/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (innermost) 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), 175 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), 2262 ms]
    (14) BOUNDS(1, INF)
(15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(16) CpxTRS
(17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 0 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 6 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 2 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(36) CdtProblem
    (37) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (38) CdtProblem
    (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) CdtProblem
    (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (44) CdtProblem
    (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CdtProblem
    (49) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) CdtProblem
    (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) CdtProblem
    (57) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms]
    (60) CdtProblem
    (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (64) CdtProblem
    (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (66) CdtProblem
    (67) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1 ms]
    (70) CdtProblem
    (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
    (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (76) CdtProblem
    (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (78) CdtProblem
    (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) CdtProblem
    (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) CdtProblem
    (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (88) CdtProblem
    (89) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (90) CdtProblem
    (91) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1 ms]
    (92) CdtProblem
    (93) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (94) CdtProblem
    (95) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem


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

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


The TRS R consists of the following rules:

   g(x, x) -> g(a, b)
   g(c, g(c, x)) -> g(e, g(d, x))
   g(d, g(d, x)) -> g(c, g(e, x))
   g(e, g(e, x)) -> g(d, g(c, x))
   f(g(x, y)) -> g(y, g(f(f(x)), a))

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

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

   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   encode_e -> e
   encode_d -> d
   encode_f(x_1) -> f(encArg(x_1))


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

(2)
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(x, x) -> g(a, b)
   g(c, g(c, x)) -> g(e, g(d, x))
   g(d, g(d, x)) -> g(c, g(e, x))
   g(e, g(e, x)) -> g(d, g(c, x))
   f(g(x, y)) -> g(y, g(f(f(x)), a))

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

   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   encode_e -> e
   encode_d -> d
   encode_f(x_1) -> f(encArg(x_1))

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

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

(4)
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(x, x) -> g(a, b)
   g(c, g(c, x)) -> g(e, g(d, x))
   g(d, g(d, x)) -> g(c, g(e, x))
   g(e, g(e, x)) -> g(d, g(c, x))
   f(g(x, y)) -> g(y, g(f(f(x)), a))

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

   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   encode_e -> e
   encode_d -> d
   encode_f(x_1) -> f(encArg(x_1))

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

(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 (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   g(x, x) -> g(a, b)
   g(c, g(c, x)) -> g(e, g(d, x))
   g(d, g(d, x)) -> g(c, g(e, x))
   g(e, g(e, x)) -> g(d, g(c, x))
   f(g(x, y)) -> g(y, g(f(f(x)), a))

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

   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   encode_e -> e
   encode_d -> d
   encode_f(x_1) -> f(encArg(x_1))

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

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

(8)
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(x, x) -> g(a, b)
   g(c, g(c, x)) -> g(e, g(d, x))
   g(d, g(d, x)) -> g(c, g(e, x))
   g(e, g(e, x)) -> g(d, g(c, x))
   f(g(x, y)) -> g(y, g(f(f(x)), a))

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

   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   encode_e -> e
   encode_d -> d
   encode_f(x_1) -> f(encArg(x_1))

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

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

(10)
Obligation:
Innermost TRS:
Rules:
g(x, x) -> g(a, b)
g(c, g(c, x)) -> g(e, g(d, x))
g(d, g(d, x)) -> g(c, g(e, x))
g(e, g(e, x)) -> g(d, g(c, x))
f(g(x, y)) -> g(y, g(f(f(x)), a))
encArg(a) -> a
encArg(b) -> b
encArg(c) -> c
encArg(e) -> e
encArg(d) -> d
encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
encArg(cons_f(x_1)) -> f(encArg(x_1))
encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))
encode_a -> a
encode_b -> b
encode_c -> c
encode_e -> e
encode_d -> d
encode_f(x_1) -> f(encArg(x_1))

Types:
g :: a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f
a :: a:b:c:e:d:cons_g:cons_f
b :: a:b:c:e:d:cons_g:cons_f
c :: a:b:c:e:d:cons_g:cons_f
e :: a:b:c:e:d:cons_g:cons_f
d :: a:b:c:e:d:cons_g:cons_f
f :: a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f
encArg :: a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f
cons_g :: a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f
cons_f :: a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f
encode_g :: a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f
encode_a :: a:b:c:e:d:cons_g:cons_f
encode_b :: a:b:c:e:d:cons_g:cons_f
encode_c :: a:b:c:e:d:cons_g:cons_f
encode_e :: a:b:c:e:d:cons_g:cons_f
encode_d :: a:b:c:e:d:cons_g:cons_f
encode_f :: a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f
hole_a:b:c:e:d:cons_g:cons_f1_0 :: a:b:c:e:d:cons_g:cons_f
gen_a:b:c:e:d:cons_g:cons_f2_0 :: Nat -> a:b:c:e:d: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:
Innermost TRS:
Rules:
g(x, x) -> g(a, b)
g(c, g(c, x)) -> g(e, g(d, x))
g(d, g(d, x)) -> g(c, g(e, x))
g(e, g(e, x)) -> g(d, g(c, x))
f(g(x, y)) -> g(y, g(f(f(x)), a))
encArg(a) -> a
encArg(b) -> b
encArg(c) -> c
encArg(e) -> e
encArg(d) -> d
encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
encArg(cons_f(x_1)) -> f(encArg(x_1))
encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))
encode_a -> a
encode_b -> b
encode_c -> c
encode_e -> e
encode_d -> d
encode_f(x_1) -> f(encArg(x_1))

Types:
g :: a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f
a :: a:b:c:e:d:cons_g:cons_f
b :: a:b:c:e:d:cons_g:cons_f
c :: a:b:c:e:d:cons_g:cons_f
e :: a:b:c:e:d:cons_g:cons_f
d :: a:b:c:e:d:cons_g:cons_f
f :: a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f
encArg :: a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f
cons_g :: a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f
cons_f :: a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f
encode_g :: a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f
encode_a :: a:b:c:e:d:cons_g:cons_f
encode_b :: a:b:c:e:d:cons_g:cons_f
encode_c :: a:b:c:e:d:cons_g:cons_f
encode_e :: a:b:c:e:d:cons_g:cons_f
encode_d :: a:b:c:e:d:cons_g:cons_f
encode_f :: a:b:c:e:d:cons_g:cons_f -> a:b:c:e:d:cons_g:cons_f
hole_a:b:c:e:d:cons_g:cons_f1_0 :: a:b:c:e:d:cons_g:cons_f
gen_a:b:c:e:d:cons_g:cons_f2_0 :: Nat -> a:b:c:e:d:cons_g:cons_f


Generator Equations:
gen_a:b:c:e:d:cons_g:cons_f2_0(0) <=> a
gen_a:b:c:e:d:cons_g:cons_f2_0(+(x, 1)) <=> cons_g(a, gen_a:b:c:e:d:cons_g:cons_f2_0(x))


The following defined symbols remain to be analysed:
g, f, 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_a:b:c:e:d:cons_g:cons_f2_0(n62_0)) -> *3_0, rt in Omega(0)

Induction Base:
encArg(gen_a:b:c:e:d:cons_g:cons_f2_0(0))

Induction Step:
encArg(gen_a:b:c:e:d:cons_g:cons_f2_0(+(n62_0, 1))) ->_R^Omega(0)
g(encArg(a), encArg(gen_a:b:c:e:d:cons_g:cons_f2_0(n62_0))) ->_R^Omega(0)
g(a, encArg(gen_a:b:c:e:d:cons_g:cons_f2_0(n62_0))) ->_IH
g(a, *3_0)

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

(14)
BOUNDS(1, INF)

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

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

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


The TRS R consists of the following rules:

   g(x, x) -> g(a, b)
   g(c, g(c, x)) -> g(e, g(d, x))
   g(d, g(d, x)) -> g(c, g(e, x))
   g(e, g(e, x)) -> g(d, g(c, x))
   f(g(x, y)) -> g(y, g(f(f(x)), a))
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   encode_e -> e
   encode_d -> d
   encode_f(x_1) -> f(encArg(x_1))

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

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

(18)
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(x, x) -> g(a, b)
   g(e, c_g(e, x)) -> g(d, g(c, x))
   g(c, c_g(c, x)) -> g(e, g(d, x))
   g(d, c_g(d, x)) -> g(c, g(e, x))
   f(c_g(x, y)) -> g(y, g(f(f(x)), a))

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

   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2))
   encArg(cons_f(x_1)) -> f(encArg(x_1))
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   encode_e -> e
   encode_d -> d
   encode_f(x_1) -> f(encArg(x_1))
   g(x0, x1) -> c_g(x0, x1)

