/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 46 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 0 ms]
    (12) typed CpxTrs
    (13) RewriteLemmaProof [LOWER BOUND(ID), 456 ms]
    (14) BOUNDS(1, INF)
(15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(16) CpxTRS
(17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(18) CpxRelTRS
    (19) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxRelTRS
    (21) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (28) CpxRNTS
        (29) CompletionProof [UPPER BOUND(ID), 0 ms]
        (30) CpxTypedWeightedCompleteTrs
            (31) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
            (32) CpxTypedWeightedCompleteTrs
            (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (34) CpxRNTS
            (35) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (40) CdtProblem
        (41) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CdtProblem
        (43) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (44) CdtProblem
        (45) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (46) CdtProblem
        (47) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
        (48) CdtProblem
        (49) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 232 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (54) CdtProblem
        (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (58) CdtProblem
        (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (60) CdtProblem
        (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (62) CdtProblem
        (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (64) CdtProblem
        (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (66) CdtProblem
        (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (68) CdtProblem
        (69) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (70) CdtProblem
        (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (72) CdtProblem
        (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (74) CdtProblem
        (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (76) CdtProblem
        (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (78) CdtProblem
        (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (80) CdtProblem
        (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (82) CdtProblem
        (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (84) CdtProblem
        (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (86) CdtProblem
        (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (88) CdtProblem
        (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (90) CdtProblem
        (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (92) CdtProblem
        (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (94) CdtProblem
        (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (96) CdtProblem
        (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (98) CdtProblem
        (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (100) CdtProblem
        (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (102) CdtProblem
        (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (104) CdtProblem
        (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (106) CdtProblem
        (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (108) CdtProblem
        (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (110) CdtProblem
        (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (112) CdtProblem
        (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (114) CdtProblem
        (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 211 ms]
        (116) CdtProblem
        (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (118) CdtProblem
        (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 177 ms]
        (120) CdtProblem
        (121) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (122) CdtProblem
        (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 156 ms]
        (124) CdtProblem
        (125) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (126) CdtProblem
        (127) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (128) CdtProblem
        (129) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (130) CdtProblem
        (131) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (132) CdtProblem
        (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (134) CdtProblem
        (135) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 119 ms]
        (136) CdtProblem
        (137) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (138) CdtProblem
        (139) CdtRewritingProof [BOTH BOUNDS(ID, ID), 11 ms]
        (140) CdtProblem
        (141) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (142) CdtProblem
        (143) CdtRewritingProof [BOTH BOUNDS(ID, ID), 11 ms]
        (144) CdtProblem
        (145) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (146) CdtProblem
        (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (148) CdtProblem
        (149) CdtRewritingProof [BOTH BOUNDS(ID, ID), 14 ms]
        (150) CdtProblem
        (151) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (152) CdtProblem
        (153) CdtRewritingProof [BOTH BOUNDS(ID, ID), 22 ms]
        (154) CdtProblem
        (155) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (156) CdtProblem
        (157) CdtRewritingProof [BOTH BOUNDS(ID, ID), 18 ms]
        (158) CdtProblem
        (159) CdtRewritingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (160) CdtProblem
        (161) CdtRewritingProof [BOTH BOUNDS(ID, ID), 7 ms]
        (162) CdtProblem
        (163) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 31 ms]
        (164) CdtProblem
        (165) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (166) CdtProblem
        (167) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 10 ms]
        (168) 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:

   g(c(x1)) -> g(f(c(x1)))
   g(f(c(x1))) -> g(f(f(c(x1))))
   g(g(x1)) -> g(f(g(x1)))
   f(f(g(x1))) -> g(f(x1))

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

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

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

   g(c(x1)) -> g(f(c(x1)))
   g(f(c(x1))) -> g(f(f(c(x1))))
   g(g(x1)) -> g(f(g(x1)))
   f(f(g(x1))) -> g(f(x1))

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

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

   g(c(x1)) -> g(f(c(x1)))
   g(f(c(x1))) -> g(f(f(c(x1))))
   g(g(x1)) -> g(f(g(x1)))
   f(f(g(x1))) -> g(f(x1))

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

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

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

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

(6)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

   g(c(x1)) -> g(f(c(x1)))
   g(f(c(x1))) -> g(f(f(c(x1))))
   g(g(x1)) -> g(f(g(x1)))
   f(f(g(x1))) -> g(f(x1))

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

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

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

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

(8)
Obligation:
The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   g(c(x1)) -> g(f(c(x1)))
   g(f(c(x1))) -> g(f(f(c(x1))))
   g(g(x1)) -> g(f(g(x1)))
   f(f(g(x1))) -> g(f(x1))

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

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

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

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

(10)
Obligation:
TRS:
Rules:
g(c(x1)) -> g(f(c(x1)))
g(f(c(x1))) -> g(f(f(c(x1))))
g(g(x1)) -> g(f(g(x1)))
f(f(g(x1))) -> g(f(x1))
encArg(c(x_1)) -> c(encArg(x_1))
encArg(cons_g(x_1)) -> g(encArg(x_1))
encArg(cons_f(x_1)) -> f(encArg(x_1))
encode_g(x_1) -> g(encArg(x_1))
encode_c(x_1) -> c(encArg(x_1))
encode_f(x_1) -> f(encArg(x_1))

Types:
g :: c:cons_g:cons_f -> c:cons_g:cons_f
c :: c:cons_g:cons_f -> c:cons_g:cons_f
f :: c:cons_g:cons_f -> c:cons_g:cons_f
encArg :: c:cons_g:cons_f -> c:cons_g:cons_f
cons_g :: c:cons_g:cons_f -> c:cons_g:cons_f
cons_f :: c:cons_g:cons_f -> c:cons_g:cons_f
encode_g :: c:cons_g:cons_f -> c:cons_g:cons_f
encode_c :: c:cons_g:cons_f -> c:cons_g:cons_f
encode_f :: c:cons_g:cons_f -> c:cons_g:cons_f
hole_c:cons_g:cons_f1_0 :: c:cons_g:cons_f
gen_c:cons_g:cons_f2_0 :: Nat -> c:cons_g:cons_f

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

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

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

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

(12)
Obligation:
TRS:
Rules:
g(c(x1)) -> g(f(c(x1)))
g(f(c(x1))) -> g(f(f(c(x1))))
g(g(x1)) -> g(f(g(x1)))
f(f(g(x1))) -> g(f(x1))
encArg(c(x_1)) -> c(encArg(x_1))
encArg(cons_g(x_1)) -> g(encArg(x_1))
encArg(cons_f(x_1)) -> f(encArg(x_1))
encode_g(x_1) -> g(encArg(x_1))
encode_c(x_1) -> c(encArg(x_1))
encode_f(x_1) -> f(encArg(x_1))

Types:
g :: c:cons_g:cons_f -> c:cons_g:cons_f
c :: c:cons_g:cons_f -> c:cons_g:cons_f
f :: c:cons_g:cons_f -> c:cons_g:cons_f
encArg :: c:cons_g:cons_f -> c:cons_g:cons_f
cons_g :: c:cons_g:cons_f -> c:cons_g:cons_f
cons_f :: c:cons_g:cons_f -> c:cons_g:cons_f
encode_g :: c:cons_g:cons_f -> c:cons_g:cons_f
encode_c :: c:cons_g:cons_f -> c:cons_g:cons_f
encode_f :: c:cons_g:cons_f -> c:cons_g:cons_f
hole_c:cons_g:cons_f1_0 :: c:cons_g:cons_f
gen_c:cons_g:cons_f2_0 :: Nat -> c:cons_g:cons_f


Generator Equations:
gen_c:cons_g:cons_f2_0(0) <=> hole_c:cons_g:cons_f1_0
gen_c:cons_g:cons_f2_0(+(x, 1)) <=> c(gen_c:cons_g:cons_f2_0(x))


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

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

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

(13) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_c:cons_g:cons_f2_0(+(1, n124_0))) -> *3_0, rt in Omega(0)

Induction Base:
encArg(gen_c:cons_g:cons_f2_0(+(1, 0)))

Induction Step:
encArg(gen_c:cons_g:cons_f2_0(+(1, +(n124_0, 1)))) ->_R^Omega(0)
c(encArg(gen_c:cons_g:cons_f2_0(+(1, n124_0)))) ->_IH
c(*3_0)

