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


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 141 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 0 ms]
    (10) typed CpxTrs
    (11) RewriteLemmaProof [LOWER BOUND(ID), 747 ms]
    (12) BOUNDS(1, INF)
(13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(14) TRS for Loop Detection
(15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(16) CpxTRS
(17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(18) CpxRelTRS
    (19) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxRelTRS
    (21) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (28) CpxRNTS
        (29) CompletionProof [UPPER BOUND(ID), 0 ms]
        (30) CpxTypedWeightedCompleteTrs
            (31) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
            (32) CpxTypedWeightedCompleteTrs
            (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (34) CpxRNTS
            (35) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [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), 5 ms]
        (48) CdtProblem
        (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms]
        (58) CdtProblem
        (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (60) CdtProblem
        (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms]
        (62) CdtProblem
        (63) CdtRhsSimplificationProcessorProof [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), 0 ms]
        (70) CdtProblem
        (71) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (72) CdtProblem
        (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms]
        (74) CdtProblem
        (75) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (76) CdtProblem
        (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (78) CdtProblem
        (79) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (80) CdtProblem
        (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (82) CdtProblem
        (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (84) CdtProblem
        (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (86) CdtProblem
        (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (88) CdtProblem
        (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (90) CdtProblem
        (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (92) CdtProblem
        (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (94) CdtProblem
        (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (96) CdtProblem
        (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (98) CdtProblem
        (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (100) CdtProblem
        (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (102) CdtProblem
        (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (104) CdtProblem
        (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (106) CdtProblem
        (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (108) CdtProblem
        (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (110) CdtProblem
        (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (112) CdtProblem
        (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (114) CdtProblem
        (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (116) CdtProblem
        (117) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (118) CdtProblem
        (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (120) CdtProblem
        (121) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (122) CdtProblem
        (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (124) CdtProblem
        (125) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (126) CdtProblem
        (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (128) CdtProblem
        (129) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 20 ms]
        (130) CdtProblem
        (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (132) CdtProblem
        (133) CdtRewritingProof [BOTH BOUNDS(ID, ID), 22 ms]
        (134) CdtProblem
        (135) CdtRewritingProof [BOTH BOUNDS(ID, ID), 32 ms]
        (136) CdtProblem
        (137) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 106 ms]
        (138) CdtProblem
        (139) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 427 ms]
        (140) CdtProblem
        (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (142) CdtProblem
        (143) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1551 ms]
        (144) CdtProblem
        (145) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 2829 ms]
        (146) CdtProblem


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

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


The TRS R consists of the following rules:

   f(f(f(a, b), c), x) -> f(b, f(a, f(c, f(b, x))))
   f(x, f(y, z)) -> f(f(x, y), z)

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

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

   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a
   encode_b -> b
   encode_c -> c


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

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


The TRS R consists of the following rules:

   f(f(f(a, b), c), x) -> f(b, f(a, f(c, f(b, x))))
   f(x, f(y, z)) -> f(f(x, y), z)

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

   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a
   encode_b -> b
   encode_c -> c

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

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

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


The TRS R consists of the following rules:

   f(f(f(a, b), c), x) -> f(b, f(a, f(c, f(b, x))))
   f(x, f(y, z)) -> f(f(x, y), z)

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

   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a
   encode_b -> b
   encode_c -> c

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

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

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


The TRS R consists of the following rules:

   f(f(f(a, b), c), x) -> f(b, f(a, f(c, f(b, x))))
   f(x, f(y, z)) -> f(f(x, y), z)

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

   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a
   encode_b -> b
   encode_c -> c

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

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

(8)
Obligation:
TRS:
Rules:
f(f(f(a, b), c), x) -> f(b, f(a, f(c, f(b, x))))
f(x, f(y, z)) -> f(f(x, y), z)
encArg(a) -> a
encArg(b) -> b
encArg(c) -> c
encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
encode_a -> a
encode_b -> b
encode_c -> c

Types:
f :: a:b:c:cons_f -> a:b:c:cons_f -> a:b:c:cons_f
a :: a:b:c:cons_f
b :: a:b:c:cons_f
c :: a:b:c:cons_f
encArg :: a:b:c:cons_f -> a:b:c:cons_f
cons_f :: a:b:c:cons_f -> a:b:c:cons_f -> a:b:c:cons_f
encode_f :: a:b:c:cons_f -> a:b:c:cons_f -> a:b:c:cons_f
encode_a :: a:b:c:cons_f
encode_b :: a:b:c:cons_f
encode_c :: a:b:c:cons_f
hole_a:b:c:cons_f1_0 :: a:b:c:cons_f
gen_a:b:c:cons_f2_0 :: Nat -> a:b:c:cons_f

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

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

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

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

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

Types:
f :: a:b:c:cons_f -> a:b:c:cons_f -> a:b:c:cons_f
a :: a:b:c:cons_f
b :: a:b:c:cons_f
c :: a:b:c:cons_f
encArg :: a:b:c:cons_f -> a:b:c:cons_f
cons_f :: a:b:c:cons_f -> a:b:c:cons_f -> a:b:c:cons_f
encode_f :: a:b:c:cons_f -> a:b:c:cons_f -> a:b:c:cons_f
encode_a :: a:b:c:cons_f
encode_b :: a:b:c:cons_f
encode_c :: a:b:c:cons_f
hole_a:b:c:cons_f1_0 :: a:b:c:cons_f
gen_a:b:c:cons_f2_0 :: Nat -> a:b:c:cons_f


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


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

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

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

(11) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_a:b:c:cons_f2_0(n15_0)) -> *3_0, rt in Omega(0)

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

Induction Step:
encArg(gen_a:b:c:cons_f2_0(+(n15_0, 1))) ->_R^Omega(0)
f(encArg(a), encArg(gen_a:b:c:cons_f2_0(n15_0))) ->_R^Omega(0)
f(a, encArg(gen_a:b:c:cons_f2_0(n15_0))) ->_IH
f(a, *3_0)

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

(12)
BOUNDS(1, INF)

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

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

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

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


The TRS R consists of the following rules:

   f(f(f(a, b), c), x) -> f(b, f(a, f(c, f(b, x))))
   f(x, f(y, z)) -> f(f(x, y), z)

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

   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a
   encode_b -> b
   encode_c -> c

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

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

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


The TRS R consists of the following rules:

   f(f(f(a, b), c), x) -> f(b, f(a, f(c, f(b, x))))
   f(x, f(y, z)) -> f(f(x, y), z)
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2))
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2))
   encode_a -> a
   encode_b -> b
   encode_c -> c

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

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

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


The TRS R consists of the following rules:

   f(x, c_f(y, z)) -> f(f(x, y), z)
   f(c_f(c_f(a, b), c), x) -> f(b, f(a, f(c, f(b, x))))

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

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

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

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

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

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


The TRS R consists of the following rules:

   f(x, c_f(y, z)) -> f(f(x, y), z)
   f(c_f(c_f(a, b), c), x) -> f(b, f(a, f(c, f(b, x))))

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

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

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

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

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


The TRS R consists of the following rules:

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

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

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

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

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

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

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

(25) CompletionProof (UPPER BOUND(ID))
The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:

   encArg(v0) -> null_encArg [0]
   encode_f(v0, v1) -> null_encode_f [0]
   encode_a -> null_encode_a [0]
   encode_b -> null_encode_b [0]
   encode_c -> null_encode_c [0]
   f(v0, v1) -> null_f [0]

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

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

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

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

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

The TRS has the following type information:
f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
c_f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
a :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
b :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
c :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
encArg :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
cons_f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
encode_f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
encode_a :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
encode_b :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
encode_c :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_encArg :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_encode_f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_encode_a :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_encode_b :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_encode_c :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c: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
   c => 2
   null_encArg => 0
   null_encode_f => 0
   null_encode_a => 0
   null_encode_b => 0
   null_encode_c => 0
   null_f => 0

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

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

   encArg(z') -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2
   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_f(z', z'') -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z' = x_1, x_2 >= 0, z'' = x_2
   encode_f(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0
   f(z', z'') -{ 1 }-> f(f(x, y), z) :|: z >= 0, z' = x, x >= 0, y >= 0, z'' = 1 + y + z
   f(z', z'') -{ 1 }-> f(1, f(0, f(2, f(1, x)))) :|: z' = 1 + (1 + 0 + 1) + 2, x >= 0, z'' = x
   f(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0
   f(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = x1, x0 >= 0, x1 >= 0, z' = x0

Only complete derivations are relevant for the runtime complexity.