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

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

(20)
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(x, x) -> g(a, b) [1]
   g(e, c_g(e, x)) -> g(d, g(c, x)) [1]
   g(c, c_g(c, x)) -> g(e, g(d, x)) [1]
   g(d, c_g(d, x)) -> g(c, g(e, x)) [1]
   f(c_g(x, y)) -> g(y, g(f(f(x)), a)) [1]
   encArg(a) -> a [0]
   encArg(b) -> b [0]
   encArg(c) -> c [0]
   encArg(e) -> e [0]
   encArg(d) -> d [0]
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0]
   encode_a -> a [0]
   encode_b -> b [0]
   encode_c -> c [0]
   encode_e -> e [0]
   encode_d -> d [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   g(x0, x1) -> c_g(x0, x1) [0]

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

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

(22)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   g(x, x) -> g(a, b) [1]
   g(e, c_g(e, x)) -> g(d, g(c, x)) [1]
   g(c, c_g(c, x)) -> g(e, g(d, x)) [1]
   g(d, c_g(d, x)) -> g(c, g(e, x)) [1]
   f(c_g(x, y)) -> g(y, g(f(f(x)), a)) [1]
   encArg(a) -> a [0]
   encArg(b) -> b [0]
   encArg(c) -> c [0]
   encArg(e) -> e [0]
   encArg(d) -> d [0]
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0]
   encode_a -> a [0]
   encode_b -> b [0]
   encode_c -> c [0]
   encode_e -> e [0]
   encode_d -> d [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   g(x0, x1) -> c_g(x0, x1) [0]

The TRS has the following type information:
g :: a:b:e:c_g:d:c:cons_g:cons_f -> a:b:e:c_g:d:c:cons_g:cons_f -> a:b:e:c_g:d:c:cons_g:cons_f
a :: a:b:e:c_g:d:c:cons_g:cons_f
b :: a:b:e:c_g:d:c:cons_g:cons_f
e :: a:b:e:c_g:d:c:cons_g:cons_f
c_g :: a:b:e:c_g:d:c:cons_g:cons_f -> a:b:e:c_g:d:c:cons_g:cons_f -> a:b:e:c_g:d:c:cons_g:cons_f
d :: a:b:e:c_g:d:c:cons_g:cons_f
c :: a:b:e:c_g:d:c:cons_g:cons_f
f :: a:b:e:c_g:d:c:cons_g:cons_f -> a:b:e:c_g:d:c:cons_g:cons_f
encArg :: a:b:e:c_g:d:c:cons_g:cons_f -> a:b:e:c_g:d:c:cons_g:cons_f
cons_g :: a:b:e:c_g:d:c:cons_g:cons_f -> a:b:e:c_g:d:c:cons_g:cons_f -> a:b:e:c_g:d:c:cons_g:cons_f
cons_f :: a:b:e:c_g:d:c:cons_g:cons_f -> a:b:e:c_g:d:c:cons_g:cons_f
encode_g :: a:b:e:c_g:d:c:cons_g:cons_f -> a:b:e:c_g:d:c:cons_g:cons_f -> a:b:e:c_g:d:c:cons_g:cons_f
encode_a :: a:b:e:c_g:d:c:cons_g:cons_f
encode_b :: a:b:e:c_g:d:c:cons_g:cons_f
encode_c :: a:b:e:c_g:d:c:cons_g:cons_f
encode_e :: a:b:e:c_g:d:c:cons_g:cons_f
encode_d :: a:b:e:c_g:d:c:cons_g:cons_f
encode_f :: a:b:e:c_g:d:c:cons_g:cons_f -> a:b:e:c_g:d:c:cons_g:cons_f

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

(23) 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:

   f_1
   encArg_1
   encode_g_2
   encode_a
   encode_b
   encode_c
   encode_e
   encode_d
   encode_f_1
   g_2

Due to the following rules being added:

   encArg(v0) -> null_encArg [0]
   encode_g(v0, v1) -> null_encode_g [0]
   encode_a -> null_encode_a [0]
   encode_b -> null_encode_b [0]
   encode_c -> null_encode_c [0]
   encode_e -> null_encode_e [0]
   encode_d -> null_encode_d [0]
   encode_f(v0) -> null_encode_f [0]
   g(v0, v1) -> null_g [0]
   f(v0) -> null_f [0]

And the following fresh constants:    null_encArg, null_encode_g, null_encode_a, null_encode_b, null_encode_c, null_encode_e, null_encode_d, null_encode_f, null_g, null_f

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

(24)
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(x, x) -> g(a, b) [1]
   g(e, c_g(e, x)) -> g(d, g(c, x)) [1]
   g(c, c_g(c, x)) -> g(e, g(d, x)) [1]
   g(d, c_g(d, x)) -> g(c, g(e, x)) [1]
   f(c_g(x, y)) -> g(y, g(f(f(x)), a)) [1]
   encArg(a) -> a [0]
   encArg(b) -> b [0]
   encArg(c) -> c [0]
   encArg(e) -> e [0]
   encArg(d) -> d [0]
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0]
   encode_a -> a [0]
   encode_b -> b [0]
   encode_c -> c [0]
   encode_e -> e [0]
   encode_d -> d [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   g(x0, x1) -> c_g(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_g(v0, v1) -> null_encode_g [0]
   encode_a -> null_encode_a [0]
   encode_b -> null_encode_b [0]
   encode_c -> null_encode_c [0]
   encode_e -> null_encode_e [0]
   encode_d -> null_encode_d [0]
   encode_f(v0) -> null_encode_f [0]
   g(v0, v1) -> null_g [0]
   f(v0) -> null_f [0]

The TRS has the following type information:
g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
a :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
b :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
e :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
c_g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
d :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
c :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
f :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encArg :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
cons_g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
cons_f :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_a :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_b :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_c :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_e :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_d :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_f :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encArg :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_a :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_b :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_c :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_e :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_d :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_f :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_f :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f

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

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

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

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

   g(x, x) -> g(a, b) [1]
   g(e, c_g(e, c)) -> g(d, g(a, b)) [2]
   g(e, c_g(e, c_g(c, x'))) -> g(d, g(e, g(d, x'))) [2]
   g(e, c_g(e, x)) -> g(d, c_g(c, x)) [1]
   g(e, c_g(e, x)) -> g(d, null_g) [1]
   g(c, c_g(c, d)) -> g(e, g(a, b)) [2]
   g(c, c_g(c, c_g(d, x''))) -> g(e, g(c, g(e, x''))) [2]
   g(c, c_g(c, x)) -> g(e, c_g(d, x)) [1]
   g(c, c_g(c, x)) -> g(e, null_g) [1]
   g(d, c_g(d, e)) -> g(c, g(a, b)) [2]
   g(d, c_g(d, c_g(e, x2))) -> g(c, g(d, g(c, x2))) [2]
   g(d, c_g(d, x)) -> g(c, c_g(e, x)) [1]
   g(d, c_g(d, x)) -> g(c, null_g) [1]
   f(c_g(c_g(x3, y'), y)) -> g(y, g(f(g(y', g(f(f(x3)), a))), a)) [2]
   f(c_g(x, y)) -> g(y, g(f(null_f), a)) [1]
   encArg(a) -> a [0]
   encArg(b) -> b [0]
   encArg(c) -> c [0]
   encArg(e) -> e [0]
   encArg(d) -> d [0]
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_f(a)) -> f(a) [0]
   encArg(cons_f(b)) -> f(b) [0]
   encArg(cons_f(c)) -> f(c) [0]
   encArg(cons_f(e)) -> f(e) [0]
   encArg(cons_f(d)) -> f(d) [0]
   encArg(cons_f(cons_g(x_117, x_28))) -> f(g(encArg(x_117), encArg(x_28))) [0]
   encArg(cons_f(cons_f(x_118))) -> f(f(encArg(x_118))) [0]
   encArg(cons_f(x_1)) -> f(null_encArg) [0]
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0]
   encode_a -> a [0]
   encode_b -> b [0]
   encode_c -> c [0]
   encode_e -> e [0]
   encode_d -> d [0]
   encode_f(a) -> f(a) [0]
   encode_f(b) -> f(b) [0]
   encode_f(c) -> f(c) [0]
   encode_f(e) -> f(e) [0]
   encode_f(d) -> f(d) [0]
   encode_f(cons_g(x_137, x_218)) -> f(g(encArg(x_137), encArg(x_218))) [0]
   encode_f(cons_f(x_138)) -> f(f(encArg(x_138))) [0]
   encode_f(x_1) -> f(null_encArg) [0]
   g(x0, x1) -> c_g(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_g(v0, v1) -> null_encode_g [0]
   encode_a -> null_encode_a [0]
   encode_b -> null_encode_b [0]
   encode_c -> null_encode_c [0]
   encode_e -> null_encode_e [0]
   encode_d -> null_encode_d [0]
   encode_f(v0) -> null_encode_f [0]
   g(v0, v1) -> null_g [0]
   f(v0) -> null_f [0]