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

(14)
BOUNDS(1, INF)

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

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

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


The TRS R consists of the following rules:

   g(c(x1)) -> g(f(c(x1)))
   g(f(c(x1))) -> g(f(f(c(x1))))
   g(g(x1)) -> g(f(g(x1)))
   f(f(g(x1))) -> g(f(x1))
   encArg(c(x_1)) -> c(encArg(x_1))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encode_g(x_1) -> g(encArg(x_1))
   encode_c(x_1) -> c(encArg(x_1))
   encode_f(x_1) -> f(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:

   g(c(x1)) -> g(f(c(x1)))
   g(c_g(x1)) -> g(f(g(x1)))
   f(c_f(c_g(x1))) -> g(f(x1))
   g(c_f(c(x1))) -> g(f(f(c(x1))))

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

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

   g(c(x1)) -> g(f(c(x1)))
   g(c_g(x1)) -> g(f(g(x1)))
   f(c_f(c_g(x1))) -> g(f(x1))
   g(c_f(c(x1))) -> g(f(f(c(x1))))

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

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

   g(c(x1)) -> g(f(c(x1))) [1]
   g(c_g(x1)) -> g(f(g(x1))) [1]
   f(c_f(c_g(x1))) -> g(f(x1)) [1]
   g(c_f(c(x1))) -> g(f(f(c(x1)))) [1]
   encArg(c(x_1)) -> c(encArg(x_1)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   encode_c(x_1) -> c(encArg(x_1)) [0]
   encode_f(x_1) -> f(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:

   g(c(x1)) -> g(f(c(x1))) [1]
   g(c_g(x1)) -> g(f(g(x1))) [1]
   f(c_f(c_g(x1))) -> g(f(x1)) [1]
   g(c_f(c(x1))) -> g(f(f(c(x1)))) [1]
   encArg(c(x_1)) -> c(encArg(x_1)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   encode_c(x_1) -> c(encArg(x_1)) [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   f(x0) -> c_f(x0) [0]
   g(x0) -> c_g(x0) [0]

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

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

(25) 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_g(v0) -> null_encode_g [0]
   encode_c(v0) -> null_encode_c [0]
   encode_f(v0) -> null_encode_f [0]
   f(v0) -> null_f [0]
   g(v0) -> null_g [0]

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

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

(26)
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:

   g(c(x1)) -> g(f(c(x1))) [1]
   g(c_g(x1)) -> g(f(g(x1))) [1]
   f(c_f(c_g(x1))) -> g(f(x1)) [1]
   g(c_f(c(x1))) -> g(f(f(c(x1)))) [1]
   encArg(c(x_1)) -> c(encArg(x_1)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   encode_c(x_1) -> c(encArg(x_1)) [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   f(x0) -> c_f(x0) [0]
   g(x0) -> c_g(x0) [0]
   encArg(v0) -> null_encArg [0]
   encode_g(v0) -> null_encode_g [0]
   encode_c(v0) -> null_encode_c [0]
   encode_f(v0) -> null_encode_f [0]
   f(v0) -> null_f [0]
   g(v0) -> null_g [0]

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

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

(27) 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_g => 0
   null_encode_c => 0
   null_encode_f => 0
   null_f => 0
   null_g => 0

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

(28)
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
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_c(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_c(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   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(x1)) :|: z = 1 + (1 + x1), x1 >= 0
   f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   f(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   g(z) -{ 1 }-> g(f(g(x1))) :|: x1 >= 0, z = 1 + x1
   g(z) -{ 1 }-> g(f(f(1 + x1))) :|: z = 1 + (1 + x1), x1 >= 0
   g(z) -{ 1 }-> g(f(1 + x1)) :|: x1 >= 0, z = 1 + x1
   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.

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

(29) 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_g_1
   encode_c_1
   encode_f_1
   f_1
   g_1

Due to the following rules being added:

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

And the following fresh constants:    const

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

(30)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   g(c(x1)) -> g(f(c(x1))) [1]
   g(c_g(x1)) -> g(f(g(x1))) [1]
   f(c_f(c_g(x1))) -> g(f(x1)) [1]
   g(c_f(c(x1))) -> g(f(f(c(x1)))) [1]
   encArg(c(x_1)) -> c(encArg(x_1)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   encode_c(x_1) -> c(encArg(x_1)) [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   f(x0) -> c_f(x0) [0]
   g(x0) -> c_g(x0) [0]
   encArg(v0) -> const [0]
   encode_g(v0) -> const [0]
   encode_c(v0) -> const [0]
   encode_f(v0) -> const [0]
   f(v0) -> const [0]
   g(v0) -> const [0]

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

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

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

(32)
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:

   g(c(x1)) -> g(c_f(c(x1))) [1]
   g(c(x1)) -> g(const) [1]
   g(c_g(c(x1'))) -> g(f(g(f(c(x1'))))) [2]
   g(c_g(c_g(x1''))) -> g(f(g(f(g(x1''))))) [2]
   g(c_g(c_f(c(x11)))) -> g(f(g(f(f(c(x11)))))) [2]
   g(c_g(x1)) -> g(f(c_g(x1))) [1]
   g(c_g(x1)) -> g(f(const)) [1]
   f(c_f(c_g(c_f(c_g(x12))))) -> g(g(f(x12))) [2]
   f(c_f(c_g(x1))) -> g(c_f(x1)) [1]
   f(c_f(c_g(x1))) -> g(const) [1]
   g(c_f(c(x1))) -> g(f(c_f(c(x1)))) [1]
   g(c_f(c(x1))) -> g(f(const)) [1]
   encArg(c(x_1)) -> c(encArg(x_1)) [0]
   encArg(cons_g(c(x_1'))) -> g(c(encArg(x_1'))) [0]
   encArg(cons_g(cons_g(x_1''))) -> g(g(encArg(x_1''))) [0]
   encArg(cons_g(cons_f(x_11))) -> g(f(encArg(x_11))) [0]
   encArg(cons_g(x_1)) -> g(const) [0]
   encArg(cons_f(c(x_12))) -> f(c(encArg(x_12))) [0]
   encArg(cons_f(cons_g(x_13))) -> f(g(encArg(x_13))) [0]
   encArg(cons_f(cons_f(x_14))) -> f(f(encArg(x_14))) [0]
   encArg(cons_f(x_1)) -> f(const) [0]
   encode_g(c(x_15)) -> g(c(encArg(x_15))) [0]
   encode_g(cons_g(x_16)) -> g(g(encArg(x_16))) [0]
   encode_g(cons_f(x_17)) -> g(f(encArg(x_17))) [0]
   encode_g(x_1) -> g(const) [0]
   encode_c(x_1) -> c(encArg(x_1)) [0]
   encode_f(c(x_18)) -> f(c(encArg(x_18))) [0]
   encode_f(cons_g(x_19)) -> f(g(encArg(x_19))) [0]
   encode_f(cons_f(x_110)) -> f(f(encArg(x_110))) [0]
   encode_f(x_1) -> f(const) [0]
   f(x0) -> c_f(x0) [0]
   g(x0) -> c_g(x0) [0]
   encArg(v0) -> const [0]
   encode_g(v0) -> const [0]
   encode_c(v0) -> const [0]
   encode_f(v0) -> const [0]
   f(v0) -> const [0]
   g(v0) -> const [0]