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

(29) CompletionProof (UPPER BOUND(ID))
The transformation into a RNTS is sound, since:

(a) The obligation is a constructor system where every type has a constant constructor,

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:
none

(c) The following functions are completely defined:

   encArg_1
   encode_f_2
   encode_a
   encode_b
   encode_c
   f_2

Due to the following rules being added:

   encArg(v0) -> null_encArg [0]
   encode_f(v0, v1) -> null_encode_f [0]
   encode_a -> null_encode_a [0]
   encode_b -> null_encode_b [0]
   encode_c -> null_encode_c [0]
   f(v0, v1) -> null_f [0]

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

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

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

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

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

The TRS has the following type information:
f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
c_f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
a :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
b :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
c :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
encArg :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
cons_f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
encode_f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
encode_a :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
encode_b :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
encode_c :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_encArg :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_encode_f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_encode_a :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_encode_b :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_encode_c :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f

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

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

(32)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   f(x, c_f(c_f(y', z'), z)) -> f(f(f(x, y'), z'), z) [2]
   f(c_f(c_f(a, b), c), c_f(y, z)) -> f(f(b, f(a, f(c, f(b, y)))), z) [2]
   f(x, c_f(y, z)) -> f(c_f(x, y), z) [1]
   f(x, c_f(y, z)) -> f(null_f, z) [1]
   f(c_f(c_f(a, b), c), c_f(y'', z'')) -> f(b, f(a, f(c, f(f(b, y''), z'')))) [2]
   f(c_f(c_f(a, b), c), x) -> f(b, f(a, f(c, c_f(b, x)))) [1]
   f(c_f(c_f(a, b), c), x) -> f(b, f(a, f(c, null_f))) [1]
   encArg(a) -> a [0]
   encArg(b) -> b [0]
   encArg(c) -> c [0]
   encArg(cons_f(x_1, x_2)) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_f(x_1, x_2) -> f(encArg(x_1), encArg(x_2)) [0]
   encode_a -> a [0]
   encode_b -> b [0]
   encode_c -> c [0]
   f(x0, x1) -> c_f(x0, x1) [0]
   encArg(v0) -> null_encArg [0]
   encode_f(v0, v1) -> null_encode_f [0]
   encode_a -> null_encode_a [0]
   encode_b -> null_encode_b [0]
   encode_c -> null_encode_c [0]
   f(v0, v1) -> null_f [0]

The TRS has the following type information:
f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
c_f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
a :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
b :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
c :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
encArg :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
cons_f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
encode_f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f -> c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
encode_a :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
encode_b :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
encode_c :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_encArg :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_encode_f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_encode_a :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_encode_b :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_encode_c :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c:null_f
null_f :: c_f:a:b:c:cons_f:null_encArg:null_encode_f:null_encode_a:null_encode_b:null_encode_c: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
   c => 2
   null_encArg => 0
   null_encode_f => 0
   null_encode_a => 0
   null_encode_b => 0
   null_encode_c => 0
   null_f => 0

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

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

   encArg(z1) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z1 = 1 + x_1 + x_2, x_2 >= 0
   encArg(z1) -{ 0 }-> 2 :|: z1 = 2
   encArg(z1) -{ 0 }-> 1 :|: z1 = 1
   encArg(z1) -{ 0 }-> 0 :|: z1 = 0
   encArg(z1) -{ 0 }-> 0 :|: z1 = v0, v0 >= 0
   encode_a -{ 0 }-> 0 :|: 
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_c -{ 0 }-> 2 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z1, z2) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z1 = x_1, z2 = x_2, x_2 >= 0
   encode_f(z1, z2) -{ 0 }-> 0 :|: z1 = v0, v0 >= 0, z2 = v1, v1 >= 0
   f(z1, z2) -{ 2 }-> f(f(f(x, y'), z'), z) :|: z >= 0, x >= 0, z' >= 0, y' >= 0, z2 = 1 + (1 + y' + z') + z, z1 = x
   f(z1, z2) -{ 2 }-> f(f(1, f(0, f(2, f(1, y)))), z) :|: z2 = 1 + y + z, z >= 0, y >= 0, z1 = 1 + (1 + 0 + 1) + 2
   f(z1, z2) -{ 2 }-> f(1, f(0, f(2, f(f(1, y''), z'')))) :|: z2 = 1 + y'' + z'', z'' >= 0, z1 = 1 + (1 + 0 + 1) + 2, y'' >= 0
   f(z1, z2) -{ 1 }-> f(1, f(0, f(2, 0))) :|: z2 = x, x >= 0, z1 = 1 + (1 + 0 + 1) + 2
   f(z1, z2) -{ 1 }-> f(1, f(0, f(2, 1 + 1 + x))) :|: z2 = x, x >= 0, z1 = 1 + (1 + 0 + 1) + 2
   f(z1, z2) -{ 1 }-> f(0, z) :|: z2 = 1 + y + z, z >= 0, x >= 0, y >= 0, z1 = x
   f(z1, z2) -{ 1 }-> f(1 + x + y, z) :|: z2 = 1 + y + z, z >= 0, x >= 0, y >= 0, z1 = x
   f(z1, z2) -{ 0 }-> 0 :|: z1 = v0, v0 >= 0, z2 = v1, v1 >= 0
   f(z1, z2) -{ 0 }-> 1 + x0 + x1 :|: z1 = x0, x0 >= 0, x1 >= 0, z2 = x1


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

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

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

   encArg(z1) -{ 0 }-> f(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z1 = 1 + x_1 + x_2, x_2 >= 0
   encArg(z1) -{ 0 }-> 2 :|: z1 = 2
   encArg(z1) -{ 0 }-> 1 :|: z1 = 1
   encArg(z1) -{ 0 }-> 0 :|: z1 = 0
   encArg(z1) -{ 0 }-> 0 :|: z1 >= 0
   encode_a -{ 0 }-> 0 :|: 
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_c -{ 0 }-> 2 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z1, z2) -{ 0 }-> f(encArg(z1), encArg(z2)) :|: z1 >= 0, z2 >= 0
   encode_f(z1, z2) -{ 0 }-> 0 :|: z1 >= 0, z2 >= 0
   f(z1, z2) -{ 2 }-> f(f(f(z1, y'), z'), z) :|: z >= 0, z1 >= 0, z' >= 0, y' >= 0, z2 = 1 + (1 + y' + z') + z
   f(z1, z2) -{ 2 }-> f(f(1, f(0, f(2, f(1, y)))), z) :|: z2 = 1 + y + z, z >= 0, y >= 0, z1 = 1 + (1 + 0 + 1) + 2
   f(z1, z2) -{ 2 }-> f(1, f(0, f(2, f(f(1, y''), z'')))) :|: z2 = 1 + y'' + z'', z'' >= 0, z1 = 1 + (1 + 0 + 1) + 2, y'' >= 0
   f(z1, z2) -{ 1 }-> f(1, f(0, f(2, 0))) :|: z2 >= 0, z1 = 1 + (1 + 0 + 1) + 2
   f(z1, z2) -{ 1 }-> f(1, f(0, f(2, 1 + 1 + z2))) :|: z2 >= 0, z1 = 1 + (1 + 0 + 1) + 2
   f(z1, z2) -{ 1 }-> f(0, z) :|: z2 = 1 + y + z, z >= 0, z1 >= 0, y >= 0
   f(z1, z2) -{ 1 }-> f(1 + z1 + y, z) :|: z2 = 1 + y + z, z >= 0, z1 >= 0, y >= 0
   f(z1, z2) -{ 0 }-> 0 :|: z1 >= 0, z2 >= 0
   f(z1, z2) -{ 0 }-> 1 + z1 + z2 :|: z1 >= 0, z2 >= 0


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

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   encode_f(z0, z1) -> f(encArg(z0), encArg(z1))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(a) -> c1
   ENCARG(b) -> c2
   ENCARG(c) -> c3
   ENCARG(cons_f(z0, z1)) -> c4(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_F(z0, z1) -> c5(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_A -> c6
   ENCODE_B -> c7
   ENCODE_C -> c8
   F(z0, z1) -> c9
   F(z0, c_f(z1, z2)) -> c10(F(f(z0, z1), z2), F(z0, z1))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
S tuples:
   F(z0, c_f(z1, z2)) -> c10(F(f(z0, z1), z2), F(z0, z1))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
K tuples:none
Defined Rule Symbols:   f_2, encArg_1, encode_f_2, encode_a, encode_b, encode_c

Defined Pair Symbols:   ENCARG_1, ENCODE_F_2, ENCODE_A, ENCODE_B, ENCODE_C, F_2

Compound Symbols:   c1, c2, c3, c4_3, c5_3, c6, c7, c8, c9, c10_2, c11_4


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

(39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 7 trailing nodes:
   ENCODE_A -> c6
   ENCODE_B -> c7
   ENCARG(c) -> c3
   ENCARG(b) -> c2
   ENCODE_C -> c8
   ENCARG(a) -> c1
   F(z0, z1) -> c9

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   encode_f(z0, z1) -> f(encArg(z0), encArg(z1))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(z0, z1)) -> c4(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   ENCODE_F(z0, z1) -> c5(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   F(z0, c_f(z1, z2)) -> c10(F(f(z0, z1), z2), F(z0, z1))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
S tuples:
   F(z0, c_f(z1, z2)) -> c10(F(f(z0, z1), z2), F(z0, z1))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
K tuples:none
Defined Rule Symbols:   f_2, encArg_1, encode_f_2, encode_a, encode_b, encode_c

Defined Pair Symbols:   ENCARG_1, ENCODE_F_2, F_2

Compound Symbols:   c4_3, c5_3, c10_2, c11_4


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

(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(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   encode_f(z0, z1) -> f(encArg(z0), encArg(z1))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(z0, z1)) -> c4(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   F(z0, c_f(z1, z2)) -> c10(F(f(z0, z1), z2), F(z0, z1))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   ENCODE_F(z0, z1) -> c1(F(encArg(z0), encArg(z1)))
   ENCODE_F(z0, z1) -> c1(ENCARG(z0))
   ENCODE_F(z0, z1) -> c1(ENCARG(z1))
S tuples:
   F(z0, c_f(z1, z2)) -> c10(F(f(z0, z1), z2), F(z0, z1))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
K tuples:none
Defined Rule Symbols:   f_2, encArg_1, encode_f_2, encode_a, encode_b, encode_c