The TRS has the following type information:
g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
a :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
b :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
e :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
c_g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
d :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
c :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
f :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encArg :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
cons_g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
cons_f :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_a :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_b :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_c :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_e :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_d :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_f :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encArg :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_a :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_b :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_c :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_e :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_d :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_f :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_f :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f

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:

   a => 0
   b => 1
   e => 4
   d => 3
   c => 2
   null_encArg => 0
   null_encode_g => 0
   null_encode_a => 0
   null_encode_b => 0
   null_encode_c => 0
   null_encode_e => 0
   null_encode_d => 0
   null_encode_f => 0
   null_g => 0
   null_f => 0

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

(28)
Obligation:
Complexity RNTS consisting of the following rules:

   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z = 1 + (1 + x_117 + x_28), x_28 >= 0
   encArg(z) -{ 0 }-> f(f(encArg(x_118))) :|: z = 1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> f(4) :|: z = 1 + 4
   encArg(z) -{ 0 }-> f(3) :|: z = 1 + 3
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> 4 :|: z = 4
   encArg(z) -{ 0 }-> 3 :|: z = 3
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_a -{ 0 }-> 0 :|: 
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_c -{ 0 }-> 2 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_d -{ 0 }-> 3 :|: 
   encode_d -{ 0 }-> 0 :|: 
   encode_e -{ 0 }-> 4 :|: 
   encode_e -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(g(encArg(x_137), encArg(x_218))) :|: x_218 >= 0, z = 1 + x_137 + x_218, x_137 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(x_138))) :|: x_138 >= 0, z = 1 + x_138
   encode_f(z) -{ 0 }-> f(4) :|: z = 4
   encode_f(z) -{ 0 }-> f(3) :|: z = 3
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: x_1 >= 0, z = x_1
   encode_f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_g(z, z') -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_g(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   f(z) -{ 2 }-> g(y, g(f(g(y', g(f(f(x3)), 0))), 0)) :|: y >= 0, y' >= 0, z = 1 + (1 + x3 + y') + y, x3 >= 0
   f(z) -{ 1 }-> g(y, g(f(0), 0)) :|: z = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   g(z, z') -{ 2 }-> g(4, g(2, g(4, x''))) :|: z = 2, z' = 1 + 2 + (1 + 3 + x''), x'' >= 0
   g(z, z') -{ 2 }-> g(4, g(0, 1)) :|: z = 2, z' = 1 + 2 + 3
   g(z, z') -{ 1 }-> g(4, 0) :|: z = 2, z' = 1 + 2 + x, x >= 0
   g(z, z') -{ 1 }-> g(4, 1 + 3 + x) :|: z = 2, z' = 1 + 2 + x, x >= 0
   g(z, z') -{ 2 }-> g(3, g(4, g(3, x'))) :|: x' >= 0, z' = 1 + 4 + (1 + 2 + x'), z = 4
   g(z, z') -{ 2 }-> g(3, g(0, 1)) :|: z' = 1 + 4 + 2, z = 4
   g(z, z') -{ 1 }-> g(3, 0) :|: x >= 0, z = 4, z' = 1 + 4 + x
   g(z, z') -{ 1 }-> g(3, 1 + 2 + x) :|: x >= 0, z = 4, z' = 1 + 4 + x
   g(z, z') -{ 2 }-> g(2, g(3, g(2, x2))) :|: z = 3, z' = 1 + 3 + (1 + 4 + x2), x2 >= 0
   g(z, z') -{ 2 }-> g(2, g(0, 1)) :|: z = 3, z' = 1 + 3 + 4
   g(z, z') -{ 1 }-> g(2, 0) :|: z = 3, z' = 1 + 3 + x, x >= 0
   g(z, z') -{ 1 }-> g(2, 1 + 4 + x) :|: z = 3, z' = 1 + 3 + x, x >= 0
   g(z, z') -{ 1 }-> g(0, 1) :|: z' = x, x >= 0, z = x
   g(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   g(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1


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

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

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

   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(g(encArg(x_117), encArg(x_28))) :|: x_117 >= 0, z = 1 + (1 + x_117 + x_28), x_28 >= 0
   encArg(z) -{ 0 }-> f(f(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> f(4) :|: z = 1 + 4
   encArg(z) -{ 0 }-> f(3) :|: z = 1 + 3
   encArg(z) -{ 0 }-> f(2) :|: z = 1 + 2
   encArg(z) -{ 0 }-> f(1) :|: z = 1 + 1
   encArg(z) -{ 0 }-> f(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> f(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> 4 :|: z = 4
   encArg(z) -{ 0 }-> 3 :|: z = 3
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_a -{ 0 }-> 0 :|: 
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_c -{ 0 }-> 2 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_d -{ 0 }-> 3 :|: 
   encode_d -{ 0 }-> 0 :|: 
   encode_e -{ 0 }-> 4 :|: 
   encode_e -{ 0 }-> 0 :|: 
   encode_f(z) -{ 0 }-> f(g(encArg(x_137), encArg(x_218))) :|: x_218 >= 0, z = 1 + x_137 + x_218, x_137 >= 0
   encode_f(z) -{ 0 }-> f(f(encArg(z - 1))) :|: z - 1 >= 0
   encode_f(z) -{ 0 }-> f(4) :|: z = 4
   encode_f(z) -{ 0 }-> f(3) :|: z = 3
   encode_f(z) -{ 0 }-> f(2) :|: z = 2
   encode_f(z) -{ 0 }-> f(1) :|: z = 1
   encode_f(z) -{ 0 }-> f(0) :|: z = 0
   encode_f(z) -{ 0 }-> f(0) :|: z >= 0
   encode_f(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z, z') -{ 0 }-> g(encArg(z), encArg(z')) :|: z >= 0, z' >= 0
   encode_g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   f(z) -{ 2 }-> g(y, g(f(g(y', g(f(f(x3)), 0))), 0)) :|: y >= 0, y' >= 0, z = 1 + (1 + x3 + y') + y, x3 >= 0
   f(z) -{ 1 }-> g(y, g(f(0), 0)) :|: z = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 0 }-> 0 :|: z >= 0
   g(z, z') -{ 2 }-> g(4, g(2, g(4, z' - 7))) :|: z = 2, z' - 7 >= 0
   g(z, z') -{ 2 }-> g(4, g(0, 1)) :|: z = 2, z' = 1 + 2 + 3
   g(z, z') -{ 1 }-> g(4, 0) :|: z = 2, z' - 3 >= 0
   g(z, z') -{ 1 }-> g(4, 1 + 3 + (z' - 3)) :|: z = 2, z' - 3 >= 0
   g(z, z') -{ 2 }-> g(3, g(4, g(3, z' - 8))) :|: z' - 8 >= 0, z = 4
   g(z, z') -{ 2 }-> g(3, g(0, 1)) :|: z' = 1 + 4 + 2, z = 4
   g(z, z') -{ 1 }-> g(3, 0) :|: z' - 5 >= 0, z = 4
   g(z, z') -{ 1 }-> g(3, 1 + 2 + (z' - 5)) :|: z' - 5 >= 0, z = 4
   g(z, z') -{ 2 }-> g(2, g(3, g(2, z' - 9))) :|: z = 3, z' - 9 >= 0
   g(z, z') -{ 2 }-> g(2, g(0, 1)) :|: z = 3, z' = 1 + 3 + 4
   g(z, z') -{ 1 }-> g(2, 0) :|: z = 3, z' - 4 >= 0
   g(z, z') -{ 1 }-> g(2, 1 + 4 + (z' - 4)) :|: z = 3, z' - 4 >= 0
   g(z, z') -{ 1 }-> g(0, 1) :|: z' >= 0, z = z'
   g(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   g(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0


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

(31) 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, v1) -> null_encode_g [0]
   encode_a -> null_encode_a [0]
   encode_b -> null_encode_b [0]
   encode_c -> null_encode_c [0]
   encode_e -> null_encode_e [0]
   encode_d -> null_encode_d [0]
   encode_f(v0) -> null_encode_f [0]
   g(v0, v1) -> null_g [0]
   f(v0) -> null_f [0]

And the following fresh constants:    null_encArg, null_encode_g, null_encode_a, null_encode_b, null_encode_c, null_encode_e, null_encode_d, null_encode_f, null_g, null_f