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

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

(33) 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

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

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

   encArg(z) -{ 0 }-> g(g(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 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 }-> g(1 + encArg(x_1')) :|: z = 1 + (1 + x_1'), x_1' >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_13))) :|: z = 1 + (1 + x_13), x_13 >= 0
   encArg(z) -{ 0 }-> f(f(encArg(x_14))) :|: x_14 >= 0, z = 1 + (1 + x_14)
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> f(1 + encArg(x_12)) :|: z = 1 + (1 + x_12), x_12 >= 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_c(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_c(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   encode_f(z) -{ 0 }-> f(g(encArg(x_19))) :|: z = 1 + x_19, x_19 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(x_110))) :|: z = 1 + x_110, x_110 >= 0
   encode_f(z) -{ 0 }-> f(0) :|: x_1 >= 0, z = x_1
   encode_f(z) -{ 0 }-> f(1 + encArg(x_18)) :|: z = 1 + x_18, x_18 >= 0
   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_17))) :|: x_17 >= 0, z = 1 + x_17
   encode_g(z) -{ 0 }-> g(0) :|: x_1 >= 0, z = x_1
   encode_g(z) -{ 0 }-> g(1 + encArg(x_15)) :|: x_15 >= 0, z = 1 + x_15
   encode_g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   f(z) -{ 2 }-> g(g(f(x12))) :|: x12 >= 0, z = 1 + (1 + (1 + (1 + x12)))
   f(z) -{ 1 }-> g(0) :|: z = 1 + (1 + x1), x1 >= 0
   f(z) -{ 1 }-> g(1 + x1) :|: z = 1 + (1 + x1), x1 >= 0
   f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   f(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   g(z) -{ 2 }-> g(f(g(f(g(x1''))))) :|: z = 1 + (1 + x1''), x1'' >= 0
   g(z) -{ 2 }-> g(f(g(f(f(1 + x11))))) :|: z = 1 + (1 + (1 + x11)), x11 >= 0
   g(z) -{ 2 }-> g(f(g(f(1 + x1')))) :|: x1' >= 0, z = 1 + (1 + x1')
   g(z) -{ 1 }-> g(f(0)) :|: x1 >= 0, z = 1 + x1
   g(z) -{ 1 }-> g(f(0)) :|: z = 1 + (1 + x1), x1 >= 0
   g(z) -{ 1 }-> g(f(1 + x1)) :|: x1 >= 0, z = 1 + x1
   g(z) -{ 1 }-> g(f(1 + (1 + x1))) :|: z = 1 + (1 + x1), x1 >= 0
   g(z) -{ 1 }-> g(0) :|: x1 >= 0, z = 1 + x1
   g(z) -{ 1 }-> g(1 + (1 + x1)) :|: x1 >= 0, z = 1 + x1
   g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   g(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0


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

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

(36)
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 }-> g(1 + encArg(z - 2)) :|: z - 2 >= 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 }-> f(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_c(z) -{ 0 }-> 0 :|: z >= 0
   encode_c(z) -{ 0 }-> 1 + encArg(z) :|: 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 }-> f(1 + encArg(z - 1)) :|: z - 1 >= 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 }-> g(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 2 }-> g(g(f(z - 4))) :|: z - 4 >= 0
   f(z) -{ 1 }-> g(0) :|: z - 2 >= 0
   f(z) -{ 1 }-> g(1 + (z - 2)) :|: z - 2 >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   f(z) -{ 0 }-> 1 + z :|: z >= 0
   g(z) -{ 2 }-> g(f(g(f(g(z - 2))))) :|: z - 2 >= 0
   g(z) -{ 2 }-> g(f(g(f(f(1 + (z - 3)))))) :|: z - 3 >= 0
   g(z) -{ 2 }-> g(f(g(f(1 + (z - 2))))) :|: z - 2 >= 0
   g(z) -{ 1 }-> g(f(0)) :|: z - 1 >= 0
   g(z) -{ 1 }-> g(f(0)) :|: z - 2 >= 0
   g(z) -{ 1 }-> g(f(1 + (z - 1))) :|: z - 1 >= 0
   g(z) -{ 1 }-> g(f(1 + (1 + (z - 2)))) :|: z - 2 >= 0
   g(z) -{ 1 }-> g(0) :|: z - 1 >= 0
   g(z) -{ 1 }-> g(1 + (1 + (z - 1))) :|: z - 1 >= 0
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0


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

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   encode_g(z0) -> g(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   encode_f(z0) -> f(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(z0)) -> c2(G(encArg(z0)), ENCARG(z0))
   ENCARG(cons_f(z0)) -> c3(F(encArg(z0)), ENCARG(z0))
   ENCODE_G(z0) -> c4(G(encArg(z0)), ENCARG(z0))
   ENCODE_C(z0) -> c5(ENCARG(z0))
   ENCODE_F(z0) -> c6(F(encArg(z0)), ENCARG(z0))
   F(z0) -> c7
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(z0) -> c9
   G(c(z0)) -> c10(G(f(c(z0))), F(c(z0)))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))), F(c(z0)))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c(z0)) -> c10(G(f(c(z0))), F(c(z0)))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))), F(c(z0)))
K tuples:none
Defined Rule Symbols:   g_1, f_1, encArg_1, encode_g_1, encode_c_1, encode_f_1

Defined Pair Symbols:   ENCARG_1, ENCODE_G_1, ENCODE_C_1, ENCODE_F_1, F_1, G_1

Compound Symbols:   c1_1, c2_2, c3_2, c4_2, c5_1, c6_2, c7, c8_2, c9, c10_2, c11_3, c12_3


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

(39) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   ENCODE_C(z0) -> c5(ENCARG(z0))
Removed 2 trailing nodes:
   G(z0) -> c9
   F(z0) -> c7

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   encode_g(z0) -> g(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   encode_f(z0) -> f(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(z0)) -> c2(G(encArg(z0)), ENCARG(z0))
   ENCARG(cons_f(z0)) -> c3(F(encArg(z0)), ENCARG(z0))
   ENCODE_G(z0) -> c4(G(encArg(z0)), ENCARG(z0))
   ENCODE_F(z0) -> c6(F(encArg(z0)), ENCARG(z0))
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c(z0)) -> c10(G(f(c(z0))), F(c(z0)))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))), F(c(z0)))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c(z0)) -> c10(G(f(c(z0))), F(c(z0)))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))), F(c(z0)))
K tuples:none
Defined Rule Symbols:   g_1, f_1, encArg_1, encode_g_1, encode_c_1, encode_f_1

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

Compound Symbols:   c1_1, c2_2, c3_2, c4_2, c6_2, c8_2, c10_2, c11_3, c12_3


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

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   encode_g(z0) -> g(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   encode_f(z0) -> f(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(z0)) -> c2(G(encArg(z0)), ENCARG(z0))
   ENCARG(cons_f(z0)) -> c3(F(encArg(z0)), ENCARG(z0))
   ENCODE_G(z0) -> c4(G(encArg(z0)), ENCARG(z0))
   ENCODE_F(z0) -> c6(F(encArg(z0)), ENCARG(z0))
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c(z0)) -> c10(G(f(c(z0))))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c(z0)) -> c10(G(f(c(z0))))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
K tuples:none
Defined Rule Symbols:   g_1, f_1, encArg_1, encode_g_1, encode_c_1, encode_f_1

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

Compound Symbols:   c1_1, c2_2, c3_2, c4_2, c6_2, c8_2, c11_3, c10_1, c12_2


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

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   encode_g(z0) -> g(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   encode_f(z0) -> f(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(z0)) -> c2(G(encArg(z0)), ENCARG(z0))
   ENCARG(cons_f(z0)) -> c3(F(encArg(z0)), ENCARG(z0))
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c(z0)) -> c10(G(f(c(z0))))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
   ENCODE_G(z0) -> c5(G(encArg(z0)))
   ENCODE_G(z0) -> c5(ENCARG(z0))
   ENCODE_F(z0) -> c5(F(encArg(z0)))
   ENCODE_F(z0) -> c5(ENCARG(z0))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c(z0)) -> c10(G(f(c(z0))))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
K tuples:none
Defined Rule Symbols:   g_1, f_1, encArg_1, encode_g_1, encode_c_1, encode_f_1

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

Compound Symbols:   c1_1, c2_2, c3_2, c8_2, c11_3, c10_1, c12_2, c5_1


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

(45) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 2 leading nodes:
   ENCODE_G(z0) -> c5(ENCARG(z0))
   ENCODE_F(z0) -> c5(ENCARG(z0))

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   encode_g(z0) -> g(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   encode_f(z0) -> f(encArg(z0))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(z0)) -> c2(G(encArg(z0)), ENCARG(z0))
   ENCARG(cons_f(z0)) -> c3(F(encArg(z0)), ENCARG(z0))
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c(z0)) -> c10(G(f(c(z0))))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
   ENCODE_G(z0) -> c5(G(encArg(z0)))
   ENCODE_F(z0) -> c5(F(encArg(z0)))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c(z0)) -> c10(G(f(c(z0))))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
K tuples:none
Defined Rule Symbols:   g_1, f_1, encArg_1, encode_g_1, encode_c_1, encode_f_1

