(f(f(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c4(F(f(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c4(F(g(f(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c4(F(g(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c4(G(f(f(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c4(G(f(g(encArg(z0)))))
   ENCODE_G(cons_g(x0)) -> c4(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(cons_f(z0))) -> c4(G(g(f(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c4(G(g(g(encArg(z0)))))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(y0))) -> c5(F(c_f(y0)))
   F(c_f(c_f(c_f(y0)))) -> c5(F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(F(c_f(c_f(c_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(cons_g(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_g(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(cons_f(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(cons_g(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(cons_f(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(cons_g(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))))
   G(c_g(c_f(c_f(c_f(c_f(y0)))))) -> c7(F(c_f(c_f(c_f(c_f(y0))))))
   F(c_f(c_f(c_f(y0)))) -> c5(G(c_g(c_f(c_f(y0)))), F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(G(c_g(c_f(c_f(c_f(y0))))), F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(c_f(c_f(c_f(y0)))))) -> c5(G(c_g(c_f(c_f(c_f(c_f(y0)))))), F(c_f(c_f(c_f(c_f(y0))))))
S tuples:
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(y0))) -> c5(F(c_f(y0)))
   F(c_f(c_f(c_f(y0)))) -> c5(F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(F(c_f(c_f(c_f(y0)))))
   G(c_g(c_f(c_f(c_f(c_f(y0)))))) -> c7(F(c_f(c_f(c_f(c_f(y0))))))
   F(c_f(c_f(c_f(y0)))) -> c5(G(c_g(c_f(c_f(y0)))), F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(G(c_g(c_f(c_f(c_f(y0))))), F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(c_f(c_f(c_f(y0)))))) -> c5(G(c_g(c_f(c_f(c_f(c_f(y0)))))), F(c_f(c_f(c_f(c_f(y0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   ENCARG_1, F_1, ENCODE_F_1, ENCODE_G_1, G_1

Compound Symbols:   c_2, c1_2, c5_2, c4_1, c7_1, c5_1, c_1, c1_1


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

(99) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(c_f(c_f(y0))) -> c5(F(c_f(y0))) by 
   F(c_f(c_f(c_f(y0)))) -> c5(F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(c_f(c_f(c_f(y0)))))) -> c5(F(c_f(c_f(c_f(c_f(y0))))))
   F(c_f(c_f(c_f(c_f(c_f(c_f(y0))))))) -> c5(F(c_f(c_f(c_f(c_f(c_f(y0)))))))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   ENCODE_F(cons_f(x0)) -> c4(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(cons_f(z0))) -> c4(F(f(f(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c4(F(f(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c4(F(g(f(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c4(F(g(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c4(G(f(f(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c4(G(f(g(encArg(z0)))))
   ENCODE_G(cons_g(x0)) -> c4(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(cons_f(z0))) -> c4(G(g(f(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c4(G(g(g(encArg(z0)))))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(c_f(y0)))) -> c5(F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(F(c_f(c_f(c_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(cons_g(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_g(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(cons_f(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(cons_g(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(cons_f(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(cons_g(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))))
   G(c_g(c_f(c_f(c_f(c_f(y0)))))) -> c7(F(c_f(c_f(c_f(c_f(y0))))))
   F(c_f(c_f(c_f(y0)))) -> c5(G(c_g(c_f(c_f(y0)))), F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(G(c_g(c_f(c_f(c_f(y0))))), F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(c_f(c_f(c_f(y0)))))) -> c5(G(c_g(c_f(c_f(c_f(c_f(y0)))))), F(c_f(c_f(c_f(c_f(y0))))))
   F(c_f(c_f(c_f(c_f(c_f(y0)))))) -> c5(F(c_f(c_f(c_f(c_f(y0))))))
   F(c_f(c_f(c_f(c_f(c_f(c_f(y0))))))) -> c5(F(c_f(c_f(c_f(c_f(c_f(y0)))))))
S tuples:
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(c_f(y0)))) -> c5(F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(F(c_f(c_f(c_f(y0)))))
   G(c_g(c_f(c_f(c_f(c_f(y0)))))) -> c7(F(c_f(c_f(c_f(c_f(y0))))))
   F(c_f(c_f(c_f(y0)))) -> c5(G(c_g(c_f(c_f(y0)))), F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(G(c_g(c_f(c_f(c_f(y0))))), F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(c_f(c_f(c_f(y0)))))) -> c5(G(c_g(c_f(c_f(c_f(c_f(y0)))))), F(c_f(c_f(c_f(c_f(y0))))))
   F(c_f(c_f(c_f(c_f(c_f(y0)))))) -> c5(F(c_f(c_f(c_f(c_f(y0))))))
   F(c_f(c_f(c_f(c_f(c_f(c_f(y0))))))) -> c5(F(c_f(c_f(c_f(c_f(c_f(y0)))))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   ENCARG_1, F_1, ENCODE_F_1, ENCODE_G_1, G_1