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

(32)
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(x, x) -> g(a, b) [1]
   g(e, c_g(e, x)) -> g(d, g(c, x)) [1]
   g(c, c_g(c, x)) -> g(e, g(d, x)) [1]
   g(d, c_g(d, x)) -> g(c, g(e, x)) [1]
   f(c_g(x, y)) -> g(y, g(f(f(x)), a)) [1]
   encArg(a) -> a [0]
   encArg(b) -> b [0]
   encArg(c) -> c [0]
   encArg(e) -> e [0]
   encArg(d) -> d [0]
   encArg(cons_g(x_1, x_2)) -> g(encArg(x_1), encArg(x_2)) [0]
   encArg(cons_f(x_1)) -> f(encArg(x_1)) [0]
   encode_g(x_1, x_2) -> g(encArg(x_1), encArg(x_2)) [0]
   encode_a -> a [0]
   encode_b -> b [0]
   encode_c -> c [0]
   encode_e -> e [0]
   encode_d -> d [0]
   encode_f(x_1) -> f(encArg(x_1)) [0]
   g(x0, x1) -> c_g(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_g(v0, v1) -> null_encode_g [0]
   encode_a -> null_encode_a [0]
   encode_b -> null_encode_b [0]
   encode_c -> null_encode_c [0]
   encode_e -> null_encode_e [0]
   encode_d -> null_encode_d [0]
   encode_f(v0) -> null_encode_f [0]
   g(v0, v1) -> null_g [0]
   f(v0) -> null_f [0]

The TRS has the following type information:
g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
a :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
b :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
e :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
c_g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
d :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
c :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
f :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encArg :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
cons_g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
cons_f :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_a :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_b :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_c :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_e :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_d :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
encode_f :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f -> a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encArg :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_a :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_b :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_c :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_e :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_d :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_encode_f :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_g :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f
null_f :: a:b:e:c_g:d:c:cons_g:cons_f:null_encArg:null_encode_g:null_encode_a:null_encode_b:null_encode_c:null_encode_e:null_encode_d:null_encode_f:null_g:null_f

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:

   a => 0
   b => 1
   e => 4
   d => 3
   c => 2
   null_encArg => 0
   null_encode_g => 0
   null_encode_a => 0
   null_encode_b => 0
   null_encode_c => 0
   null_encode_e => 0
   null_encode_d => 0
   null_encode_f => 0
   null_g => 0
   null_f => 0

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

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

   encArg(z) -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> 4 :|: z = 4
   encArg(z) -{ 0 }-> 3 :|: z = 3
   encArg(z) -{ 0 }-> 2 :|: z = 2
   encArg(z) -{ 0 }-> 1 :|: z = 1
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_a -{ 0 }-> 0 :|: 
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_c -{ 0 }-> 2 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_d -{ 0 }-> 3 :|: 
   encode_d -{ 0 }-> 0 :|: 
   encode_e -{ 0 }-> 4 :|: 
   encode_e -{ 0 }-> 0 :|: 
   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, z') -{ 0 }-> g(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2
   encode_g(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   f(z) -{ 1 }-> g(y, g(f(f(x)), 0)) :|: z = 1 + x + y, x >= 0, y >= 0
   f(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   g(z, z') -{ 1 }-> g(4, g(3, x)) :|: z = 2, z' = 1 + 2 + x, x >= 0
   g(z, z') -{ 1 }-> g(3, g(2, x)) :|: x >= 0, z = 4, z' = 1 + 4 + x
   g(z, z') -{ 1 }-> g(2, g(4, x)) :|: z = 3, z' = 1 + 3 + x, x >= 0
   g(z, z') -{ 1 }-> g(0, 1) :|: z' = x, x >= 0, z = x
   g(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   g(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1

Only complete derivations are relevant for the runtime complexity.

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

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

(36)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   encode_g(z0, z1) -> g(encArg(z0), encArg(z1))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   encode_e -> e
   encode_d -> d
   encode_f(z0) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(a) -> c1
   ENCARG(b) -> c2
   ENCARG(c) -> c3
   ENCARG(e) -> c4
   ENCARG(d) -> c5
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCARG(cons_f(z0)) -> c7(F(encArg(z0)), ENCARG(z0))
   ENCODE_G(z0, z1) -> c8(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_A -> c9
   ENCODE_B -> c10
   ENCODE_C -> c11
   ENCODE_E -> c12
   ENCODE_D -> c13
   ENCODE_F(z0) -> c14(F(encArg(z0)), ENCARG(z0))
   G(z0, z0) -> c15(G(a, b))
   G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
S tuples:
   G(z0, z0) -> c15(G(a, b))
   G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
K tuples:none
Defined Rule Symbols:   g_2, f_1, encArg_1, encode_g_2, encode_a, encode_b, encode_c, encode_e, encode_d, encode_f_1

Defined Pair Symbols:   ENCARG_1, ENCODE_G_2, ENCODE_A, ENCODE_B, ENCODE_C, ENCODE_E, ENCODE_D, ENCODE_F_1, G_2, F_1

Compound Symbols:   c1, c2, c3, c4, c5, c6_3, c7_2, c8_3, c9, c10, c11, c12, c13, c14_2, c15_1, c16_2, c17_2, c18_2, c19_4


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

(37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 10 trailing nodes:
   ENCODE_A -> c9
   ENCODE_C -> c11
   ENCARG(b) -> c2
   ENCARG(c) -> c3
   ENCARG(a) -> c1
   ENCODE_B -> c10
   ENCARG(d) -> c5
   ENCODE_D -> c13
   ENCODE_E -> c12
   ENCARG(e) -> c4

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   encode_g(z0, z1) -> g(encArg(z0), encArg(z1))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   encode_e -> e
   encode_d -> d
   encode_f(z0) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCARG(cons_f(z0)) -> c7(F(encArg(z0)), ENCARG(z0))
   ENCODE_G(z0, z1) -> c8(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_F(z0) -> c14(F(encArg(z0)), ENCARG(z0))
   G(z0, z0) -> c15(G(a, b))
   G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
S tuples:
   G(z0, z0) -> c15(G(a, b))
   G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
K tuples:none
Defined Rule Symbols:   g_2, f_1, encArg_1, encode_g_2, encode_a, encode_b, encode_c, encode_e, encode_d, encode_f_1

Defined Pair Symbols:   ENCARG_1, ENCODE_G_2, ENCODE_F_1, G_2, F_1

Compound Symbols:   c6_3, c7_2, c8_3, c14_2, c15_1, c16_2, c17_2, c18_2, c19_4


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

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   encode_g(z0, z1) -> g(encArg(z0), encArg(z1))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   encode_e -> e
   encode_d -> d
   encode_f(z0) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCARG(cons_f(z0)) -> c7(F(encArg(z0)), ENCARG(z0))
   ENCODE_G(z0, z1) -> c8(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_F(z0) -> c14(F(encArg(z0)), ENCARG(z0))
   G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
S tuples:
   G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
K tuples:none
Defined Rule Symbols:   g_2, f_1, encArg_1, encode_g_2, encode_a, encode_b, encode_c, encode_e, encode_d, encode_f_1

Defined Pair Symbols:   ENCARG_1, ENCODE_G_2, ENCODE_F_1, G_2, F_1

Compound Symbols:   c6_3, c7_2, c8_3, c14_2, c16_2, c17_2, c18_2, c19_4, c15


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

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   encode_g(z0, z1) -> g(encArg(z0), encArg(z1))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   encode_e -> e
   encode_d -> d
   encode_f(z0) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCARG(cons_f(z0)) -> c7(F(encArg(z0)), ENCARG(z0))
   G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCODE_G(z0, z1) -> c1(ENCARG(z0))
   ENCODE_G(z0, z1) -> c1(ENCARG(z1))
   ENCODE_F(z0) -> c1(F(encArg(z0)))
   ENCODE_F(z0) -> c1(ENCARG(z0))
S tuples:
   G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
K tuples:none
Defined Rule Symbols:   g_2, f_1, encArg_1, encode_g_2, encode_a, encode_b, encode_c, encode_e, encode_d, encode_f_1

Defined Pair Symbols:   ENCARG_1, G_2, F_1, ENCODE_G_2, ENCODE_F_1

Compound Symbols:   c6_3, c7_2, c16_2, c17_2, c18_2, c19_4, c15, c1_1


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

(43) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 3 leading nodes:
   ENCODE_G(z0, z1) -> c1(ENCARG(z0))
   ENCODE_G(z0, z1) -> c1(ENCARG(z1))
   ENCODE_F(z0) -> c1(ENCARG(z0))