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

Compound Symbols:   c1_1, c2_2, c3_2, c8_2, c11_3, c10_1, c12_2, c5_1


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

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

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(z0)) -> c2(G(encArg(z0)), ENCARG(z0))
   ENCARG(cons_f(z0)) -> c3(F(encArg(z0)), ENCARG(z0))
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c(z0)) -> c10(G(f(c(z0))))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
   ENCODE_G(z0) -> c5(G(encArg(z0)))
   ENCODE_F(z0) -> c5(F(encArg(z0)))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c(z0)) -> c10(G(f(c(z0))))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_2, c8_2, c11_3, c10_1, c12_2, c5_1


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

(49) CdtRuleRemovalProof (UPPER BOUND(ADD(n^2)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   G(c(z0)) -> c10(G(f(c(z0))))
We considered the (Usable) Rules:
   f(z0) -> c_f(z0)
   g(z0) -> c_g(z0)
   g(c_g(z0)) -> g(f(g(z0)))
   encArg(c(z0)) -> c(encArg(z0))
   f(c_f(c_g(z0))) -> g(f(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(c(z0)) -> g(f(c(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
And the Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(z0)) -> c2(G(encArg(z0)), ENCARG(z0))
   ENCARG(cons_f(z0)) -> c3(F(encArg(z0)), ENCARG(z0))
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c(z0)) -> c10(G(f(c(z0))))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
   ENCODE_G(z0) -> c5(G(encArg(z0)))
   ENCODE_F(z0) -> c5(F(encArg(z0)))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(ENCARG(x_1)) = [2]x_1 + x_1^2
   POL(ENCODE_F(x_1)) = [1] + [2]x_1 + [2]x_1^2
   POL(ENCODE_G(x_1)) = [2] + [2]x_1 + [2]x_1^2
   POL(F(x_1)) = 0
   POL(G(x_1)) = [2]x_1
   POL(c(x_1)) = [1] + x_1
   POL(c1(x_1)) = x_1
   POL(c10(x_1)) = x_1
   POL(c11(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c12(x_1, x_2)) = x_1 + x_2
   POL(c2(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c5(x_1)) = x_1
   POL(c8(x_1, x_2)) = x_1 + x_2
   POL(c_f(x_1)) = 0
   POL(c_g(x_1)) = x_1
   POL(cons_f(x_1)) = x_1
   POL(cons_g(x_1)) = [1] + x_1
   POL(encArg(x_1)) = x_1
   POL(f(x_1)) = 0
   POL(g(x_1)) = x_1

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(z0)) -> c2(G(encArg(z0)), ENCARG(z0))
   ENCARG(cons_f(z0)) -> c3(F(encArg(z0)), ENCARG(z0))
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c(z0)) -> c10(G(f(c(z0))))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
   ENCODE_G(z0) -> c5(G(encArg(z0)))
   ENCODE_F(z0) -> c5(F(encArg(z0)))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
K tuples:
   G(c(z0)) -> c10(G(f(c(z0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_2, c8_2, c11_3, c10_1, c12_2, c5_1


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_g(z0)) -> c2(G(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c2(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c2(G(f(encArg(z0))), ENCARG(cons_f(z0)))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_f(z0)) -> c3(F(encArg(z0)), ENCARG(z0))
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c(z0)) -> c10(G(f(c(z0))))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
   ENCODE_G(z0) -> c5(G(encArg(z0)))
   ENCODE_F(z0) -> c5(F(encArg(z0)))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c2(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c2(G(f(encArg(z0))), ENCARG(cons_f(z0)))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
K tuples:
   G(c(z0)) -> c10(G(f(c(z0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c3_2, c8_2, c11_3, c10_1, c12_2, c5_1, c2_2


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

(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(z0)) -> c3(F(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_f(c(z0))) -> c3(F(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c3(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c3(F(f(encArg(z0))), ENCARG(cons_f(z0)))

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c(z0)) -> c10(G(f(c(z0))))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
   ENCODE_G(z0) -> c5(G(encArg(z0)))
   ENCODE_F(z0) -> c5(F(encArg(z0)))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c2(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c2(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(c(z0))) -> c3(F(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c3(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c3(F(f(encArg(z0))), ENCARG(cons_f(z0)))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
K tuples:
   G(c(z0)) -> c10(G(f(c(z0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c8_2, c11_3, c10_1, c12_2, c5_1, c2_2, c3_2


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

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c(z0)) -> c10(G(f(c(z0))))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
   ENCODE_G(z0) -> c5(G(encArg(z0)))
   ENCODE_F(z0) -> c5(F(encArg(z0)))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c2(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c2(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c3(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c3(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
K tuples:
   G(c(z0)) -> c10(G(f(c(z0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c8_2, c11_3, c10_1, c12_2, c5_1, c2_2, c3_2, c3_1


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

(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(c_f(c_g(z0))) -> c8(G(f(z0)), F(z0)) by 
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c(z0)) -> c10(G(f(c(z0))))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
   ENCODE_G(z0) -> c5(G(encArg(z0)))
   ENCODE_F(z0) -> c5(F(encArg(z0)))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c2(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c2(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c3(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c3(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
S tuples:
   G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
K tuples:
   G(c(z0)) -> c10(G(f(c(z0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c11_3, c10_1, c12_2, c5_1, c2_2, c3_2, c3_1, c8_2


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(c_g(z0)) -> c11(G(f(g(z0))), F(g(z0)), G(z0)) by 
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   G(c(z0)) -> c10(G(f(c(z0))))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
   ENCODE_G(z0) -> c5(G(encArg(z0)))
   ENCODE_F(z0) -> c5(F(encArg(z0)))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c2(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c2(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c3(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c3(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
S tuples:
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
K tuples:
   G(c(z0)) -> c10(G(f(c(z0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c10_1, c12_2, c5_1, c2_2, c3_2, c3_1, c8_2, c11_3


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

(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(c(z0)) -> c10(G(f(c(z0)))) by 
   G(c(x0)) -> c10(G(c_f(c(x0))))

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
   ENCODE_G(z0) -> c5(G(encArg(z0)))
   ENCODE_F(z0) -> c5(F(encArg(z0)))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c2(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c2(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c3(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c3(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
S tuples:
   G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0))))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
K tuples:
   G(c(z0)) -> c10(G(f(c(z0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c12_2, c5_1, c2_2, c3_2, c3_1, c8_2, c11_3, c10_1


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(c_f(c(z0))) -> c12(G(f(f(c(z0)))), F(f(c(z0)))) by 
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCODE_G(z0) -> c5(G(encArg(z0)))
   ENCODE_F(z0) -> c5(F(encArg(z0)))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c2(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c2(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c3(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c3(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
K tuples:
   G(c(z0)) -> c10(G(f(c(z0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c5_1, c2_2, c3_2, c3_1, c8_2, c11_3, c10_1, c12_2


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

(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_G(z0) -> c5(G(encArg(z0))) by 
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCODE_F(z0) -> c5(F(encArg(z0)))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c2(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c2(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c3(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c3(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
K tuples:
   G(c(z0)) -> c10(G(f(c(z0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c5_1, c2_2, c3_2, c3_1, c8_2, c11_3, c10_1, c12_2


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

(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(z0) -> c5(F(encArg(z0))) by 
   ENCODE_F(c(z0)) -> c5(F(c(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c2(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c2(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c3(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c3(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(c(z0)) -> c5(F(c(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
K tuples:
   G(c(z0)) -> c10(G(f(c(z0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_2, c3_1, c8_2, c11_3, c10_1, c12_2, c5_1


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

(69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   ENCODE_F(c(z0)) -> c5(F(c(encArg(z0))))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_g(cons_g(z0))) -> c2(G(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c2(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c3(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c3(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_2, c3_1, c8_2, c11_3, c10_1, c12_2, c5_1


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_g(cons_g(z0))) -> c2(G(g(encArg(z0))), ENCARG(cons_g(z0))) by 
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_g(cons_f(z0))) -> c2(G(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c3(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c3(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_2, c3_1, c8_2, c11_3, c10_1, c12_2, c5_1


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

(73) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_g(cons_f(z0))) -> c2(G(f(encArg(z0))), ENCARG(cons_f(z0))) by 
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(cons_g(z0))) -> c3(F(g(encArg(z0))), ENCARG(cons_g(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c3(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_2, c3_1, c8_2, c11_3, c10_1, c12_2, c5_1