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_3, c10_2, c11_4, c1_1


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

(43) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 2 leading nodes:
   ENCODE_F(z0, z1) -> c1(ENCARG(z0))
   ENCODE_F(z0, z1) -> c1(ENCARG(z1))

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   encode_f(z0, z1) -> f(encArg(z0), encArg(z1))
   encode_a -> a
   encode_b -> b
   encode_c -> c
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(z0, z1)) -> c4(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   F(z0, c_f(z1, z2)) -> c10(F(f(z0, z1), z2), F(z0, z1))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   ENCODE_F(z0, z1) -> c1(F(encArg(z0), encArg(z1)))
S tuples:
   F(z0, c_f(z1, z2)) -> c10(F(f(z0, z1), z2), F(z0, z1))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
K tuples:none
Defined Rule Symbols:   f_2, encArg_1, encode_f_2, encode_a, encode_b, encode_c

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_3, c10_2, c11_4, c1_1


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

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

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(z0, z1)) -> c4(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1))
   F(z0, c_f(z1, z2)) -> c10(F(f(z0, z1), z2), F(z0, z1))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   ENCODE_F(z0, z1) -> c1(F(encArg(z0), encArg(z1)))
S tuples:
   F(z0, c_f(z1, z2)) -> c10(F(f(z0, z1), z2), F(z0, z1))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_3, c10_2, c11_4, c1_1


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

(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(z0, z1)) -> c4(F(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by 
   ENCARG(cons_f(x0, a)) -> c4(F(encArg(x0), a), ENCARG(x0), ENCARG(a))
   ENCARG(cons_f(x0, b)) -> c4(F(encArg(x0), b), ENCARG(x0), ENCARG(b))
   ENCARG(cons_f(x0, c)) -> c4(F(encArg(x0), c), ENCARG(x0), ENCARG(c))
   ENCARG(cons_f(x0, cons_f(z0, z1))) -> c4(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1)))
   ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(a), ENCARG(x1))
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(b), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(c), ENCARG(x1))
   ENCARG(cons_f(cons_f(z0, z1), x1)) -> c4(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, z2)) -> c10(F(f(z0, z1), z2), F(z0, z1))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   ENCODE_F(z0, z1) -> c1(F(encArg(z0), encArg(z1)))
   ENCARG(cons_f(x0, a)) -> c4(F(encArg(x0), a), ENCARG(x0), ENCARG(a))
   ENCARG(cons_f(x0, b)) -> c4(F(encArg(x0), b), ENCARG(x0), ENCARG(b))
   ENCARG(cons_f(x0, c)) -> c4(F(encArg(x0), c), ENCARG(x0), ENCARG(c))
   ENCARG(cons_f(x0, cons_f(z0, z1))) -> c4(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1)))
   ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(a), ENCARG(x1))
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(b), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(c), ENCARG(x1))
   ENCARG(cons_f(cons_f(z0, z1), x1)) -> c4(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1))
S tuples:
   F(z0, c_f(z1, z2)) -> c10(F(f(z0, z1), z2), F(z0, z1))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c11_4, c1_1, c4_3


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

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, z2)) -> c10(F(f(z0, z1), z2), F(z0, z1))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   ENCODE_F(z0, z1) -> c1(F(encArg(z0), encArg(z1)))
   ENCARG(cons_f(x0, cons_f(z0, z1))) -> c4(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1)))
   ENCARG(cons_f(cons_f(z0, z1), x1)) -> c4(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1))
   ENCARG(cons_f(x0, a)) -> c4(F(encArg(x0), a), ENCARG(x0))
   ENCARG(cons_f(x0, b)) -> c4(F(encArg(x0), b), ENCARG(x0))
   ENCARG(cons_f(x0, c)) -> c4(F(encArg(x0), c), ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
S tuples:
   F(z0, c_f(z1, z2)) -> c10(F(f(z0, z1), z2), F(z0, z1))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c11_4, c1_1, c4_3, c4_2


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(z0, c_f(z1, z2)) -> c10(F(f(z0, z1), z2), F(z0, z1)) by 
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   ENCODE_F(z0, z1) -> c1(F(encArg(z0), encArg(z1)))
   ENCARG(cons_f(x0, cons_f(z0, z1))) -> c4(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1)))
   ENCARG(cons_f(cons_f(z0, z1), x1)) -> c4(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1))
   ENCARG(cons_f(x0, a)) -> c4(F(encArg(x0), a), ENCARG(x0))
   ENCARG(cons_f(x0, b)) -> c4(F(encArg(x0), b), ENCARG(x0))
   ENCARG(cons_f(x0, c)) -> c4(F(encArg(x0), c), ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
S tuples:
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c11_4, c1_1, c4_3, c4_2, c10_2


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

(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c, f(b, z0)))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0)) by 
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCODE_F(z0, z1) -> c1(F(encArg(z0), encArg(z1)))
   ENCARG(cons_f(x0, cons_f(z0, z1))) -> c4(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1)))
   ENCARG(cons_f(cons_f(z0, z1), x1)) -> c4(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1))
   ENCARG(cons_f(x0, a)) -> c4(F(encArg(x0), a), ENCARG(x0))
   ENCARG(cons_f(x0, b)) -> c4(F(encArg(x0), b), ENCARG(x0))
   ENCARG(cons_f(x0, c)) -> c4(F(encArg(x0), c), ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCODE_F_2, ENCARG_1, F_2

Compound Symbols:   c1_1, c4_3, c4_2, c10_2, c11_4


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

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

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(x0, cons_f(z0, z1))) -> c4(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1)))
   ENCARG(cons_f(cons_f(z0, z1), x1)) -> c4(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1))
   ENCARG(cons_f(x0, a)) -> c4(F(encArg(x0), a), ENCARG(x0))
   ENCARG(cons_f(x0, b)) -> c4(F(encArg(x0), b), ENCARG(x0))
   ENCARG(cons_f(x0, c)) -> c4(F(encArg(x0), c), ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_3, c4_2, c10_2, c11_4, c1_1


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

(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(x0, cons_f(z0, z1))) -> c4(F(encArg(x0), f(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_f(z0, z1))) by 
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(a), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(b), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(c), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(cons_f(z0, z1), x1)) -> c4(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1))
   ENCARG(cons_f(x0, a)) -> c4(F(encArg(x0), a), ENCARG(x0))
   ENCARG(cons_f(x0, b)) -> c4(F(encArg(x0), b), ENCARG(x0))
   ENCARG(cons_f(x0, c)) -> c4(F(encArg(x0), c), ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(a), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(b), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(c), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_3, c4_2, c10_2, c11_4, c1_1


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

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(cons_f(z0, z1), x1)) -> c4(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1))
   ENCARG(cons_f(x0, a)) -> c4(F(encArg(x0), a), ENCARG(x0))
   ENCARG(cons_f(x0, b)) -> c4(F(encArg(x0), b), ENCARG(x0))
   ENCARG(cons_f(x0, c)) -> c4(F(encArg(x0), c), ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_3, c4_2, c10_2, c11_4, c1_1


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

(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(cons_f(z0, z1), x1)) -> c4(F(f(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_f(z0, z1)), ENCARG(x1)) by 
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)), ENCARG(a))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)), ENCARG(b))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)), ENCARG(c))
   ENCARG(cons_f(cons_f(x0, x1), cons_f(z0, z1))) -> c4(F(f(encArg(x0), encArg(x1)), f(encArg(z0), encArg(z1))), ENCARG(cons_f(x0, x1)), ENCARG(cons_f(z0, z1)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(x0, a)) -> c4(F(encArg(x0), a), ENCARG(x0))
   ENCARG(cons_f(x0, b)) -> c4(F(encArg(x0), b), ENCARG(x0))
   ENCARG(cons_f(x0, c)) -> c4(F(encArg(x0), c), ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)), ENCARG(a))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)), ENCARG(b))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)), ENCARG(c))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_2, c10_2, c11_4, c1_1, c4_3


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

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(x0, a)) -> c4(F(encArg(x0), a), ENCARG(x0))
   ENCARG(cons_f(x0, b)) -> c4(F(encArg(x0), b), ENCARG(x0))
   ENCARG(cons_f(x0, c)) -> c4(F(encArg(x0), c), ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_2, c10_2, c11_4, c1_1, c4_3


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

(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(x0, a)) -> c4(F(encArg(x0), a), ENCARG(x0)) by 
   ENCARG(cons_f(a, a)) -> c4(F(a, a), ENCARG(a))
   ENCARG(cons_f(b, a)) -> c4(F(b, a), ENCARG(b))
   ENCARG(cons_f(c, a)) -> c4(F(c, a), ENCARG(c))
   ENCARG(cons_f(cons_f(z0, z1), a)) -> c4(F(f(encArg(z0), encArg(z1)), a), ENCARG(cons_f(z0, z1)))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(x0, b)) -> c4(F(encArg(x0), b), ENCARG(x0))
   ENCARG(cons_f(x0, c)) -> c4(F(encArg(x0), c), ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(a, a)) -> c4(F(a, a), ENCARG(a))
   ENCARG(cons_f(b, a)) -> c4(F(b, a), ENCARG(b))
   ENCARG(cons_f(c, a)) -> c4(F(c, a), ENCARG(c))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_2, c10_2, c11_4, c1_1, c4_3