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   encode_g(z0, z1) -> g(encArg(z0), encArg(z1))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   encode_e -> e
   encode_d -> d
   encode_f(z0) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCARG(cons_f(z0)) -> c7(F(encArg(z0)), ENCARG(z0))
   G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCODE_F(z0) -> c1(F(encArg(z0)))
S tuples:
   G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
K tuples:none
Defined Rule Symbols:   g_2, f_1, encArg_1, encode_g_2, encode_a, encode_b, encode_c, encode_e, encode_d, encode_f_1

Defined Pair Symbols:   ENCARG_1, G_2, F_1, ENCODE_G_2, ENCODE_F_1

Compound Symbols:   c6_3, c7_2, c16_2, c17_2, c18_2, c19_4, c15, c1_1


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

(45) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   encode_g(z0, z1) -> g(encArg(z0), encArg(z1))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   encode_e -> e
   encode_d -> d
   encode_f(z0) -> f(encArg(z0))

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCARG(cons_f(z0)) -> c7(F(encArg(z0)), ENCARG(z0))
   G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCODE_F(z0) -> c1(F(encArg(z0)))
S tuples:
   G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, F_1, ENCODE_G_2, ENCODE_F_1

Compound Symbols:   c6_3, c7_2, c16_2, c17_2, c18_2, c19_4, c15, c1_1


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

(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(z0)) -> c7(F(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_f(a)) -> c7(F(a), ENCARG(a))
   ENCARG(cons_f(b)) -> c7(F(b), ENCARG(b))
   ENCARG(cons_f(c)) -> c7(F(c), ENCARG(c))
   ENCARG(cons_f(e)) -> c7(F(e), ENCARG(e))
   ENCARG(cons_f(d)) -> c7(F(d), ENCARG(d))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   ENCARG(cons_f(cons_f(z0))) -> c7(F(f(encArg(z0))), ENCARG(cons_f(z0)))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCODE_F(z0) -> c1(F(encArg(z0)))
   ENCARG(cons_f(a)) -> c7(F(a), ENCARG(a))
   ENCARG(cons_f(b)) -> c7(F(b), ENCARG(b))
   ENCARG(cons_f(c)) -> c7(F(c), ENCARG(c))
   ENCARG(cons_f(e)) -> c7(F(e), ENCARG(e))
   ENCARG(cons_f(d)) -> c7(F(d), ENCARG(d))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   ENCARG(cons_f(cons_f(z0))) -> c7(F(f(encArg(z0))), ENCARG(cons_f(z0)))
S tuples:
   G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, F_1, ENCODE_G_2, ENCODE_F_1

Compound Symbols:   c6_3, c16_2, c17_2, c18_2, c19_4, c15, c1_1, c7_2


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

(49) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing nodes:
   ENCARG(cons_f(e)) -> c7(F(e), ENCARG(e))
   ENCARG(cons_f(c)) -> c7(F(c), ENCARG(c))
   ENCARG(cons_f(b)) -> c7(F(b), ENCARG(b))
   ENCARG(cons_f(d)) -> c7(F(d), ENCARG(d))
   ENCARG(cons_f(a)) -> c7(F(a), ENCARG(a))

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCODE_F(z0) -> c1(F(encArg(z0)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   ENCARG(cons_f(cons_f(z0))) -> c7(F(f(encArg(z0))), ENCARG(cons_f(z0)))
S tuples:
   G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, F_1, ENCODE_G_2, ENCODE_F_1

Compound Symbols:   c6_3, c16_2, c17_2, c18_2, c19_4, c15, c1_1, c7_2


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(c, g(c, z0)) -> c16(G(e, g(d, z0)), G(d, z0)) by 
   G(c, g(c, d)) -> c16(G(e, g(a, b)), G(d, d))
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCODE_F(z0) -> c1(F(encArg(z0)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   ENCARG(cons_f(cons_f(z0))) -> c7(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   G(c, g(c, d)) -> c16(G(e, g(a, b)), G(d, d))
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
S tuples:
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   G(c, g(c, d)) -> c16(G(e, g(a, b)), G(d, d))
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, F_1, ENCODE_G_2, ENCODE_F_1

Compound Symbols:   c6_3, c17_2, c18_2, c19_4, c15, c1_1, c7_2, c16_2


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

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCODE_F(z0) -> c1(F(encArg(z0)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   ENCARG(cons_f(cons_f(z0))) -> c7(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
S tuples:
   G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, F_1, ENCODE_G_2, ENCODE_F_1

Compound Symbols:   c6_3, c17_2, c18_2, c19_4, c15, c1_1, c7_2, c16_2, c16_1


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(d, g(d, z0)) -> c17(G(c, g(e, z0)), G(e, z0)) by 
   G(d, g(d, e)) -> c17(G(c, g(a, b)), G(e, e))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCODE_F(z0) -> c1(F(encArg(z0)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   ENCARG(cons_f(cons_f(z0))) -> c7(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(c, g(a, b)), G(e, e))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
S tuples:
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(c, g(a, b)), G(e, e))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, F_1, ENCODE_G_2, ENCODE_F_1

Compound Symbols:   c6_3, c18_2, c19_4, c15, c1_1, c7_2, c16_2, c16_1, c17_2


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

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCODE_F(z0) -> c1(F(encArg(z0)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   ENCARG(cons_f(cons_f(z0))) -> c7(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
S tuples:
   G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, F_1, ENCODE_G_2, ENCODE_F_1

Compound Symbols:   c6_3, c18_2, c19_4, c15, c1_1, c7_2, c16_2, c16_1, c17_2, c17_1


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(e, g(e, z0)) -> c18(G(d, g(c, z0)), G(c, z0)) by 
   G(e, g(e, c)) -> c18(G(d, g(a, b)), G(c, c))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCODE_F(z0) -> c1(F(encArg(z0)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   ENCARG(cons_f(cons_f(z0))) -> c7(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(d, g(a, b)), G(c, c))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
S tuples:
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(d, g(a, b)), G(c, c))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, F_1, G_2, ENCODE_G_2, ENCODE_F_1

Compound Symbols:   c6_3, c19_4, c15, c1_1, c7_2, c16_2, c16_1, c17_2, c17_1, c18_2


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

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCODE_F(z0) -> c1(F(encArg(z0)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   ENCARG(cons_f(cons_f(z0))) -> c7(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
S tuples:
   F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0))
   G(z0, z0) -> c15
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, F_1, G_2, ENCODE_G_2, ENCODE_F_1

Compound Symbols:   c6_3, c19_4, c15, c1_1, c7_2, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(g(z0, z1)) -> c19(G(z1, g(f(f(z0)), a)), G(f(f(z0)), a), F(f(z0)), F(z0)) by 
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCODE_F(z0) -> c1(F(encArg(z0)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   ENCARG(cons_f(cons_f(z0))) -> c7(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, ENCODE_F_1, F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c19_4, c19_1


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

(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(z0) -> c1(F(encArg(z0))) by 
   ENCODE_F(a) -> c1(F(a))
   ENCODE_F(b) -> c1(F(b))
   ENCODE_F(c) -> c1(F(c))
   ENCODE_F(e) -> c1(F(e))
   ENCODE_F(d) -> c1(F(d))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCODE_F(cons_f(z0)) -> c1(F(f(encArg(z0))))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   ENCARG(cons_f(cons_f(z0))) -> c7(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(a) -> c1(F(a))
   ENCODE_F(b) -> c1(F(b))
   ENCODE_F(c) -> c1(F(c))
   ENCODE_F(e) -> c1(F(e))
   ENCODE_F(d) -> c1(F(d))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCODE_F(cons_f(z0)) -> c1(F(f(encArg(z0))))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c19_4, c19_1


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

(67) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing nodes:
   ENCODE_F(a) -> c1(F(a))
   ENCODE_F(d) -> c1(F(d))
   ENCODE_F(c) -> c1(F(c))
   ENCODE_F(e) -> c1(F(e))
   ENCODE_F(b) -> c1(F(b))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   ENCARG(cons_f(cons_f(z0))) -> c7(F(f(encArg(z0))), ENCARG(cons_f(z0)))
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCODE_F(cons_f(z0)) -> c1(F(f(encArg(z0))))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c19_4, c19_1