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(cons_g(z0))) -> c3(F(g(encArg(z0))), ENCARG(cons_g(z0))) by 
   ENCARG(cons_f(cons_g(x0))) -> c3(F(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c3(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(F(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_2, c3_1, c8_2, c11_3, c10_1, c12_2, c5_1


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

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(cons_f(z0))) -> c3(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_2, c3_1, c8_2, c11_3, c10_1, c12_2, c5_1


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(cons_f(z0))) -> c3(F(f(encArg(z0))), ENCARG(cons_f(z0))) by 
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0))))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c11_3, c10_1, c12_2, c5_1, c3_2


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

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(f(z0))), F(c_f(c_g(z0)))) by 
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c11_3, c10_1, c12_2, c5_1, c3_2


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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(c_g(x0)) -> c11(G(c_f(g(x0))), F(g(x0)), G(x0)) by 
   G(c_g(z0)) -> c11(G(c_f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(z0)) -> c11(G(c_f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(z0)) -> c11(G(c_f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c11_3, c10_1, c12_2, c5_1, c3_2


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

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c11_3, c10_1, c12_2, c5_1, c3_2, c11_2


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(c_g(z0)) -> c11(G(f(c_g(z0))), F(g(z0)), G(z0)) by 
   G(c_g(x0)) -> c11(G(c_f(c_g(x0))), F(g(x0)), G(x0))
   G(c_g(x0)) -> c11(F(g(x0)), G(x0))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(x0)) -> c11(G(c_f(c_g(x0))), F(g(x0)), G(x0))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(x0)) -> c11(G(c_f(c_g(x0))), F(g(x0)), G(x0))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c11_3, c10_1, c12_2, c5_1, c3_2, c11_2


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

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c11_3, c10_1, c12_2, c5_1, c3_2, c11_2


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(c_g(c(z0))) -> c11(G(f(g(f(c(z0))))), F(g(c(z0))), G(c(z0))) by 
   G(c_g(c(x0))) -> c11(G(c_f(g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c11_3, c10_1, c12_2, c5_1, c3_2, c11_2


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

(93) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(c_g(c_g(z0))) -> c11(G(f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0))) by 
   G(c_g(c_g(x0))) -> c11(G(c_f(g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c11_3, c10_1, c12_2, c5_1, c3_2, c11_2, c11_1


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

(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(c_g(c_f(c(z0)))) -> c11(G(f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0)))) by 
   G(c_g(c_f(c(x0)))) -> c11(G(c_f(g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c10_1, c12_2, c5_1, c3_2, c11_3, c11_2, c11_1


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

(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(c_f(c(x0))) -> c12(G(c_f(f(c(x0)))), F(f(c(x0)))) by 
   G(c_f(c(x0))) -> c12(G(c_f(c_f(c(x0)))), F(f(c(x0))))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(c_f(c(x0)))), F(f(c(x0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(c_f(c(x0)))), F(f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c10_1, c12_2, c5_1, c3_2, c11_3, c11_2, c11_1


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

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c10_1, c12_2, c5_1, c3_2, c11_3, c11_2, c11_1, c12_1


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

(101) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(c_f(c(x0))) -> c12(G(f(c_f(c(x0)))), F(f(c(x0)))) by 
   G(c_f(c(x0))) -> c12(G(c_f(c_f(c(x0)))), F(f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(c_f(c(x0)))), F(f(c(x0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
   G(c_f(c(x0))) -> c12(G(c_f(c_f(c(x0)))), F(f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c10_1, c5_1, c3_2, c11_3, c11_2, c11_1, c12_1, c12_2


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

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c10_1, c5_1, c3_2, c11_3, c11_2, c11_1, c12_1


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

(105) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_G(cons_g(z0)) -> c5(G(g(encArg(z0)))) by 
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c10_1, c5_1, c3_2, c11_3, c11_2, c11_1, c12_1


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

(107) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_G(cons_f(z0)) -> c5(G(f(encArg(z0)))) by 
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c10_1, c5_1, c3_2, c11_3, c11_2, c11_1, c12_1


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

(109) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(cons_g(z0)) -> c5(F(g(encArg(z0)))) by 
   ENCODE_F(cons_g(x0)) -> c5(F(c_g(encArg(x0))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(x0)) -> c5(F(c_g(encArg(x0))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c10_1, c5_1, c3_2, c11_3, c11_2, c11_1, c12_1


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

(111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   ENCODE_F(cons_g(x0)) -> c5(F(c_g(encArg(x0))))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c10_1, c5_1, c3_2, c11_3, c11_2, c11_1, c12_1


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

(113) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(cons_f(z0)) -> c5(F(f(encArg(z0)))) by 
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c10_1, c5_1, c3_2, c11_3, c11_2, c11_1, c12_1


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

(115) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(c_f(c(x0))) -> c12(F(f(c(x0)))) by 
   G(c_f(c(x0))) -> c12(F(c_f(c(x0))))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12(F(c_f(c(x0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(c_f(c(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c10_1, c5_1, c3_2, c11_3, c11_2, c11_1, c12_1


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

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c10_1, c5_1, c3_2, c11_3, c11_2, c11_1, c12_1, c12


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

(119) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(c_f(c(x0))) -> c12(F(f(c(x0)))) by 
   G(c_f(c(x0))) -> c12(F(c_f(c(x0))))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   G(c_f(c(x0))) -> c12(F(c_f(c(x0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c10_1, c5_1, c3_2, c11_3, c11_2, c11_1, c12_1, c12


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

(121) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   G(c_f(c(x0))) -> c12(F(c_f(c(x0))))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12(F(f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c10_1, c5_1, c3_2, c11_3, c11_2, c11_1, c12_1, c12


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

(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(c_f(c(x0))) -> c12(F(f(c(x0)))) by 
   G(c_f(c(x0))) -> c12(F(c_f(c(x0))))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   G(c_f(c(x0))) -> c12(F(c_f(c(x0))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c10_1, c5_1, c3_2, c11_3, c11_2, c11_1, c12, c12_1


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

(125) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   G(c_f(c(x0))) -> c12(F(c_f(c(x0))))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c1_1, c2_2, c3_1, c8_2, c10_1, c5_1, c3_2, c11_3, c11_2, c11_1, c12


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

(127) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(c(z0)) -> c1(ENCARG(z0)) by 
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c3_1, c8_2, c10_1, c5_1, c3_2, c11_3, c11_2, c11_1, c12, c1_1


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

(129) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(cons_f(c(z0))) -> c3(ENCARG(c(z0))) by 
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
S tuples:
   F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c8_2, c10_1, c5_1, c3_2, c3_1, c11_3, c11_2, c11_1, c12, c1_1


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

(131) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(c_f(c_g(z0))) -> c8(G(c_f(z0)), F(z0)) by 
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(G(c_f(c_f(c_g(y0)))), F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(G(c_f(c_f(c_g(c_f(c_g(y0)))))), F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(G(c_f(c_f(c_g(c_f(c_g(c_f(c_g(y0)))))))), F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))), F(c(y0)))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(G(c_f(c_f(c_g(y0)))), F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(G(c_f(c_f(c_g(c_f(c_g(y0)))))), F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(G(c_f(c_f(c_g(c_f(c_g(c_f(c_g(y0)))))))), F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))), F(c(y0)))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(G(c_f(c_f(c_g(y0)))), F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(G(c_f(c_f(c_g(c_f(c_g(y0)))))), F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(G(c_f(c_f(c_g(c_f(c_g(c_f(c_g(y0)))))))), F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))), F(c(y0)))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c3_1, c8_2, c11_3, c11_2, c11_1, c12, c1_1


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

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c3_1, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c8_1


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

(135) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
We considered the (Usable) Rules:
   g(z0) -> c_g(z0)
   f(z0) -> c_f(z0)
   g(c_g(z0)) -> g(f(g(z0)))
   f(c_f(c_g(z0))) -> g(f(z0))
   g(c(z0)) -> g(f(c(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
And the Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(ENCARG(x_1)) = x_1
   POL(ENCODE_F(x_1)) = [1] + x_1
   POL(ENCODE_G(x_1)) = 0
   POL(F(x_1)) = x_1
   POL(G(x_1)) = 0
   POL(c(x_1)) = x_1
   POL(c1(x_1)) = x_1
   POL(c10(x_1)) = x_1
   POL(c11(x_1)) = x_1
   POL(c11(x_1, x_2)) = x_1 + x_2
   POL(c11(x_1, x_2, x_3)) = x_1 + x_2 + x_3
   POL(c12) = 0
   POL(c2(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1)) = x_1
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c5(x_1)) = x_1
   POL(c8(x_1)) = x_1
   POL(c8(x_1, x_2)) = x_1 + x_2
   POL(c_f(x_1)) = [1]
   POL(c_g(x_1)) = 0
   POL(cons_f(x_1)) = [1] + x_1
   POL(cons_g(x_1)) = x_1
   POL(encArg(x_1)) = 0
   POL(f(x_1)) = [1]
   POL(g(x_1)) = 0