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

(67) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   ENCARG(cons_f(b, a)) -> c4(F(b, a), ENCARG(b))
   ENCARG(cons_f(a, a)) -> c4(F(a, a), ENCARG(a))
   ENCARG(cons_f(c, a)) -> c4(F(c, a), ENCARG(c))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(x0, b)) -> c4(F(encArg(x0), b), ENCARG(x0))
   ENCARG(cons_f(x0, c)) -> c4(F(encArg(x0), c), ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_2, c10_2, c11_4, c1_1, c4_3


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

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(x0, b)) -> c4(F(encArg(x0), b), ENCARG(x0)) by 
   ENCARG(cons_f(a, b)) -> c4(F(a, b), ENCARG(a))
   ENCARG(cons_f(b, b)) -> c4(F(b, b), ENCARG(b))
   ENCARG(cons_f(c, b)) -> c4(F(c, b), ENCARG(c))
   ENCARG(cons_f(cons_f(z0, z1), b)) -> c4(F(f(encArg(z0), encArg(z1)), b), ENCARG(cons_f(z0, z1)))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(x0, c)) -> c4(F(encArg(x0), c), ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(a, b)) -> c4(F(a, b), ENCARG(a))
   ENCARG(cons_f(b, b)) -> c4(F(b, b), ENCARG(b))
   ENCARG(cons_f(c, b)) -> c4(F(c, b), ENCARG(c))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_2, c10_2, c11_4, c1_1, c4_3


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

(71) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   ENCARG(cons_f(a, b)) -> c4(F(a, b), ENCARG(a))
   ENCARG(cons_f(b, b)) -> c4(F(b, b), ENCARG(b))
   ENCARG(cons_f(c, b)) -> c4(F(c, b), ENCARG(c))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(x0, c)) -> c4(F(encArg(x0), c), ENCARG(x0))
   ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_2, c10_2, c11_4, c1_1, c4_3


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

(73) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(x0, c)) -> c4(F(encArg(x0), c), ENCARG(x0)) by 
   ENCARG(cons_f(a, c)) -> c4(F(a, c), ENCARG(a))
   ENCARG(cons_f(b, c)) -> c4(F(b, c), ENCARG(b))
   ENCARG(cons_f(c, c)) -> c4(F(c, c), ENCARG(c))
   ENCARG(cons_f(cons_f(z0, z1), c)) -> c4(F(f(encArg(z0), encArg(z1)), c), ENCARG(cons_f(z0, z1)))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(a, c)) -> c4(F(a, c), ENCARG(a))
   ENCARG(cons_f(b, c)) -> c4(F(b, c), ENCARG(b))
   ENCARG(cons_f(c, c)) -> c4(F(c, c), ENCARG(c))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_2, c10_2, c11_4, c1_1, c4_3


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

(75) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   ENCARG(cons_f(b, c)) -> c4(F(b, c), ENCARG(b))
   ENCARG(cons_f(a, c)) -> c4(F(a, c), ENCARG(a))
   ENCARG(cons_f(c, c)) -> c4(F(c, c), ENCARG(c))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_2, c10_2, c11_4, c1_1, c4_3


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

(77) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(a, x1)) -> c4(F(a, encArg(x1)), ENCARG(x1)) by 
   ENCARG(cons_f(a, a)) -> c4(F(a, a), ENCARG(a))
   ENCARG(cons_f(a, b)) -> c4(F(a, b), ENCARG(b))
   ENCARG(cons_f(a, c)) -> c4(F(a, c), ENCARG(c))
   ENCARG(cons_f(a, cons_f(z0, z1))) -> c4(F(a, f(encArg(z0), encArg(z1))), ENCARG(cons_f(z0, z1)))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(a, a)) -> c4(F(a, a), ENCARG(a))
   ENCARG(cons_f(a, b)) -> c4(F(a, b), ENCARG(b))
   ENCARG(cons_f(a, c)) -> c4(F(a, c), ENCARG(c))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_2, c10_2, c11_4, c1_1, c4_3


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

(79) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   ENCARG(cons_f(a, b)) -> c4(F(a, b), ENCARG(b))
   ENCARG(cons_f(a, a)) -> c4(F(a, a), ENCARG(a))
   ENCARG(cons_f(a, c)) -> c4(F(a, c), ENCARG(c))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1))
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_2, c10_2, c11_4, c1_1, c4_3


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

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(b, x1)) -> c4(F(b, encArg(x1)), ENCARG(x1)) by 
   ENCARG(cons_f(b, a)) -> c4(F(b, a), ENCARG(a))
   ENCARG(cons_f(b, b)) -> c4(F(b, b), ENCARG(b))
   ENCARG(cons_f(b, c)) -> c4(F(b, c), ENCARG(c))
   ENCARG(cons_f(b, cons_f(z0, z1))) -> c4(F(b, f(encArg(z0), encArg(z1))), ENCARG(cons_f(z0, z1)))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(b, a)) -> c4(F(b, a), ENCARG(a))
   ENCARG(cons_f(b, b)) -> c4(F(b, b), ENCARG(b))
   ENCARG(cons_f(b, c)) -> c4(F(b, c), ENCARG(c))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_2, c10_2, c11_4, c1_1, c4_3


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

(83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   ENCARG(cons_f(b, a)) -> c4(F(b, a), ENCARG(a))
   ENCARG(cons_f(b, c)) -> c4(F(b, c), ENCARG(c))
   ENCARG(cons_f(b, b)) -> c4(F(b, b), ENCARG(b))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1))
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_2, c10_2, c11_4, c1_1, c4_3


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

(85) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_f(c, x1)) -> c4(F(c, encArg(x1)), ENCARG(x1)) by 
   ENCARG(cons_f(c, a)) -> c4(F(c, a), ENCARG(a))
   ENCARG(cons_f(c, b)) -> c4(F(c, b), ENCARG(b))
   ENCARG(cons_f(c, c)) -> c4(F(c, c), ENCARG(c))
   ENCARG(cons_f(c, cons_f(z0, z1))) -> c4(F(c, f(encArg(z0), encArg(z1))), ENCARG(cons_f(z0, z1)))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(c, a)) -> c4(F(c, a), ENCARG(a))
   ENCARG(cons_f(c, b)) -> c4(F(c, b), ENCARG(b))
   ENCARG(cons_f(c, c)) -> c4(F(c, c), ENCARG(c))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c11_4, c1_1, c4_3, c4_2


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

(87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   ENCARG(cons_f(c, b)) -> c4(F(c, b), ENCARG(b))
   ENCARG(cons_f(c, a)) -> c4(F(c, a), ENCARG(a))
   ENCARG(cons_f(c, c)) -> c4(F(c, c), ENCARG(c))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c11_4, c1_1, c4_3, c4_2


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

(89) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(z0, c_f(c_f(z1, z2), x2)) -> c10(F(f(f(z0, z1), z2), x2), F(z0, c_f(z1, z2))) by 
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c11_4, c1_1, c4_3, c4_2, c10_1


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(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(c_f(c_f(a, b), c), c_f(z0, x2)) -> c10(F(f(b, f(a, f(c, f(b, z0)))), x2), F(c_f(c_f(a, b), c), z0)) by 
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c11_4, c1_1, c4_3, c4_2, c10_1


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

(93) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0)) by 
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c11_4, c1_1, c4_3, c4_2, c10_1


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

(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0)) by 
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c11_4, c1_1, c4_3, c4_2, c10_1, c11_1


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

(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1)) by 
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, f(c, c_f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(a, c_f(c, c_f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c11_4, c1_1, c4_3, c4_2, c10_1, c11_1, c11_3


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

(99) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2))) by 
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(b, c_f(a, f(c, f(f(b, x0), x1)))), F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))), F(b, c_f(x0, x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(b, f(a, c_f(c, f(f(b, x0), x1)))), F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))), F(b, c_f(x0, x1)))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   ENCODE_F(x0, a) -> c1(F(encArg(x0), a))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c1_1, c4_3, c4_2, c10_1, c11_4, c11_1, c11_3, c11_2


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

(101) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(x0, a) -> c1(F(encArg(x0), a)) by 
   ENCODE_F(a, a) -> c1(F(a, a))
   ENCODE_F(b, a) -> c1(F(b, a))
   ENCODE_F(c, a) -> c1(F(c, a))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(a, a) -> c1(F(a, a))
   ENCODE_F(b, a) -> c1(F(b, a))
   ENCODE_F(c, a) -> c1(F(c, a))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c1_1, c4_3, c4_2, c10_1, c11_4, c11_1, c11_3, c11_2


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

(103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   ENCODE_F(a, a) -> c1(F(a, a))
   ENCODE_F(b, a) -> c1(F(b, a))
   ENCODE_F(c, a) -> c1(F(c, a))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   ENCODE_F(x0, b) -> c1(F(encArg(x0), b))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c1_1, c4_3, c4_2, c10_1, c11_4, c11_1, c11_3, c11_2