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

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(cons_f(z0))) -> c7(F(f(encArg(z0))), ENCARG(cons_f(z0))) by 
   ENCARG(cons_f(cons_f(a))) -> c7(F(f(a)), ENCARG(cons_f(a)))
   ENCARG(cons_f(cons_f(b))) -> c7(F(f(b)), ENCARG(cons_f(b)))
   ENCARG(cons_f(cons_f(c))) -> c7(F(f(c)), ENCARG(cons_f(c)))
   ENCARG(cons_f(cons_f(e))) -> c7(F(f(e)), ENCARG(cons_f(e)))
   ENCARG(cons_f(cons_f(d))) -> c7(F(f(d)), ENCARG(cons_f(d)))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCODE_F(cons_f(z0)) -> c1(F(f(encArg(z0))))
   ENCARG(cons_f(cons_f(a))) -> c7(F(f(a)), ENCARG(cons_f(a)))
   ENCARG(cons_f(cons_f(b))) -> c7(F(f(b)), ENCARG(cons_f(b)))
   ENCARG(cons_f(cons_f(c))) -> c7(F(f(c)), ENCARG(cons_f(c)))
   ENCARG(cons_f(cons_f(e))) -> c7(F(f(e)), ENCARG(cons_f(e)))
   ENCARG(cons_f(cons_f(d))) -> c7(F(f(d)), ENCARG(cons_f(d)))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c19_4, c19_1


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

(71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing nodes:
   ENCARG(cons_f(cons_f(d))) -> c7(F(f(d)), ENCARG(cons_f(d)))
   ENCARG(cons_f(cons_f(c))) -> c7(F(f(c)), ENCARG(cons_f(c)))
   ENCARG(cons_f(cons_f(e))) -> c7(F(f(e)), ENCARG(cons_f(e)))
   ENCARG(cons_f(cons_f(b))) -> c7(F(f(b)), ENCARG(cons_f(b)))
   ENCARG(cons_f(cons_f(a))) -> c7(F(f(a)), ENCARG(cons_f(a)))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCODE_F(cons_f(z0)) -> c1(F(f(encArg(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_2, c16_1, c17_2, c17_1, c18_2, c18_1, c19_4, c19_1


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

(73) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(c, g(c, g(d, z0))) -> c16(G(e, g(c, g(e, z0))), G(d, g(d, z0))) by 
   G(c, g(c, g(d, e))) -> c16(G(e, g(c, g(a, b))), G(d, g(d, e)))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCODE_F(cons_f(z0)) -> c1(F(f(encArg(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   G(c, g(c, g(d, e))) -> c16(G(e, g(c, g(a, b))), G(d, g(d, e)))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   G(c, g(c, g(d, e))) -> c16(G(e, g(c, g(a, b))), G(d, g(d, e)))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_1, c17_2, c17_1, c18_2, c18_1, c19_4, c19_1, c16_2


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

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCODE_F(cons_f(z0)) -> c1(F(f(encArg(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0)))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_1, c17_2, c17_1, c18_2, c18_1, c19_4, c19_1, c16_2


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

(77) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(d, g(d, g(e, z0))) -> c17(G(c, g(d, g(c, z0))), G(e, g(e, z0))) by 
   G(d, g(d, g(e, c))) -> c17(G(c, g(d, g(a, b))), G(e, g(e, c)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCODE_F(cons_f(z0)) -> c1(F(f(encArg(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, c))) -> c17(G(c, g(d, g(a, b))), G(e, g(e, c)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, c))) -> c17(G(c, g(d, g(a, b))), G(e, g(e, c)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_1, c17_1, c18_2, c18_1, c19_4, c19_1, c16_2, c17_2


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

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCODE_F(cons_f(z0)) -> c1(F(f(encArg(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0)))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_1, c17_1, c18_2, c18_1, c19_4, c19_1, c16_2, c17_2


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

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace G(e, g(e, g(c, z0))) -> c18(G(d, g(e, g(d, z0))), G(c, g(c, z0))) by 
   G(e, g(e, g(c, d))) -> c18(G(d, g(e, g(a, b))), G(c, g(c, d)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, x0))) -> c18(G(c, g(c, x0)))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCODE_F(cons_f(z0)) -> c1(F(f(encArg(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, d))) -> c18(G(d, g(e, g(a, b))), G(c, g(c, d)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, x0))) -> c18(G(c, g(c, x0)))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, d))) -> c18(G(d, g(e, g(a, b))), G(c, g(c, d)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, x0))) -> c18(G(c, g(c, x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_1, c17_1, c18_1, c19_4, c19_1, c16_2, c17_2, c18_2


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

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCODE_F(cons_f(z0)) -> c1(F(f(encArg(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, x0))) -> c18(G(c, g(c, x0)))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, x0))) -> c18(G(c, g(c, x0)))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_1, c17_1, c18_1, c19_4, c19_1, c16_2, c17_2, c18_2


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

(85) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(g(g(z0, z1), x1)) -> c19(G(x1, g(f(f(g(z0, z1))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1))) by 
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCODE_F(cons_f(z0)) -> c1(F(f(encArg(z0))))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, x0))) -> c18(G(c, g(c, x0)))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, x0))) -> c18(G(c, g(c, x0)))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_1, c17_1, c18_1, c19_1, c16_2, c17_2, c18_2, c19_4


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(cons_f(z0)) -> c1(F(f(encArg(z0)))) by 
   ENCODE_F(cons_f(a)) -> c1(F(f(a)))
   ENCODE_F(cons_f(b)) -> c1(F(f(b)))
   ENCODE_F(cons_f(c)) -> c1(F(f(c)))
   ENCODE_F(cons_f(e)) -> c1(F(f(e)))
   ENCODE_F(cons_f(d)) -> c1(F(f(d)))
   ENCODE_F(cons_f(cons_g(z0, z1))) -> c1(F(f(g(encArg(z0), encArg(z1)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c1(F(f(f(encArg(z0)))))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, x0))) -> c18(G(c, g(c, x0)))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))
   ENCODE_F(cons_f(a)) -> c1(F(f(a)))
   ENCODE_F(cons_f(b)) -> c1(F(f(b)))
   ENCODE_F(cons_f(c)) -> c1(F(f(c)))
   ENCODE_F(cons_f(e)) -> c1(F(f(e)))
   ENCODE_F(cons_f(d)) -> c1(F(f(d)))
   ENCODE_F(cons_f(cons_g(z0, z1))) -> c1(F(f(g(encArg(z0), encArg(z1)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c1(F(f(f(encArg(z0)))))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, x0))) -> c18(G(c, g(c, x0)))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_1, c17_1, c18_1, c19_1, c16_2, c17_2, c18_2, c19_4


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

(89) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing nodes:
   ENCODE_F(cons_f(d)) -> c1(F(f(d)))
   ENCODE_F(cons_f(a)) -> c1(F(f(a)))
   ENCODE_F(cons_f(b)) -> c1(F(f(b)))
   ENCODE_F(cons_f(c)) -> c1(F(f(c)))
   ENCODE_F(cons_f(e)) -> c1(F(f(e)))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, x0))) -> c18(G(c, g(c, x0)))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))
   ENCODE_F(cons_f(cons_g(z0, z1))) -> c1(F(f(g(encArg(z0), encArg(z1)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c1(F(f(f(encArg(z0)))))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0)))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, x0))) -> c18(G(c, g(c, x0)))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_1, c17_1, c18_1, c19_1, c16_2, c17_2, c18_2, c19_4


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

(91) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace G(c, g(c, g(d, x0))) -> c16(G(d, g(d, x0))) by 
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(c, g(c, g(d, g(e, g(c, y0))))) -> c16(G(d, g(d, g(e, g(c, y0)))))
   G(c, g(c, g(d, g(e, y0)))) -> c16(G(d, g(d, g(e, y0))))
   G(c, g(c, g(d, g(e, c)))) -> c16(G(d, g(d, g(e, c))))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, x0))) -> c18(G(c, g(c, x0)))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))
   ENCODE_F(cons_f(cons_g(z0, z1))) -> c1(F(f(g(encArg(z0), encArg(z1)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c1(F(f(f(encArg(z0)))))
   G(c, g(c, g(d, g(e, g(c, y0))))) -> c16(G(d, g(d, g(e, g(c, y0)))))
   G(c, g(c, g(d, g(e, y0)))) -> c16(G(d, g(d, g(e, y0))))
   G(c, g(c, g(d, g(e, c)))) -> c16(G(d, g(d, g(e, c))))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0)))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, x0))) -> c18(G(c, g(c, x0)))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))
   G(c, g(c, g(d, g(e, g(c, y0))))) -> c16(G(d, g(d, g(e, g(c, y0)))))
   G(c, g(c, g(d, g(e, y0)))) -> c16(G(d, g(d, g(e, y0))))
   G(c, g(c, g(d, g(e, c)))) -> c16(G(d, g(d, g(e, c))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_1, c17_1, c18_1, c19_1, c16_2, c17_2, c18_2, c19_4