Compound Symbols:   c_2, c1_2, c5_2, c4_1, c7_1, c5_1, c_1, c1_1


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

(101) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(cons_f(cons_g(cons_f(y0)))) -> c(ENCARG(cons_g(cons_f(y0)))) by 
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(cons_f(y0)))))) -> c(ENCARG(cons_g(cons_f(cons_f(cons_f(y0))))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(cons_g(y0)))))) -> c(ENCARG(cons_g(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(cons_f(y0)))))) -> c(ENCARG(cons_g(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(cons_g(y0)))))) -> c(ENCARG(cons_g(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(cons_f(cons_f(y0))))))) -> c(ENCARG(cons_g(cons_f(cons_g(cons_f(cons_f(y0)))))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(cons_f(cons_g(y0))))))) -> c(ENCARG(cons_g(cons_f(cons_g(cons_f(cons_g(y0)))))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(cons_g(cons_f(y0))))))) -> c(ENCARG(cons_g(cons_f(cons_g(cons_g(cons_f(y0)))))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(cons_g(cons_g(y0))))))) -> c(ENCARG(cons_g(cons_f(cons_g(cons_g(cons_g(y0)))))))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_f(z0)) -> f(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(z0)) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> f(z0)
Tuples:
   ENCARG(cons_f(cons_f(x0))) -> c(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c1(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c1(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c1(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c1(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c1(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   ENCODE_F(cons_f(x0)) -> c4(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(cons_f(z0))) -> c4(F(f(f(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c4(F(f(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c4(F(g(f(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c4(F(g(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c4(G(f(f(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c4(G(f(g(encArg(z0)))))
   ENCODE_G(cons_g(x0)) -> c4(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(cons_f(z0))) -> c4(G(g(f(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c4(G(g(g(encArg(z0)))))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(c_f(y0)))) -> c5(F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(F(c_f(c_f(c_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(cons_g(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_g(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(cons_f(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_f(cons_g(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(cons_f(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_g(cons_f(cons_g(cons_g(cons_g(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))))
   G(c_g(c_f(c_f(c_f(c_f(y0)))))) -> c7(F(c_f(c_f(c_f(c_f(y0))))))
   F(c_f(c_f(c_f(y0)))) -> c5(G(c_g(c_f(c_f(y0)))), F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(G(c_g(c_f(c_f(c_f(y0))))), F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(c_f(c_f(c_f(y0)))))) -> c5(G(c_g(c_f(c_f(c_f(c_f(y0)))))), F(c_f(c_f(c_f(c_f(y0))))))
   F(c_f(c_f(c_f(c_f(c_f(y0)))))) -> c5(F(c_f(c_f(c_f(c_f(y0))))))
   F(c_f(c_f(c_f(c_f(c_f(c_f(y0))))))) -> c5(F(c_f(c_f(c_f(c_f(c_f(y0)))))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(cons_f(y0)))))) -> c(ENCARG(cons_g(cons_f(cons_f(cons_f(y0))))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(cons_g(y0)))))) -> c(ENCARG(cons_g(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(cons_f(y0)))))) -> c(ENCARG(cons_g(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(cons_g(y0)))))) -> c(ENCARG(cons_g(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(cons_f(cons_f(y0))))))) -> c(ENCARG(cons_g(cons_f(cons_g(cons_f(cons_f(y0)))))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(cons_f(cons_g(y0))))))) -> c(ENCARG(cons_g(cons_f(cons_g(cons_f(cons_g(y0)))))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(cons_g(cons_f(y0))))))) -> c(ENCARG(cons_g(cons_f(cons_g(cons_g(cons_f(y0)))))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(cons_g(cons_g(y0))))))) -> c(ENCARG(cons_g(cons_f(cons_g(cons_g(cons_g(y0)))))))
S tuples:
   F(c_f(c_f(x0))) -> c5(G(c_g(f(x0))), F(c_f(x0)))
   F(c_f(c_f(c_f(z0)))) -> c5(G(g(g(f(z0)))), F(c_f(c_f(z0))))
   G(c_g(c_f(c_f(y0)))) -> c7(F(c_f(c_f(y0))))
   G(c_g(c_f(c_f(c_f(y0))))) -> c7(F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(c_f(y0)))) -> c5(F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(F(c_f(c_f(c_f(y0)))))
   G(c_g(c_f(c_f(c_f(c_f(y0)))))) -> c7(F(c_f(c_f(c_f(c_f(y0))))))
   F(c_f(c_f(c_f(y0)))) -> c5(G(c_g(c_f(c_f(y0)))), F(c_f(c_f(y0))))
   F(c_f(c_f(c_f(c_f(y0))))) -> c5(G(c_g(c_f(c_f(c_f(y0))))), F(c_f(c_f(c_f(y0)))))
   F(c_f(c_f(c_f(c_f(c_f(y0)))))) -> c5(G(c_g(c_f(c_f(c_f(c_f(y0)))))), F(c_f(c_f(c_f(c_f(y0))))))
   F(c_f(c_f(c_f(c_f(c_f(y0)))))) -> c5(F(c_f(c_f(c_f(c_f(y0))))))
   F(c_f(c_f(c_f(c_f(c_f(c_f(y0))))))) -> c5(F(c_f(c_f(c_f(c_f(c_f(y0)))))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_1, g_1

Defined Pair Symbols:   ENCARG_1, F_1, ENCODE_F_1, ENCODE_G_1, G_1

Compound Symbols:   c_2, c1_2, c5_2, c4_1, c7_1, c5_1, c_1, c1_1