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

(105) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(x0, b) -> c1(F(encArg(x0), b)) by 
   ENCODE_F(a, b) -> c1(F(a, b))
   ENCODE_F(b, b) -> c1(F(b, b))
   ENCODE_F(c, b) -> c1(F(c, b))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(a, b) -> c1(F(a, b))
   ENCODE_F(b, b) -> c1(F(b, b))
   ENCODE_F(c, b) -> c1(F(c, b))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c1_1, c4_3, c4_2, c10_1, c11_4, c11_1, c11_3, c11_2


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

(107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   ENCODE_F(a, b) -> c1(F(a, b))
   ENCODE_F(c, b) -> c1(F(c, b))
   ENCODE_F(b, b) -> c1(F(b, b))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   ENCODE_F(x0, c) -> c1(F(encArg(x0), c))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c1_1, c4_3, c4_2, c10_1, c11_4, c11_1, c11_3, c11_2


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

(109) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(x0, c) -> c1(F(encArg(x0), c)) by 
   ENCODE_F(a, c) -> c1(F(a, c))
   ENCODE_F(b, c) -> c1(F(b, c))
   ENCODE_F(c, c) -> c1(F(c, c))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(a, c) -> c1(F(a, c))
   ENCODE_F(b, c) -> c1(F(b, c))
   ENCODE_F(c, c) -> c1(F(c, c))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c1_1, c4_3, c4_2, c10_1, c11_4, c11_1, c11_3, c11_2


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

(111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   ENCODE_F(c, c) -> c1(F(c, c))
   ENCODE_F(b, c) -> c1(F(b, c))
   ENCODE_F(a, c) -> c1(F(a, c))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   ENCODE_F(x0, cons_f(z0, z1)) -> c1(F(encArg(x0), f(encArg(z0), encArg(z1))))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c1_1, c4_3, c4_2, c10_1, c11_4, c11_1, c11_3, c11_2


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

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

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   ENCODE_F(a, x1) -> c1(F(a, encArg(x1)))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c1_1, c4_3, c4_2, c10_1, c11_4, c11_1, c11_3, c11_2


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

(115) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(a, x1) -> c1(F(a, encArg(x1))) by 
   ENCODE_F(a, a) -> c1(F(a, a))
   ENCODE_F(a, b) -> c1(F(a, b))
   ENCODE_F(a, c) -> c1(F(a, c))
   ENCODE_F(a, cons_f(z0, z1)) -> c1(F(a, f(encArg(z0), encArg(z1))))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(a, a) -> c1(F(a, a))
   ENCODE_F(a, b) -> c1(F(a, b))
   ENCODE_F(a, c) -> c1(F(a, c))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c1_1, c4_3, c4_2, c10_1, c11_4, c11_1, c11_3, c11_2


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

(117) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   ENCODE_F(a, a) -> c1(F(a, a))
   ENCODE_F(a, b) -> c1(F(a, b))
   ENCODE_F(a, c) -> c1(F(a, c))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   ENCODE_F(b, x1) -> c1(F(b, encArg(x1)))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c1_1, c4_3, c4_2, c10_1, c11_4, c11_1, c11_3, c11_2


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

(119) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(b, x1) -> c1(F(b, encArg(x1))) by 
   ENCODE_F(b, a) -> c1(F(b, a))
   ENCODE_F(b, b) -> c1(F(b, b))
   ENCODE_F(b, c) -> c1(F(b, c))
   ENCODE_F(b, cons_f(z0, z1)) -> c1(F(b, f(encArg(z0), encArg(z1))))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(b, a) -> c1(F(b, a))
   ENCODE_F(b, b) -> c1(F(b, b))
   ENCODE_F(b, c) -> c1(F(b, c))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c1_1, c4_3, c4_2, c10_1, c11_4, c11_1, c11_3, c11_2


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

(121) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   ENCODE_F(b, c) -> c1(F(b, c))
   ENCODE_F(b, b) -> c1(F(b, b))
   ENCODE_F(b, a) -> c1(F(b, a))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   ENCODE_F(c, x1) -> c1(F(c, encArg(x1)))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c1_1, c4_3, c4_2, c10_1, c11_4, c11_1, c11_3, c11_2


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

(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_F(c, x1) -> c1(F(c, encArg(x1))) by 
   ENCODE_F(c, a) -> c1(F(c, a))
   ENCODE_F(c, b) -> c1(F(c, b))
   ENCODE_F(c, c) -> c1(F(c, c))
   ENCODE_F(c, cons_f(z0, z1)) -> c1(F(c, f(encArg(z0), encArg(z1))))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(c, a) -> c1(F(c, a))
   ENCODE_F(c, b) -> c1(F(c, b))
   ENCODE_F(c, c) -> c1(F(c, c))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c1_1, c4_3, c4_2, c10_1, c11_4, c11_1, c11_3, c11_2


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

(125) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   ENCODE_F(c, b) -> c1(F(c, b))
   ENCODE_F(c, a) -> c1(F(c, a))
   ENCODE_F(c, c) -> c1(F(c, c))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   ENCODE_F(cons_f(z0, z1), x1) -> c1(F(f(encArg(z0), encArg(z1)), encArg(x1)))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCODE_F_2, ENCARG_1

Compound Symbols:   c10_2, c1_1, c4_3, c4_2, c10_1, c11_4, c11_1, c11_3, c11_2


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

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

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c1(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, b), x2) -> c1(F(f(encArg(x0), b), encArg(x2)))
   ENCODE_F(cons_f(x0, c), x2) -> c1(F(f(encArg(x0), c), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c1(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(b, x1), x2) -> c1(F(f(b, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(c, x1), x2) -> c1(F(f(c, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
S tuples:
   F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   F_2, ENCARG_1, ENCODE_F_2

Compound Symbols:   c10_2, c4_3, c4_2, c10_1, c11_4, c11_1, c11_3, c11_2, c1_1


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

(129) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(z0, c_f(z1, x2)) -> c10(F(c_f(z0, z1), x2), F(z0, z1)) by 
   F(z0, c_f(z1, c_f(y1, y2))) -> c10(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1))
   F(z0, c_f(c_f(y1, y2), z2)) -> c10(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c1(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, b), x2) -> c1(F(f(encArg(x0), b), encArg(x2)))
   ENCODE_F(cons_f(x0, c), x2) -> c1(F(f(encArg(x0), c), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c1(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(b, x1), x2) -> c1(F(f(b, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(c, x1), x2) -> c1(F(f(c, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, c_f(y1, y2))) -> c10(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1))
   F(z0, c_f(c_f(y1, y2), z2)) -> c10(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
S tuples:
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   F(z0, c_f(z1, c_f(y1, y2))) -> c10(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1))
   F(z0, c_f(c_f(y1, y2), z2)) -> c10(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_3, c4_2, c10_2, c10_1, c11_4, c11_1, c11_3, c11_2, c1_1


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

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c1(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, b), x2) -> c1(F(f(encArg(x0), b), encArg(x2)))
   ENCODE_F(cons_f(x0, c), x2) -> c1(F(f(encArg(x0), c), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c1(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(b, x1), x2) -> c1(F(f(b, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(c, x1), x2) -> c1(F(f(c, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, c_f(y1, y2))) -> c10(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1))
   F(z0, c_f(c_f(y1, y2), z2)) -> c10(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
S tuples:
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   F(z0, c_f(z1, c_f(y1, y2))) -> c10(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1))
   F(z0, c_f(c_f(y1, y2), z2)) -> c10(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_3, c4_2, c10_2, c10_1, c11_4, c11_1, c11_3, c11_2, c1_1


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

(133) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(c_f(c_f(a, b), c), x0) -> c11(F(b, f(f(a, c), f(b, x0))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0)) by F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(c_f(a, c), f(b, z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
----------------------------------------

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c1(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, b), x2) -> c1(F(f(encArg(x0), b), encArg(x2)))
   ENCODE_F(cons_f(x0, c), x2) -> c1(F(f(encArg(x0), c), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c1(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(b, x1), x2) -> c1(F(f(b, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(c, x1), x2) -> c1(F(f(c, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, c_f(y1, y2))) -> c10(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1))
   F(z0, c_f(c_f(y1, y2), z2)) -> c10(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(c_f(a, c), f(b, z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
S tuples:
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   F(z0, c_f(z1, c_f(y1, y2))) -> c10(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1))
   F(z0, c_f(c_f(y1, y2), z2)) -> c10(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(c_f(a, c), f(b, z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_3, c4_2, c10_2, c10_1, c11_4, c11_1, c11_3, c11_2, c1_1


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

(135) CdtRewritingProof (BOTH BOUNDS(ID, ID))
Used rewriting to replace F(c_f(c_f(a, b), c), z2) -> c11(F(b, f(a, f(f(c, b), z2))), F(a, f(c, f(b, z2))), F(c, f(b, z2)), F(b, z2)) by F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c_f(c, b), z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
----------------------------------------