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

(93) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace G(d, g(d, g(e, x0))) -> c17(G(e, g(e, x0))) by 
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(d, g(d, g(e, g(c, g(d, y0))))) -> c17(G(e, g(e, g(c, g(d, y0)))))
   G(d, g(d, g(e, g(c, y0)))) -> c17(G(e, g(e, g(c, y0))))
   G(d, g(d, g(e, g(c, d)))) -> c17(G(e, g(e, g(c, d))))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, x0))) -> c18(G(c, g(c, x0)))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))
   ENCODE_F(cons_f(cons_g(z0, z1))) -> c1(F(f(g(encArg(z0), encArg(z1)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c1(F(f(f(encArg(z0)))))
   G(c, g(c, g(d, g(e, g(c, y0))))) -> c16(G(d, g(d, g(e, g(c, y0)))))
   G(c, g(c, g(d, g(e, y0)))) -> c16(G(d, g(d, g(e, y0))))
   G(c, g(c, g(d, g(e, c)))) -> c16(G(d, g(d, g(e, c))))
   G(d, g(d, g(e, g(c, g(d, y0))))) -> c17(G(e, g(e, g(c, g(d, y0)))))
   G(d, g(d, g(e, g(c, y0)))) -> c17(G(e, g(e, g(c, y0))))
   G(d, g(d, g(e, g(c, d)))) -> c17(G(e, g(e, g(c, d))))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, x0))) -> c18(G(c, g(c, x0)))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))
   G(c, g(c, g(d, g(e, g(c, y0))))) -> c16(G(d, g(d, g(e, g(c, y0)))))
   G(c, g(c, g(d, g(e, y0)))) -> c16(G(d, g(d, g(e, y0))))
   G(c, g(c, g(d, g(e, c)))) -> c16(G(d, g(d, g(e, c))))
   G(d, g(d, g(e, g(c, g(d, y0))))) -> c17(G(e, g(e, g(c, g(d, y0)))))
   G(d, g(d, g(e, g(c, y0)))) -> c17(G(e, g(e, g(c, y0))))
   G(d, g(d, g(e, g(c, d)))) -> c17(G(e, g(e, g(c, d))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_1, c17_1, c18_1, c19_1, c16_2, c17_2, c18_2, c19_4


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

(95) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace G(e, g(e, g(c, x0))) -> c18(G(c, g(c, x0))) by 
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   G(e, g(e, g(c, g(d, g(e, y0))))) -> c18(G(c, g(c, g(d, g(e, y0)))))
   G(e, g(e, g(c, g(d, e)))) -> c18(G(c, g(c, g(d, e))))
   G(e, g(e, g(c, g(d, g(e, g(c, y0)))))) -> c18(G(c, g(c, g(d, g(e, g(c, y0))))))
   G(e, g(e, g(c, g(d, g(e, c))))) -> c18(G(c, g(c, g(d, g(e, c)))))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))
   ENCODE_F(cons_f(cons_g(z0, z1))) -> c1(F(f(g(encArg(z0), encArg(z1)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c1(F(f(f(encArg(z0)))))
   G(c, g(c, g(d, g(e, g(c, y0))))) -> c16(G(d, g(d, g(e, g(c, y0)))))
   G(c, g(c, g(d, g(e, y0)))) -> c16(G(d, g(d, g(e, y0))))
   G(c, g(c, g(d, g(e, c)))) -> c16(G(d, g(d, g(e, c))))
   G(d, g(d, g(e, g(c, g(d, y0))))) -> c17(G(e, g(e, g(c, g(d, y0)))))
   G(d, g(d, g(e, g(c, y0)))) -> c17(G(e, g(e, g(c, y0))))
   G(d, g(d, g(e, g(c, d)))) -> c17(G(e, g(e, g(c, d))))
   G(e, g(e, g(c, g(d, g(e, y0))))) -> c18(G(c, g(c, g(d, g(e, y0)))))
   G(e, g(e, g(c, g(d, e)))) -> c18(G(c, g(c, g(d, e))))
   G(e, g(e, g(c, g(d, g(e, g(c, y0)))))) -> c18(G(c, g(c, g(d, g(e, g(c, y0))))))
   G(e, g(e, g(c, g(d, g(e, c))))) -> c18(G(c, g(c, g(d, g(e, c)))))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))
   G(c, g(c, g(d, g(e, g(c, y0))))) -> c16(G(d, g(d, g(e, g(c, y0)))))
   G(c, g(c, g(d, g(e, y0)))) -> c16(G(d, g(d, g(e, y0))))
   G(c, g(c, g(d, g(e, c)))) -> c16(G(d, g(d, g(e, c))))
   G(d, g(d, g(e, g(c, g(d, y0))))) -> c17(G(e, g(e, g(c, g(d, y0)))))
   G(d, g(d, g(e, g(c, y0)))) -> c17(G(e, g(e, g(c, y0))))
   G(d, g(d, g(e, g(c, d)))) -> c17(G(e, g(e, g(c, d))))
   G(e, g(e, g(c, g(d, g(e, y0))))) -> c18(G(c, g(c, g(d, g(e, y0)))))
   G(e, g(e, g(c, g(d, e)))) -> c18(G(c, g(c, g(d, e))))
   G(e, g(e, g(c, g(d, g(e, g(c, y0)))))) -> c18(G(c, g(c, g(d, g(e, g(c, y0))))))
   G(e, g(e, g(c, g(d, g(e, c))))) -> c18(G(c, g(c, g(d, g(e, c)))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_1, c17_1, c18_1, c19_1, c16_2, c17_2, c18_2, c19_4


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

(97) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace G(c, g(c, g(d, g(e, y0)))) -> c16(G(d, g(d, g(e, y0)))) by 
   G(c, g(c, g(d, g(e, g(c, y0))))) -> c16(G(d, g(d, g(e, g(c, y0)))))
   G(c, g(c, g(d, g(e, c)))) -> c16(G(d, g(d, g(e, c))))
   G(c, g(c, g(d, g(e, g(c, g(d, y0)))))) -> c16(G(d, g(d, g(e, g(c, g(d, y0))))))
   G(c, g(c, g(d, g(e, g(c, d))))) -> c16(G(d, g(d, g(e, g(c, d)))))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))
   ENCODE_F(cons_f(cons_g(z0, z1))) -> c1(F(f(g(encArg(z0), encArg(z1)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c1(F(f(f(encArg(z0)))))
   G(c, g(c, g(d, g(e, g(c, y0))))) -> c16(G(d, g(d, g(e, g(c, y0)))))
   G(c, g(c, g(d, g(e, c)))) -> c16(G(d, g(d, g(e, c))))
   G(d, g(d, g(e, g(c, g(d, y0))))) -> c17(G(e, g(e, g(c, g(d, y0)))))
   G(d, g(d, g(e, g(c, y0)))) -> c17(G(e, g(e, g(c, y0))))
   G(d, g(d, g(e, g(c, d)))) -> c17(G(e, g(e, g(c, d))))
   G(e, g(e, g(c, g(d, g(e, y0))))) -> c18(G(c, g(c, g(d, g(e, y0)))))
   G(e, g(e, g(c, g(d, e)))) -> c18(G(c, g(c, g(d, e))))
   G(e, g(e, g(c, g(d, g(e, g(c, y0)))))) -> c18(G(c, g(c, g(d, g(e, g(c, y0))))))
   G(e, g(e, g(c, g(d, g(e, c))))) -> c18(G(c, g(c, g(d, g(e, c)))))
   G(c, g(c, g(d, g(e, g(c, g(d, y0)))))) -> c16(G(d, g(d, g(e, g(c, g(d, y0))))))
   G(c, g(c, g(d, g(e, g(c, d))))) -> c16(G(d, g(d, g(e, g(c, d)))))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))
   G(c, g(c, g(d, g(e, g(c, y0))))) -> c16(G(d, g(d, g(e, g(c, y0)))))
   G(c, g(c, g(d, g(e, c)))) -> c16(G(d, g(d, g(e, c))))
   G(d, g(d, g(e, g(c, g(d, y0))))) -> c17(G(e, g(e, g(c, g(d, y0)))))
   G(d, g(d, g(e, g(c, y0)))) -> c17(G(e, g(e, g(c, y0))))
   G(d, g(d, g(e, g(c, d)))) -> c17(G(e, g(e, g(c, d))))
   G(e, g(e, g(c, g(d, g(e, y0))))) -> c18(G(c, g(c, g(d, g(e, y0)))))
   G(e, g(e, g(c, g(d, e)))) -> c18(G(c, g(c, g(d, e))))
   G(e, g(e, g(c, g(d, g(e, g(c, y0)))))) -> c18(G(c, g(c, g(d, g(e, g(c, y0))))))
   G(e, g(e, g(c, g(d, g(e, c))))) -> c18(G(c, g(c, g(d, g(e, c)))))
   G(c, g(c, g(d, g(e, g(c, g(d, y0)))))) -> c16(G(d, g(d, g(e, g(c, g(d, y0))))))
   G(c, g(c, g(d, g(e, g(c, d))))) -> c16(G(d, g(d, g(e, g(c, d)))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_1, c17_1, c18_1, c19_1, c16_2, c17_2, c18_2, c19_4