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0)))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c3_1, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c8_1


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

(137) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(cons_f(cons_g(x0))) -> c3(ENCARG(cons_g(x0))) by 
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c3_1, c8_1


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

(139) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0))) by G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
----------------------------------------

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c3_1, c8_1


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

(141) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0)))) by G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
----------------------------------------

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c3_1, c8_1


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

(143) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace G(c_g(c(x0))) -> c11(G(c_f(g(f(c(x0))))), F(g(c(x0))), G(c(x0))) by G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
----------------------------------------

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c3_1, c8_1


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

(145) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace G(c_g(c(x0))) -> c11(G(f(c_g(f(c(x0))))), F(g(c(x0))), G(c(x0))) by G(c_g(c(z0))) -> c11(G(c_f(c_g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
----------------------------------------

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c(z0))) -> c11(G(c_f(c_g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c(z0))) -> c11(G(c_f(c_g(f(c(z0))))), F(g(c(z0))), G(c(z0)))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c3_1, c8_1


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

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c3_1, c8_1


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

(149) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace G(c_g(c_g(z0))) -> c11(G(f(g(f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0))) by G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
----------------------------------------

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c3_1, c8_1


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

(151) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0)))) by G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
----------------------------------------

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c3_1, c8_1


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

(153) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0))))) by G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
----------------------------------------

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c3_1, c8_1


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

(155) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace G(c_g(c_f(c(x0)))) -> c11(G(c_f(g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0)))) by G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
----------------------------------------

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c3_1, c8_1


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

(157) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace G(c_g(c_f(c(x0)))) -> c11(G(f(c_g(f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0)))) by G(c_g(c_f(c(z0)))) -> c11(G(f(c_g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
----------------------------------------

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(c_g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(c_g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c3_1, c8_1


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

(159) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace G(c_g(c_f(c(x0)))) -> c11(G(f(g(c_f(f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0)))) by G(c_g(c_f(c(z0)))) -> c11(G(f(g(c_f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
----------------------------------------

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(c_g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(c_f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(c_g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(c_f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c3_1, c8_1


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

(161) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace G(c_g(c_f(c(x0)))) -> c11(G(f(g(f(c_f(c(x0)))))), F(g(c_f(c(x0)))), G(c_f(c(x0)))) by G(c_g(c_f(c(z0)))) -> c11(G(f(g(c_f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
----------------------------------------

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(c(y0))) -> c1(ENCARG(c(y0)))
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(c_g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(c_f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(c_g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(c_f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c3_1, c8_1


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

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

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_f(c(y0)))) -> c1(ENCARG(cons_f(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(c_g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(c_f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   ENCARG(c(c(c(y0)))) -> c1(ENCARG(c(c(y0))))
   ENCARG(c(c(cons_g(c(y0))))) -> c1(ENCARG(c(cons_g(c(y0)))))
   ENCARG(c(c(cons_f(c(y0))))) -> c1(ENCARG(c(cons_f(c(y0)))))
   ENCARG(c(c(cons_g(cons_g(y0))))) -> c1(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(c(c(cons_g(cons_g(c(y0)))))) -> c1(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(c(c(cons_g(cons_g(cons_g(y0)))))) -> c1(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(c(c(cons_g(cons_g(cons_f(y0)))))) -> c1(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(c(c(cons_g(cons_f(y0))))) -> c1(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(c(c(cons_g(cons_f(c(y0)))))) -> c1(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(c(c(cons_g(cons_f(cons_g(y0)))))) -> c1(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(c(c(cons_g(cons_f(cons_f(y0)))))) -> c1(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(c(c(cons_f(cons_g(c(y0)))))) -> c1(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(c(c(cons_f(cons_g(cons_g(y0)))))) -> c1(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(c(c(cons_f(cons_g(cons_f(y0)))))) -> c1(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(c(c(cons_f(cons_g(y0))))) -> c1(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(c(c(cons_f(cons_f(y0))))) -> c1(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(c(c(cons_f(cons_f(c(y0)))))) -> c1(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(c(c(cons_f(cons_f(cons_g(y0)))))) -> c1(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(c(c(cons_f(cons_f(cons_f(y0)))))) -> c1(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(c_g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(c_f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c3_1, c8_1


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

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

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(y0)))) -> c1(ENCARG(cons_f(cons_g(y0))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(c_g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(c_f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   ENCARG(c(c(c(y0)))) -> c1(ENCARG(c(c(y0))))
   ENCARG(c(c(cons_g(c(y0))))) -> c1(ENCARG(c(cons_g(c(y0)))))
   ENCARG(c(c(cons_f(c(y0))))) -> c1(ENCARG(c(cons_f(c(y0)))))
   ENCARG(c(c(cons_g(cons_g(y0))))) -> c1(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(c(c(cons_g(cons_g(c(y0)))))) -> c1(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(c(c(cons_g(cons_g(cons_g(y0)))))) -> c1(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(c(c(cons_g(cons_g(cons_f(y0)))))) -> c1(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(c(c(cons_g(cons_f(y0))))) -> c1(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(c(c(cons_g(cons_f(c(y0)))))) -> c1(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(c(c(cons_g(cons_f(cons_g(y0)))))) -> c1(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(c(c(cons_g(cons_f(cons_f(y0)))))) -> c1(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(c(c(cons_f(cons_g(c(y0)))))) -> c1(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(c(c(cons_f(cons_g(cons_g(y0)))))) -> c1(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(c(c(cons_f(cons_g(cons_f(y0)))))) -> c1(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(c(c(cons_f(cons_g(y0))))) -> c1(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(c(c(cons_f(cons_f(y0))))) -> c1(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(c(c(cons_f(cons_f(c(y0)))))) -> c1(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(c(c(cons_f(cons_f(cons_g(y0)))))) -> c1(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(c(c(cons_f(cons_f(cons_f(y0)))))) -> c1(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   ENCARG(c(cons_f(c(c(y0))))) -> c1(ENCARG(cons_f(c(c(y0)))))
   ENCARG(c(cons_f(c(cons_g(c(y0)))))) -> c1(ENCARG(cons_f(c(cons_g(c(y0))))))
   ENCARG(c(cons_f(c(cons_f(c(y0)))))) -> c1(ENCARG(cons_f(c(cons_f(c(y0))))))
   ENCARG(c(cons_f(c(cons_g(cons_g(y0)))))) -> c1(ENCARG(cons_f(c(cons_g(cons_g(y0))))))
   ENCARG(c(cons_f(c(cons_g(cons_g(c(y0))))))) -> c1(ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))))
   ENCARG(c(cons_f(c(cons_g(cons_g(cons_g(y0))))))) -> c1(ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))))
   ENCARG(c(cons_f(c(cons_g(cons_g(cons_f(y0))))))) -> c1(ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))))
   ENCARG(c(cons_f(c(cons_g(cons_f(y0)))))) -> c1(ENCARG(cons_f(c(cons_g(cons_f(y0))))))
   ENCARG(c(cons_f(c(cons_g(cons_f(c(y0))))))) -> c1(ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))))
   ENCARG(c(cons_f(c(cons_g(cons_f(cons_g(y0))))))) -> c1(ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))))
   ENCARG(c(cons_f(c(cons_g(cons_f(cons_f(y0))))))) -> c1(ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))))
   ENCARG(c(cons_f(c(cons_f(cons_g(c(y0))))))) -> c1(ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))))
   ENCARG(c(cons_f(c(cons_f(cons_g(cons_g(y0))))))) -> c1(ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))))
   ENCARG(c(cons_f(c(cons_f(cons_g(cons_f(y0))))))) -> c1(ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))))
   ENCARG(c(cons_f(c(cons_f(cons_g(y0)))))) -> c1(ENCARG(cons_f(c(cons_f(cons_g(y0))))))
   ENCARG(c(cons_f(c(cons_f(cons_f(y0)))))) -> c1(ENCARG(cons_f(c(cons_f(cons_f(y0))))))
   ENCARG(c(cons_f(c(cons_f(cons_f(c(y0))))))) -> c1(ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))))
   ENCARG(c(cons_f(c(cons_f(cons_f(cons_g(y0))))))) -> c1(ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))))
   ENCARG(c(cons_f(c(cons_f(cons_f(cons_f(y0))))))) -> c1(ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(c_g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(c_f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c3_1, c8_1