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c1(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, b), x2) -> c1(F(f(encArg(x0), b), encArg(x2)))
   ENCODE_F(cons_f(x0, c), x2) -> c1(F(f(encArg(x0), c), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c1(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(b, x1), x2) -> c1(F(f(b, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(c, x1), x2) -> c1(F(f(c, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, c_f(y1, y2))) -> c10(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1))
   F(z0, c_f(c_f(y1, y2), z2)) -> c10(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(c_f(a, c), f(b, z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c_f(c, b), z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
S tuples:
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   F(z0, c_f(z1, c_f(y1, y2))) -> c10(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1))
   F(z0, c_f(c_f(y1, y2), z2)) -> c10(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(c_f(a, c), f(b, z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c_f(c, b), z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_3, c4_2, c10_2, c10_1, c11_4, c11_1, c11_3, c11_2, c1_1


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

(137) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(x0, c_f(c_f(x1, x2), x3)) -> c10(F(x0, c_f(x1, x2))) by 
   F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c10(F(z0, c_f(c_f(y1, y2), z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, c_f(y1, y2))))
   F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c10(F(z0, c_f(z1, c_f(y2, y3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, z2), z3)) -> c10(F(c_f(a, b), c_f(c, z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c1(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, b), x2) -> c1(F(f(encArg(x0), b), encArg(x2)))
   ENCODE_F(cons_f(x0, c), x2) -> c1(F(f(encArg(x0), c), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c1(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(b, x1), x2) -> c1(F(f(b, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(c, x1), x2) -> c1(F(f(c, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, c_f(y1, y2))) -> c10(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1))
   F(z0, c_f(c_f(y1, y2), z2)) -> c10(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(c_f(a, c), f(b, z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c_f(c, b), z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c10(F(z0, c_f(c_f(y1, y2), z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, c_f(y1, y2))))
   F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c10(F(z0, c_f(z1, c_f(y2, y3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, z2), z3)) -> c10(F(c_f(a, b), c_f(c, z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
S tuples:
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   F(z0, c_f(z1, c_f(y1, y2))) -> c10(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1))
   F(z0, c_f(c_f(y1, y2), z2)) -> c10(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(c_f(a, c), f(b, z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c_f(c, b), z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c10(F(z0, c_f(c_f(y1, y2), z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, c_f(y1, y2))))
   F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c10(F(z0, c_f(z1, c_f(y2, y3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, z2), z3)) -> c10(F(c_f(a, b), c_f(c, z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_3, c4_2, c10_2, c10_1, c11_4, c11_1, c11_3, c11_2, c1_1


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

(139) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(z0, c_f(z1, c_f(y1, y2))) -> c10(F(c_f(z0, z1), c_f(y1, y2)), F(z0, z1)) by 
   F(z0, c_f(z1, c_f(c_f(y1, y2), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c), c_f(z2, z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), z1), c_f(z2, z3)), F(c_f(c_f(a, b), c), z1))
   F(c_f(a, b), c_f(c, c_f(z2, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(z2, c_f(y1, y2))), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)))
   F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), F(a, b))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(a, c_f(b, c_f(c, c_f(y0, y1)))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))), F(a, b))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, y1))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(a, c_f(b, c_f(c, z3))) -> c10(F(c_f(a, b), c_f(c, z3)), F(a, b))
   F(c_f(a, b), c_f(c_f(c, y0), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, y0)), c_f(z2, z3)), F(c_f(a, b), c_f(c, y0)))
   F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), F(a, b))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)))
   F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)), F(a, b))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)), F(a, b))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)))
   F(a, c_f(b, c_f(c_f(c, y0), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, y0), z3)), F(a, b))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), y1)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, y0), y1)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)), F(a, b))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c1(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, b), x2) -> c1(F(f(encArg(x0), b), encArg(x2)))
   ENCODE_F(cons_f(x0, c), x2) -> c1(F(f(encArg(x0), c), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c1(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(b, x1), x2) -> c1(F(f(b, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(c, x1), x2) -> c1(F(f(c, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(c_f(y1, y2), z2)) -> c10(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(c_f(a, c), f(b, z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c_f(c, b), z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c10(F(z0, c_f(c_f(y1, y2), z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, c_f(y1, y2))))
   F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c10(F(z0, c_f(z1, c_f(y2, y3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, z2), z3)) -> c10(F(c_f(a, b), c_f(c, z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c), c_f(z2, z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), z1), c_f(z2, z3)), F(c_f(c_f(a, b), c), z1))
   F(c_f(a, b), c_f(c, c_f(z2, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(z2, c_f(y1, y2))), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)))
   F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), F(a, b))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(a, c_f(b, c_f(c, c_f(y0, y1)))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))), F(a, b))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, y1))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(a, c_f(b, c_f(c, z3))) -> c10(F(c_f(a, b), c_f(c, z3)), F(a, b))
   F(c_f(a, b), c_f(c_f(c, y0), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, y0)), c_f(z2, z3)), F(c_f(a, b), c_f(c, y0)))
   F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), F(a, b))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)))
   F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)), F(a, b))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)), F(a, b))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)))
   F(a, c_f(b, c_f(c_f(c, y0), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, y0), z3)), F(a, b))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), y1)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, y0), y1)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)), F(a, b))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)))
S tuples:
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   F(z0, c_f(c_f(y1, y2), z2)) -> c10(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(c_f(a, c), f(b, z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c_f(c, b), z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c10(F(z0, c_f(c_f(y1, y2), z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, c_f(y1, y2))))
   F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c10(F(z0, c_f(z1, c_f(y2, y3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, z2), z3)) -> c10(F(c_f(a, b), c_f(c, z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c), c_f(z2, z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), z1), c_f(z2, z3)), F(c_f(c_f(a, b), c), z1))
   F(c_f(a, b), c_f(c, c_f(z2, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(z2, c_f(y1, y2))), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)))
   F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), F(a, b))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(a, c_f(b, c_f(c, c_f(y0, y1)))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))), F(a, b))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, y1))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(a, c_f(b, c_f(c, z3))) -> c10(F(c_f(a, b), c_f(c, z3)), F(a, b))
   F(c_f(a, b), c_f(c_f(c, y0), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, y0)), c_f(z2, z3)), F(c_f(a, b), c_f(c, y0)))
   F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), F(a, b))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)), F(c_f(a, b), c))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)))
   F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)), F(a, b))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)), F(a, b))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)))
   F(a, c_f(b, c_f(c_f(c, y0), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, y0), z3)), F(a, b))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), y1)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, y0), y1)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)), F(a, b))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_3, c4_2, c10_2, c10_1, c11_4, c11_1, c11_3, c11_2, c1_1


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

(141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 15 trailing tuple parts
----------------------------------------

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c1(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, b), x2) -> c1(F(f(encArg(x0), b), encArg(x2)))
   ENCODE_F(cons_f(x0, c), x2) -> c1(F(f(encArg(x0), c), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c1(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(b, x1), x2) -> c1(F(f(b, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(c, x1), x2) -> c1(F(f(c, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(c_f(y1, y2), z2)) -> c10(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(c_f(a, c), f(b, z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c_f(c, b), z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c10(F(z0, c_f(c_f(y1, y2), z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, c_f(y1, y2))))
   F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c10(F(z0, c_f(z1, c_f(y2, y3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, z2), z3)) -> c10(F(c_f(a, b), c_f(c, z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), z1), c_f(z2, z3)), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, y1))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, y0), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, y0)), c_f(z2, z3)), F(c_f(a, b), c_f(c, y0)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), y1)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, y0), y1)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z3)))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z3)))
   F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(a, c_f(b, c_f(c, c_f(y0, y1)))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(a, c_f(b, c_f(c, z3))) -> c10(F(c_f(a, b), c_f(c, z3)))
   F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)))
   F(a, c_f(b, c_f(c_f(c, y0), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, y0), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)))
S tuples:
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   F(z0, c_f(c_f(y1, y2), z2)) -> c10(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(c_f(a, c), f(b, z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c_f(c, b), z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c10(F(z0, c_f(c_f(y1, y2), z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, c_f(y1, y2))))
   F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c10(F(z0, c_f(z1, c_f(y2, y3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, z2), z3)) -> c10(F(c_f(a, b), c_f(c, z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), z1), c_f(z2, z3)), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, y1))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, y0), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, y0)), c_f(z2, z3)), F(c_f(a, b), c_f(c, y0)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), y1)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, y0), y1)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z3)))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z3)))
   F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(a, c_f(b, c_f(c, c_f(y0, y1)))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(a, c_f(b, c_f(c, z3))) -> c10(F(c_f(a, b), c_f(c, z3)))
   F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)))
   F(a, c_f(b, c_f(c_f(c, y0), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, y0), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_3, c4_2, c10_2, c10_1, c11_4, c11_1, c11_3, c11_2, c1_1