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

(99) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace G(d, g(d, g(e, g(c, y0)))) -> c17(G(e, g(e, g(c, y0)))) by 
   G(d, g(d, g(e, g(c, g(d, y0))))) -> c17(G(e, g(e, g(c, g(d, y0)))))
   G(d, g(d, g(e, g(c, d)))) -> c17(G(e, g(e, g(c, d))))
   G(d, g(d, g(e, g(c, g(d, g(e, y0)))))) -> c17(G(e, g(e, g(c, g(d, g(e, y0))))))
   G(d, g(d, g(e, g(c, g(d, e))))) -> c17(G(e, g(e, g(c, g(d, e)))))
   G(d, g(d, g(e, g(c, g(d, g(e, g(c, y0))))))) -> c17(G(e, g(e, g(c, g(d, g(e, g(c, y0)))))))
   G(d, g(d, g(e, g(c, g(d, g(e, c)))))) -> c17(G(e, g(e, g(c, g(d, g(e, c))))))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(e) -> e
   encArg(d) -> d
   encArg(cons_g(z0, z1)) -> g(encArg(z0), encArg(z1))
   encArg(cons_f(z0)) -> f(encArg(z0))
   g(z0, z0) -> g(a, b)
   g(c, g(c, z0)) -> g(e, g(d, z0))
   g(d, g(d, z0)) -> g(c, g(e, z0))
   g(e, g(e, z0)) -> g(d, g(c, z0))
   f(g(z0, z1)) -> g(z1, g(f(f(z0)), a))
Tuples:
   ENCARG(cons_g(z0, z1)) -> c6(G(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   G(z0, z0) -> c15
   ENCODE_G(z0, z1) -> c1(G(encArg(z0), encArg(z1)))
   ENCARG(cons_f(cons_g(z0, z1))) -> c7(F(g(encArg(z0), encArg(z1))), ENCARG(cons_g(z0, z1)))
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   ENCODE_F(cons_g(z0, z1)) -> c1(F(g(encArg(z0), encArg(z1))))
   ENCARG(cons_f(cons_f(cons_g(z0, z1)))) -> c7(F(f(g(encArg(z0), encArg(z1)))), ENCARG(cons_f(cons_g(z0, z1))))
   ENCARG(cons_f(cons_f(cons_f(z0)))) -> c7(F(f(f(encArg(z0)))), ENCARG(cons_f(cons_f(z0))))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))
   ENCODE_F(cons_f(cons_g(z0, z1))) -> c1(F(f(g(encArg(z0), encArg(z1)))))
   ENCODE_F(cons_f(cons_f(z0))) -> c1(F(f(f(encArg(z0)))))
   G(c, g(c, g(d, g(e, g(c, y0))))) -> c16(G(d, g(d, g(e, g(c, y0)))))
   G(c, g(c, g(d, g(e, c)))) -> c16(G(d, g(d, g(e, c))))
   G(d, g(d, g(e, g(c, g(d, y0))))) -> c17(G(e, g(e, g(c, g(d, y0)))))
   G(d, g(d, g(e, g(c, d)))) -> c17(G(e, g(e, g(c, d))))
   G(e, g(e, g(c, g(d, g(e, y0))))) -> c18(G(c, g(c, g(d, g(e, y0)))))
   G(e, g(e, g(c, g(d, e)))) -> c18(G(c, g(c, g(d, e))))
   G(e, g(e, g(c, g(d, g(e, g(c, y0)))))) -> c18(G(c, g(c, g(d, g(e, g(c, y0))))))
   G(e, g(e, g(c, g(d, g(e, c))))) -> c18(G(c, g(c, g(d, g(e, c)))))
   G(c, g(c, g(d, g(e, g(c, g(d, y0)))))) -> c16(G(d, g(d, g(e, g(c, g(d, y0))))))
   G(c, g(c, g(d, g(e, g(c, d))))) -> c16(G(d, g(d, g(e, g(c, d)))))
   G(d, g(d, g(e, g(c, g(d, g(e, y0)))))) -> c17(G(e, g(e, g(c, g(d, g(e, y0))))))
   G(d, g(d, g(e, g(c, g(d, e))))) -> c17(G(e, g(e, g(c, g(d, e)))))
   G(d, g(d, g(e, g(c, g(d, g(e, g(c, y0))))))) -> c17(G(e, g(e, g(c, g(d, g(e, g(c, y0)))))))
   G(d, g(d, g(e, g(c, g(d, g(e, c)))))) -> c17(G(e, g(e, g(c, g(d, g(e, c))))))
S tuples:
   G(z0, z0) -> c15
   G(c, g(c, d)) -> c16(G(d, d))
   G(d, g(d, e)) -> c17(G(e, e))
   G(e, g(e, c)) -> c18(G(c, c))
   F(g(x0, x1)) -> c19(G(x1, g(f(f(x0)), a)))
   G(c, g(c, g(d, g(e, z0)))) -> c16(G(e, g(c, g(d, g(c, z0)))), G(d, g(d, g(e, z0))))
   G(c, g(c, g(d, e))) -> c16(G(d, g(d, e)))
   G(d, g(d, g(e, g(c, z0)))) -> c17(G(c, g(d, g(e, g(d, z0)))), G(e, g(e, g(c, z0))))
   G(d, g(d, g(e, c))) -> c17(G(e, g(e, c)))
   G(e, g(e, g(c, g(d, z0)))) -> c18(G(d, g(e, g(c, g(e, z0)))), G(c, g(c, g(d, z0))))
   G(e, g(e, g(c, d))) -> c18(G(c, g(c, d)))
   F(g(g(z0, z1), x2)) -> c19(G(x2, g(f(g(z1, g(f(f(z0)), a))), a)), G(f(g(z1, g(f(f(z0)), a))), a), F(f(g(z0, z1))), F(g(z0, z1)))
   F(g(g(x0, x1), x2)) -> c19(G(f(g(x1, g(f(f(x0)), a))), a))
   G(c, g(c, g(d, g(e, g(c, y0))))) -> c16(G(d, g(d, g(e, g(c, y0)))))
   G(c, g(c, g(d, g(e, c)))) -> c16(G(d, g(d, g(e, c))))
   G(d, g(d, g(e, g(c, g(d, y0))))) -> c17(G(e, g(e, g(c, g(d, y0)))))
   G(d, g(d, g(e, g(c, d)))) -> c17(G(e, g(e, g(c, d))))
   G(e, g(e, g(c, g(d, g(e, y0))))) -> c18(G(c, g(c, g(d, g(e, y0)))))
   G(e, g(e, g(c, g(d, e)))) -> c18(G(c, g(c, g(d, e))))
   G(e, g(e, g(c, g(d, g(e, g(c, y0)))))) -> c18(G(c, g(c, g(d, g(e, g(c, y0))))))
   G(e, g(e, g(c, g(d, g(e, c))))) -> c18(G(c, g(c, g(d, g(e, c)))))
   G(c, g(c, g(d, g(e, g(c, g(d, y0)))))) -> c16(G(d, g(d, g(e, g(c, g(d, y0))))))
   G(c, g(c, g(d, g(e, g(c, d))))) -> c16(G(d, g(d, g(e, g(c, d)))))
   G(d, g(d, g(e, g(c, g(d, g(e, y0)))))) -> c17(G(e, g(e, g(c, g(d, g(e, y0))))))
   G(d, g(d, g(e, g(c, g(d, e))))) -> c17(G(e, g(e, g(c, g(d, e)))))
   G(d, g(d, g(e, g(c, g(d, g(e, g(c, y0))))))) -> c17(G(e, g(e, g(c, g(d, g(e, g(c, y0)))))))
   G(d, g(d, g(e, g(c, g(d, g(e, c)))))) -> c17(G(e, g(e, g(c, g(d, g(e, c))))))
K tuples:none
Defined Rule Symbols:   encArg_1, g_2, f_1

Defined Pair Symbols:   ENCARG_1, G_2, ENCODE_G_2, F_1, ENCODE_F_1

Compound Symbols:   c6_3, c15, c1_1, c7_2, c16_1, c17_1, c18_1, c19_1, c16_2, c17_2, c18_2, c19_4