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

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

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

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_g(z0)) -> g(encArg(z0))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0) -> c_g(z0)
   g(c(z0)) -> g(f(c(z0)))
   g(c_g(z0)) -> g(f(g(z0)))
   g(c_f(c(z0))) -> g(f(f(c(z0))))
   f(z0) -> c_f(z0)
   f(c_f(c_g(z0))) -> g(f(z0))
Tuples:
   ENCARG(cons_g(c(z0))) -> c2(G(c(encArg(z0))), ENCARG(c(z0)))
   G(c(x0)) -> c10(G(c_f(c(x0))))
   ENCODE_G(c(z0)) -> c5(G(c(encArg(z0))))
   ENCARG(cons_g(cons_g(x0))) -> c2(G(c_g(encArg(x0))), ENCARG(cons_g(x0)))
   ENCARG(cons_g(cons_g(c(z0)))) -> c2(G(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_g(cons_g(cons_g(z0)))) -> c2(G(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_g(cons_g(cons_f(z0)))) -> c2(G(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_g(cons_f(x0))) -> c2(G(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_g(cons_f(c(z0)))) -> c2(G(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_g(cons_f(cons_g(z0)))) -> c2(G(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_g(cons_f(cons_f(z0)))) -> c2(G(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   ENCARG(cons_f(cons_g(c(z0)))) -> c3(F(g(c(encArg(z0)))), ENCARG(cons_g(c(z0))))
   ENCARG(cons_f(cons_g(cons_g(z0)))) -> c3(F(g(g(encArg(z0)))), ENCARG(cons_g(cons_g(z0))))
   ENCARG(cons_f(cons_g(cons_f(z0)))) -> c3(F(g(f(encArg(z0)))), ENCARG(cons_g(cons_f(z0))))
   ENCARG(cons_f(cons_f(x0))) -> c3(F(c_f(encArg(x0))), ENCARG(cons_f(x0)))
   ENCARG(cons_f(cons_f(c(z0)))) -> c3(F(f(c(encArg(z0)))), ENCARG(cons_f(c(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0)))) -> c3(F(f(g(encArg(z0)))), ENCARG(cons_f(cons_g(z0))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c3(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   ENCODE_G(cons_g(x0)) -> c5(G(c_g(encArg(x0))))
   ENCODE_G(cons_g(c(z0))) -> c5(G(g(c(encArg(z0)))))
   ENCODE_G(cons_g(cons_g(z0))) -> c5(G(g(g(encArg(z0)))))
   ENCODE_G(cons_g(cons_f(z0))) -> c5(G(g(f(encArg(z0)))))
   ENCODE_G(cons_f(x0)) -> c5(G(c_f(encArg(x0))))
   ENCODE_G(cons_f(c(z0))) -> c5(G(f(c(encArg(z0)))))
   ENCODE_G(cons_f(cons_g(z0))) -> c5(G(f(g(encArg(z0)))))
   ENCODE_G(cons_f(cons_f(z0))) -> c5(G(f(f(encArg(z0)))))
   ENCODE_F(cons_g(c(z0))) -> c5(F(g(c(encArg(z0)))))
   ENCODE_F(cons_g(cons_g(z0))) -> c5(F(g(g(encArg(z0)))))
   ENCODE_F(cons_g(cons_f(z0))) -> c5(F(g(f(encArg(z0)))))
   ENCODE_F(cons_f(x0)) -> c5(F(c_f(encArg(x0))))
   ENCODE_F(cons_f(c(z0))) -> c5(F(f(c(encArg(z0)))))
   ENCODE_F(cons_f(cons_g(z0))) -> c5(F(f(g(encArg(z0)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c5(F(f(f(encArg(z0)))))
   G(c_f(c(x0))) -> c12
   ENCARG(c(cons_g(c(y0)))) -> c1(ENCARG(cons_g(c(y0))))
   ENCARG(c(cons_g(cons_g(y0)))) -> c1(ENCARG(cons_g(cons_g(y0))))
   ENCARG(c(cons_g(cons_g(c(y0))))) -> c1(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(c(cons_g(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(c(cons_g(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(c(cons_g(cons_f(y0)))) -> c1(ENCARG(cons_g(cons_f(y0))))
   ENCARG(c(cons_g(cons_f(c(y0))))) -> c1(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(c(cons_g(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(c(cons_g(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_g(cons_f(cons_f(y0)))))
   ENCARG(c(cons_f(cons_g(c(y0))))) -> c1(ENCARG(cons_f(cons_g(c(y0)))))
   ENCARG(c(cons_f(cons_g(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_g(y0)))))
   ENCARG(c(cons_f(cons_g(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_g(cons_f(y0)))))
   ENCARG(c(cons_f(cons_f(y0)))) -> c1(ENCARG(cons_f(cons_f(y0))))
   ENCARG(c(cons_f(cons_f(c(y0))))) -> c1(ENCARG(cons_f(cons_f(c(y0)))))
   ENCARG(c(cons_f(cons_f(cons_g(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_g(y0)))))
   ENCARG(c(cons_f(cons_f(cons_f(y0))))) -> c1(ENCARG(cons_f(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(c(y0)))) -> c3(ENCARG(c(c(y0))))
   ENCARG(cons_f(c(cons_g(c(y0))))) -> c3(ENCARG(c(cons_g(c(y0)))))
   ENCARG(cons_f(c(cons_f(c(y0))))) -> c3(ENCARG(c(cons_f(c(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(y0))))) -> c3(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(y0))))) -> c3(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(cons_f(c(cons_f(cons_g(y0))))) -> c3(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(y0))))) -> c3(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))) -> c3(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
   ENCARG(cons_f(cons_g(c(y0)))) -> c3(ENCARG(cons_g(c(y0))))
   ENCARG(cons_f(cons_g(cons_g(y0)))) -> c3(ENCARG(cons_g(cons_g(y0))))
   ENCARG(cons_f(cons_g(cons_g(c(y0))))) -> c3(ENCARG(cons_g(cons_g(c(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_g(cons_f(y0)))))
   ENCARG(cons_f(cons_g(cons_f(y0)))) -> c3(ENCARG(cons_g(cons_f(y0))))
   ENCARG(cons_f(cons_g(cons_f(c(y0))))) -> c3(ENCARG(cons_g(cons_f(c(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_g(y0)))))
   ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))) -> c3(ENCARG(cons_g(cons_f(cons_f(y0)))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(c_g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(c_f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   ENCARG(c(c(c(y0)))) -> c1(ENCARG(c(c(y0))))
   ENCARG(c(c(cons_g(c(y0))))) -> c1(ENCARG(c(cons_g(c(y0)))))
   ENCARG(c(c(cons_f(c(y0))))) -> c1(ENCARG(c(cons_f(c(y0)))))
   ENCARG(c(c(cons_g(cons_g(y0))))) -> c1(ENCARG(c(cons_g(cons_g(y0)))))