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

(143) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(z0, c_f(c_f(y1, y2), z2)) -> c10(F(c_f(z0, c_f(y1, y2)), z2), F(z0, c_f(y1, y2))) by 
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, y2), y3)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), z2)), z3), F(z0, c_f(c_f(y1, y2), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), z2)), z3), F(z0, c_f(c_f(y1, c_f(y2, y3)), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), z2)), z3), F(z0, c_f(c_f(c_f(y1, y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(z1, z2)), z3), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(z1, c_f(y1, y2))), z3), F(c_f(c_f(a, b), c), c_f(z1, c_f(y1, y2))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, y3), y4)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, y3), y4))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, y3), y4))), z3), F(z0, c_f(z1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), z3), F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, y1))), z3), F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, z2)), z3), F(c_f(a, b), c_f(c, z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), z3), F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z2)), z3), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z2)), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), z2)), z3), F(c_f(a, b), c_f(c_f(c, y0), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z2)), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), z3), F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), c_f(y2, y3)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(y2, y3))), z3), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(y2, y3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4))), z3), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(y3, y4))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(y3, y4)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(y3, y4))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(y3, y4)))), z3), F(z0, c_f(z1, c_f(y2, c_f(y3, y4)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), z3), F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4))), z3), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3))), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3))))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), c_f(y1, y2))), z3), F(c_f(a, b), c_f(c_f(c, y0), c_f(y1, y2))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4))), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5))), z3), F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4))), z3), F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, y0), y1), c_f(y2, y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(y2, y3))), z3), F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(y2, y3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5))), z3), F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, y1), y2), y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), y3))), z3), F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), y3))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3))), z3), F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3))))
   F(a, c_f(c_f(b, c_f(c, c_f(c_f(y0, y1), y2))), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))), z3), F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))))
   F(a, c_f(c_f(b, c_f(c, c_f(y0, y1))), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, c_f(y0, y1)))), z3), F(a, c_f(b, c_f(c, c_f(y0, y1)))))
   F(a, c_f(c_f(b, c_f(c, y0)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, y0))), z3), F(a, c_f(b, c_f(c, y0))))
   F(a, c_f(c_f(b, c_f(c, c_f(y0, c_f(y1, y2)))), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))), z3), F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))), z3), F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))), z3), F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3))), z3), F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, y1)), y2)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), y2))), z3), F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), y2))))
   F(a, c_f(c_f(b, c_f(c_f(c, y0), y1)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, y0), y1))), z3), F(a, c_f(b, c_f(c_f(c, y0), y1))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3))), z3), F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3))))

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c1(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, b), x2) -> c1(F(f(encArg(x0), b), encArg(x2)))
   ENCODE_F(cons_f(x0, c), x2) -> c1(F(f(encArg(x0), c), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c1(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(b, x1), x2) -> c1(F(f(b, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(c, x1), x2) -> c1(F(f(c, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(c_f(a, c), f(b, z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c_f(c, b), z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c10(F(z0, c_f(c_f(y1, y2), z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, c_f(y1, y2))))
   F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c10(F(z0, c_f(z1, c_f(y2, y3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, z2), z3)) -> c10(F(c_f(a, b), c_f(c, z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), z1), c_f(z2, z3)), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, y1))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, y0), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, y0)), c_f(z2, z3)), F(c_f(a, b), c_f(c, y0)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), y1)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, y0), y1)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z3)))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z3)))
   F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(a, c_f(b, c_f(c, c_f(y0, y1)))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(a, c_f(b, c_f(c, z3))) -> c10(F(c_f(a, b), c_f(c, z3)))
   F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)))
   F(a, c_f(b, c_f(c_f(c, y0), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, y0), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, y2), y3)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, y3), y4)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, y3), y4))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, y3), y4))), z3), F(z0, c_f(z1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), z3), F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, y1))), z3), F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, z2)), z3), F(c_f(a, b), c_f(c, z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), z3), F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z2)), z3), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z2)), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), z2)), z3), F(c_f(a, b), c_f(c_f(c, y0), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z2)), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), z3), F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), c_f(y2, y3)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(y2, y3))), z3), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(y2, y3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4))), z3), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(y3, y4))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(y3, y4)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(y3, y4))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(y3, y4)))), z3), F(z0, c_f(z1, c_f(y2, c_f(y3, y4)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), z3), F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4))), z3), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3))), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3))))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), c_f(y1, y2))), z3), F(c_f(a, b), c_f(c_f(c, y0), c_f(y1, y2))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4))), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5))), z3), F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4))), z3), F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, y0), y1), c_f(y2, y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(y2, y3))), z3), F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(y2, y3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5))), z3), F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, y1), y2), y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), y3))), z3), F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), y3))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3))), z3), F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3))))
   F(a, c_f(c_f(b, c_f(c, c_f(c_f(y0, y1), y2))), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))), z3), F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))))
   F(a, c_f(c_f(b, c_f(c, c_f(y0, y1))), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, c_f(y0, y1)))), z3), F(a, c_f(b, c_f(c, c_f(y0, y1)))))
   F(a, c_f(c_f(b, c_f(c, y0)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, y0))), z3), F(a, c_f(b, c_f(c, y0))))
   F(a, c_f(c_f(b, c_f(c, c_f(y0, c_f(y1, y2)))), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))), z3), F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))), z3), F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))), z3), F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3))), z3), F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, y1)), y2)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), y2))), z3), F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), y2))))
   F(a, c_f(c_f(b, c_f(c_f(c, y0), y1)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, y0), y1))), z3), F(a, c_f(b, c_f(c_f(c, y0), y1))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3))), z3), F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3))))
S tuples:
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(c_f(a, c), f(b, z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c_f(c, b), z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c10(F(z0, c_f(c_f(y1, y2), z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, c_f(y1, y2))))
   F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c10(F(z0, c_f(z1, c_f(y2, y3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, z2), z3)) -> c10(F(c_f(a, b), c_f(c, z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), z1), c_f(z2, z3)), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, y1))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, y0), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, y0)), c_f(z2, z3)), F(c_f(a, b), c_f(c, y0)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), y1)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, y0), y1)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z3)))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z3)))
   F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(a, c_f(b, c_f(c, c_f(y0, y1)))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(a, c_f(b, c_f(c, z3))) -> c10(F(c_f(a, b), c_f(c, z3)))
   F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)))
   F(a, c_f(b, c_f(c_f(c, y0), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, y0), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, y2), y3)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, y3), y4)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, y3), y4))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, y3), y4))), z3), F(z0, c_f(z1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), z3), F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, y1))), z3), F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, z2)), z3), F(c_f(a, b), c_f(c, z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), z3), F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z2)), z3), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z2)), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), z2)), z3), F(c_f(a, b), c_f(c_f(c, y0), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z2)), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), z3), F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), c_f(y2, y3)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(y2, y3))), z3), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(y2, y3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4))), z3), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(y3, y4))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(y3, y4)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(y3, y4))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(y3, y4)))), z3), F(z0, c_f(z1, c_f(y2, c_f(y3, y4)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), z3), F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4))), z3), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3))), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3))))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), c_f(y1, y2))), z3), F(c_f(a, b), c_f(c_f(c, y0), c_f(y1, y2))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4))), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5))), z3), F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4))), z3), F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, y0), y1), c_f(y2, y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(y2, y3))), z3), F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(y2, y3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5))), z3), F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, y1), y2), y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), y3))), z3), F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), y3))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3))), z3), F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3))))
   F(a, c_f(c_f(b, c_f(c, c_f(c_f(y0, y1), y2))), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))), z3), F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))))
   F(a, c_f(c_f(b, c_f(c, c_f(y0, y1))), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, c_f(y0, y1)))), z3), F(a, c_f(b, c_f(c, c_f(y0, y1)))))
   F(a, c_f(c_f(b, c_f(c, y0)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, y0))), z3), F(a, c_f(b, c_f(c, y0))))
   F(a, c_f(c_f(b, c_f(c, c_f(y0, c_f(y1, y2)))), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))), z3), F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))), z3), F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))), z3), F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3))), z3), F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, y1)), y2)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), y2))), z3), F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), y2))))
   F(a, c_f(c_f(b, c_f(c_f(c, y0), y1)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, y0), y1))), z3), F(a, c_f(b, c_f(c_f(c, y0), y1))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3))), z3), F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_3, c4_2, c10_2, c10_1, c11_4, c11_1, c11_3, c11_2, c1_1