   ENCARG(c(c(cons_g(cons_g(c(y0)))))) -> c1(ENCARG(c(cons_g(cons_g(c(y0))))))
   ENCARG(c(c(cons_g(cons_g(cons_g(y0)))))) -> c1(ENCARG(c(cons_g(cons_g(cons_g(y0))))))
   ENCARG(c(c(cons_g(cons_g(cons_f(y0)))))) -> c1(ENCARG(c(cons_g(cons_g(cons_f(y0))))))
   ENCARG(c(c(cons_g(cons_f(y0))))) -> c1(ENCARG(c(cons_g(cons_f(y0)))))
   ENCARG(c(c(cons_g(cons_f(c(y0)))))) -> c1(ENCARG(c(cons_g(cons_f(c(y0))))))
   ENCARG(c(c(cons_g(cons_f(cons_g(y0)))))) -> c1(ENCARG(c(cons_g(cons_f(cons_g(y0))))))
   ENCARG(c(c(cons_g(cons_f(cons_f(y0)))))) -> c1(ENCARG(c(cons_g(cons_f(cons_f(y0))))))
   ENCARG(c(c(cons_f(cons_g(c(y0)))))) -> c1(ENCARG(c(cons_f(cons_g(c(y0))))))
   ENCARG(c(c(cons_f(cons_g(cons_g(y0)))))) -> c1(ENCARG(c(cons_f(cons_g(cons_g(y0))))))
   ENCARG(c(c(cons_f(cons_g(cons_f(y0)))))) -> c1(ENCARG(c(cons_f(cons_g(cons_f(y0))))))
   ENCARG(c(c(cons_f(cons_g(y0))))) -> c1(ENCARG(c(cons_f(cons_g(y0)))))
   ENCARG(c(c(cons_f(cons_f(y0))))) -> c1(ENCARG(c(cons_f(cons_f(y0)))))
   ENCARG(c(c(cons_f(cons_f(c(y0)))))) -> c1(ENCARG(c(cons_f(cons_f(c(y0))))))
   ENCARG(c(c(cons_f(cons_f(cons_g(y0)))))) -> c1(ENCARG(c(cons_f(cons_f(cons_g(y0))))))
   ENCARG(c(c(cons_f(cons_f(cons_f(y0)))))) -> c1(ENCARG(c(cons_f(cons_f(cons_f(y0))))))
   ENCARG(c(cons_f(c(c(y0))))) -> c1(ENCARG(cons_f(c(c(y0)))))
   ENCARG(c(cons_f(c(cons_g(c(y0)))))) -> c1(ENCARG(cons_f(c(cons_g(c(y0))))))
   ENCARG(c(cons_f(c(cons_f(c(y0)))))) -> c1(ENCARG(cons_f(c(cons_f(c(y0))))))
   ENCARG(c(cons_f(c(cons_g(cons_g(y0)))))) -> c1(ENCARG(cons_f(c(cons_g(cons_g(y0))))))
   ENCARG(c(cons_f(c(cons_g(cons_g(c(y0))))))) -> c1(ENCARG(cons_f(c(cons_g(cons_g(c(y0)))))))
   ENCARG(c(cons_f(c(cons_g(cons_g(cons_g(y0))))))) -> c1(ENCARG(cons_f(c(cons_g(cons_g(cons_g(y0)))))))
   ENCARG(c(cons_f(c(cons_g(cons_g(cons_f(y0))))))) -> c1(ENCARG(cons_f(c(cons_g(cons_g(cons_f(y0)))))))
   ENCARG(c(cons_f(c(cons_g(cons_f(y0)))))) -> c1(ENCARG(cons_f(c(cons_g(cons_f(y0))))))
   ENCARG(c(cons_f(c(cons_g(cons_f(c(y0))))))) -> c1(ENCARG(cons_f(c(cons_g(cons_f(c(y0)))))))
   ENCARG(c(cons_f(c(cons_g(cons_f(cons_g(y0))))))) -> c1(ENCARG(cons_f(c(cons_g(cons_f(cons_g(y0)))))))
   ENCARG(c(cons_f(c(cons_g(cons_f(cons_f(y0))))))) -> c1(ENCARG(cons_f(c(cons_g(cons_f(cons_f(y0)))))))
   ENCARG(c(cons_f(c(cons_f(cons_g(c(y0))))))) -> c1(ENCARG(cons_f(c(cons_f(cons_g(c(y0)))))))
   ENCARG(c(cons_f(c(cons_f(cons_g(cons_g(y0))))))) -> c1(ENCARG(cons_f(c(cons_f(cons_g(cons_g(y0)))))))
   ENCARG(c(cons_f(c(cons_f(cons_g(cons_f(y0))))))) -> c1(ENCARG(cons_f(c(cons_f(cons_g(cons_f(y0)))))))
   ENCARG(c(cons_f(c(cons_f(cons_g(y0)))))) -> c1(ENCARG(cons_f(c(cons_f(cons_g(y0))))))
   ENCARG(c(cons_f(c(cons_f(cons_f(y0)))))) -> c1(ENCARG(cons_f(c(cons_f(cons_f(y0))))))
   ENCARG(c(cons_f(c(cons_f(cons_f(c(y0))))))) -> c1(ENCARG(cons_f(c(cons_f(cons_f(c(y0)))))))
   ENCARG(c(cons_f(c(cons_f(cons_f(cons_g(y0))))))) -> c1(ENCARG(cons_f(c(cons_f(cons_f(cons_g(y0)))))))
   ENCARG(c(cons_f(c(cons_f(cons_f(cons_f(y0))))))) -> c1(ENCARG(cons_f(c(cons_f(cons_f(cons_f(y0)))))))
   ENCARG(c(cons_f(cons_g(cons_g(c(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_g(c(y0))))))
   ENCARG(c(cons_f(cons_g(cons_g(cons_g(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_g(cons_g(y0))))))
   ENCARG(c(cons_f(cons_g(cons_g(cons_f(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_g(cons_f(y0))))))
   ENCARG(c(cons_f(cons_g(cons_f(c(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_f(c(y0))))))
   ENCARG(c(cons_f(cons_g(cons_f(cons_g(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_f(cons_g(y0))))))
   ENCARG(c(cons_f(cons_g(cons_f(cons_f(y0)))))) -> c1(ENCARG(cons_f(cons_g(cons_f(cons_f(y0))))))
S tuples:
   F(c_f(c_g(c_f(c_g(x0))))) -> c8(G(c_g(f(x0))), F(c_f(c_g(x0))))
   F(c_f(c_g(c_f(c_g(z0))))) -> c8(G(g(c_f(z0))), F(c_f(c_g(z0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(z0))))))) -> c8(G(g(g(f(z0)))), F(c_f(c_g(c_f(c_g(z0))))))
   G(c_g(c_g(z0))) -> c11(G(c_f(g(f(g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(z0)) -> c11(F(g(z0)), G(z0))
   G(c_g(c(x0))) -> c11(G(f(g(c_f(c(x0))))), F(g(c(x0))), G(c(x0)))
   G(c_g(c(x0))) -> c11(F(g(c(x0))), G(c(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(c_g(f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(x0))) -> c11(G(f(g(c_f(g(x0))))), F(g(c_g(x0))), G(c_g(x0)))
   G(c_g(c_g(c_g(z0)))) -> c11(G(f(g(f(g(f(g(z0))))))), F(g(c_g(c_g(z0)))), G(c_g(c_g(z0))))
   G(c_g(c_g(x0))) -> c11(F(g(c_g(x0))))
   G(c_g(c_f(c(x0)))) -> c11(F(g(c_f(c(x0)))), G(c_f(c(x0))))
   G(c_f(c(x0))) -> c12
   F(c_f(c_g(c_f(c_g(y0))))) -> c8(F(c_f(c_g(y0))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))) -> c8(F(c_f(c_g(c_f(c_g(y0))))))
   F(c_f(c_g(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))) -> c8(F(c_f(c_g(c_f(c_g(c_f(c_g(y0))))))))
   G(c_g(c(z0))) -> c11(G(c_f(g(c_f(c(z0))))), F(g(c(z0))), G(c(z0)))
   G(c_g(c_f(c(z0)))) -> c11(G(c_f(g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_g(z0))) -> c11(G(f(g(c_f(c_g(z0))))), F(g(c_g(z0))), G(c_g(z0)))
   G(c_g(c_g(c(z0)))) -> c11(G(f(g(f(g(c_f(c(z0))))))), F(g(c_g(c(z0)))), G(c_g(c(z0))))
   G(c_g(c_g(c_f(c(z0))))) -> c11(G(f(g(f(g(f(c_f(c(z0)))))))), F(g(c_g(c_f(c(z0))))), G(c_g(c_f(c(z0)))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(c_g(f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
   G(c_g(c_f(c(z0)))) -> c11(G(f(g(c_f(c_f(c(z0)))))), F(g(c_f(c(z0)))), G(c_f(c(z0))))
K tuples:
   F(c_f(c_g(c(y0)))) -> c8(G(c_f(c(y0))))
Defined Rule Symbols:   encArg_1, g_1, f_1

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

Compound Symbols:   c2_2, c10_1, c5_1, c3_2, c8_2, c11_3, c11_2, c11_1, c12, c1_1, c3_1, c8_1