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

(145) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace F(z0, c_f(c_f(z1, c_f(y2, y3)), z3)) -> c10(F(z0, c_f(z1, c_f(y2, y3)))) by 
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, y3), z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), z3))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), z3))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), z3)), z4)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), z3))))
   F(c_f(a, b), c_f(c_f(c, c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c, c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c, c_f(z2, c_f(y1, y2))), z4)) -> c10(F(c_f(a, b), c_f(c, c_f(z2, c_f(y1, y2)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, y0), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(z2, c_f(y3, y4))), z4)) -> c10(F(z0, c_f(z1, c_f(z2, c_f(y3, y4)))))
   F(z0, c_f(c_f(z1, c_f(z2, c_f(c_f(y3, y4), y5))), z4)) -> c10(F(z0, c_f(z1, c_f(z2, c_f(c_f(y3, y4), y5)))))
   F(z0, c_f(c_f(z1, c_f(z2, c_f(c_f(y3, c_f(y4, y5)), y6))), z4)) -> c10(F(z0, c_f(z1, c_f(z2, c_f(c_f(y3, c_f(y4, y5)), y6)))))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), z3))))
   F(z0, c_f(c_f(z1, c_f(z2, c_f(c_f(c_f(y3, y4), y5), y6))), z4)) -> c10(F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y3, y4), y5), y6)))))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), z3))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), z3))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), z3))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), z3))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), z3))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, y0), y1), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, y1), y2), z3)), z4)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), z3))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, c_f(y1, y2)), z3)), z4)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), z3))))
   F(a, c_f(c_f(b, c_f(c, c_f(c_f(y0, y1), y2))), z4)) -> c10(F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))))
   F(a, c_f(c_f(b, c_f(c, c_f(y0, y1))), z4)) -> c10(F(a, c_f(b, c_f(c, c_f(y0, y1)))))
   F(a, c_f(c_f(b, c_f(c, z3)), z4)) -> c10(F(a, c_f(b, c_f(c, z3))))
   F(a, c_f(c_f(b, c_f(c, c_f(y0, c_f(y1, y2)))), z4)) -> c10(F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)), z4)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)), z4)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)), z4)) -> c10(F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, y1)), z3)), z4)) -> c10(F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), z3))))
   F(a, c_f(c_f(b, c_f(c_f(c, y0), z3)), z4)) -> c10(F(a, c_f(b, c_f(c_f(c, y0), z3))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)), z4)) -> c10(F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, y4), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, y4), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, y5), y6))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, y5), y6)))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(y5, y6)), y7))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(y5, y6)), y7)))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, y5), y6), y7))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, y5), y6), y7)))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), c_f(y6, y7))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), c_f(y6, y7)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), c_f(y7, y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), c_f(y7, y8)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), c_f(y7, y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), c_f(y7, y8)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), c_f(y2, y3)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(y5, y6)))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(y5, y6))))))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(y3, y4))), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, c_f(y3, y4))), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), c_f(y6, y7))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), c_f(y6, y7)))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, y6), y7)))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, y6), y7))))))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), c_f(y7, y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), c_f(y7, y8)))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8))))))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), c_f(y8, y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), c_f(y8, y9)))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), c_f(y8, y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), c_f(y8, y9)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8))))))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), c_f(y8, y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), c_f(y8, y9)))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), c_f(y8, y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), c_f(y8, y9)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, y0), c_f(y1, y2)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, y0), c_f(y1, y2)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, y6), y7)), y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, y6), y7)), y8)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, y5), y6)), y7), c_f(y8, y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, y5), y6)), y7), c_f(y8, y9)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)), y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)), y9)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), y8), c_f(y9, y10))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), y8), c_f(y9, y10)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8), y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8), y9)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), y8), c_f(y9, y10))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), y8), c_f(y9, y10)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)), y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)), y9)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), y8), c_f(y9, y10))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), y8), c_f(y9, y10)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8), y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8), y9)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), y8), c_f(y9, y10))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), y8), c_f(y9, y10)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c_f(c, y0), y1), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c_f(c, y0), y1), c_f(y2, y3)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c, c_f(c_f(y0, y1), y2))), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c, c_f(y0, y1))), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c, c_f(y0, y1))), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c, y0)), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c, y0)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c, c_f(y0, c_f(y1, y2)))), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c_f(c, c_f(y0, y1)), y2)), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, y1)), y2)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c_f(c, y0), y1)), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c_f(c, y0), y1)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3))))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a) -> a
   encArg(b) -> b
   encArg(c) -> c
   encArg(cons_f(z0, z1)) -> f(encArg(z0), encArg(z1))
   f(z0, z1) -> c_f(z0, z1)
   f(z0, c_f(z1, z2)) -> f(f(z0, z1), z2)
   f(c_f(c_f(a, b), c), z0) -> f(b, f(a, f(c, f(b, z0))))
Tuples:
   ENCARG(cons_f(x0, cons_f(x1, x2))) -> c4(F(encArg(x0), c_f(encArg(x1), encArg(x2))), ENCARG(x0), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(x0, cons_f(x1, a))) -> c4(F(encArg(x0), f(encArg(x1), a)), ENCARG(x0), ENCARG(cons_f(x1, a)))
   ENCARG(cons_f(x0, cons_f(x1, b))) -> c4(F(encArg(x0), f(encArg(x1), b)), ENCARG(x0), ENCARG(cons_f(x1, b)))
   ENCARG(cons_f(x0, cons_f(x1, c))) -> c4(F(encArg(x0), f(encArg(x1), c)), ENCARG(x0), ENCARG(cons_f(x1, c)))
   ENCARG(cons_f(x0, cons_f(x1, cons_f(z0, z1)))) -> c4(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_f(x1, cons_f(z0, z1))))
   ENCARG(cons_f(x0, cons_f(a, x2))) -> c4(F(encArg(x0), f(a, encArg(x2))), ENCARG(x0), ENCARG(cons_f(a, x2)))
   ENCARG(cons_f(x0, cons_f(b, x2))) -> c4(F(encArg(x0), f(b, encArg(x2))), ENCARG(x0), ENCARG(cons_f(b, x2)))
   ENCARG(cons_f(x0, cons_f(c, x2))) -> c4(F(encArg(x0), f(c, encArg(x2))), ENCARG(x0), ENCARG(cons_f(c, x2)))
   ENCARG(cons_f(x0, cons_f(cons_f(z0, z1), x2))) -> c4(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_f(cons_f(z0, z1), x2)))
   ENCARG(cons_f(cons_f(z0, z1), cons_f(x1, x2))) -> c4(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))), ENCARG(cons_f(z0, z1)), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(a, cons_f(x1, x2))) -> c4(F(a, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(b, cons_f(x1, x2))) -> c4(F(b, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(c, cons_f(x1, x2))) -> c4(F(c, f(encArg(x1), encArg(x2))), ENCARG(cons_f(x1, x2)))
   ENCARG(cons_f(cons_f(x0, x1), x2)) -> c4(F(c_f(encArg(x0), encArg(x1)), encArg(x2)), ENCARG(cons_f(x0, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, a), x2)) -> c4(F(f(encArg(x0), a), encArg(x2)), ENCARG(cons_f(x0, a)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, b), x2)) -> c4(F(f(encArg(x0), b), encArg(x2)), ENCARG(cons_f(x0, b)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, c), x2)) -> c4(F(f(encArg(x0), c), encArg(x2)), ENCARG(cons_f(x0, c)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, cons_f(z0, z1)), x2)) -> c4(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_f(x0, cons_f(z0, z1))), ENCARG(x2))
   ENCARG(cons_f(cons_f(a, x1), x2)) -> c4(F(f(a, encArg(x1)), encArg(x2)), ENCARG(cons_f(a, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(b, x1), x2)) -> c4(F(f(b, encArg(x1)), encArg(x2)), ENCARG(cons_f(b, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(c, x1), x2)) -> c4(F(f(c, encArg(x1)), encArg(x2)), ENCARG(cons_f(c, x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(cons_f(z0, z1), x1), x2)) -> c4(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_f(cons_f(z0, z1), x1)), ENCARG(x2))
   ENCARG(cons_f(cons_f(x0, x1), a)) -> c4(F(f(encArg(x0), encArg(x1)), a), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), b)) -> c4(F(f(encArg(x0), encArg(x1)), b), ENCARG(cons_f(x0, x1)))
   ENCARG(cons_f(cons_f(x0, x1), c)) -> c4(F(f(encArg(x0), encArg(x1)), c), ENCARG(cons_f(x0, x1)))
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   ENCODE_F(cons_f(z0, z1), a) -> c1(F(f(encArg(z0), encArg(z1)), a))
   ENCODE_F(cons_f(z0, z1), b) -> c1(F(f(encArg(z0), encArg(z1)), b))
   ENCODE_F(cons_f(z0, z1), c) -> c1(F(f(encArg(z0), encArg(z1)), c))
   ENCODE_F(x0, cons_f(x1, x2)) -> c1(F(encArg(x0), c_f(encArg(x1), encArg(x2))))
   ENCODE_F(x0, cons_f(x1, a)) -> c1(F(encArg(x0), f(encArg(x1), a)))
   ENCODE_F(x0, cons_f(x1, b)) -> c1(F(encArg(x0), f(encArg(x1), b)))
   ENCODE_F(x0, cons_f(x1, c)) -> c1(F(encArg(x0), f(encArg(x1), c)))
   ENCODE_F(x0, cons_f(x1, cons_f(z0, z1))) -> c1(F(encArg(x0), f(encArg(x1), f(encArg(z0), encArg(z1)))))
   ENCODE_F(x0, cons_f(a, x2)) -> c1(F(encArg(x0), f(a, encArg(x2))))
   ENCODE_F(x0, cons_f(b, x2)) -> c1(F(encArg(x0), f(b, encArg(x2))))
   ENCODE_F(x0, cons_f(c, x2)) -> c1(F(encArg(x0), f(c, encArg(x2))))
   ENCODE_F(x0, cons_f(cons_f(z0, z1), x2)) -> c1(F(encArg(x0), f(f(encArg(z0), encArg(z1)), encArg(x2))))
   ENCODE_F(a, cons_f(x1, x2)) -> c1(F(a, f(encArg(x1), encArg(x2))))
   ENCODE_F(b, cons_f(x1, x2)) -> c1(F(b, f(encArg(x1), encArg(x2))))
   ENCODE_F(c, cons_f(x1, x2)) -> c1(F(c, f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(z0, z1), cons_f(x1, x2)) -> c1(F(f(encArg(z0), encArg(z1)), f(encArg(x1), encArg(x2))))
   ENCODE_F(cons_f(x0, x1), x2) -> c1(F(c_f(encArg(x0), encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(x0, a), x2) -> c1(F(f(encArg(x0), a), encArg(x2)))
   ENCODE_F(cons_f(x0, b), x2) -> c1(F(f(encArg(x0), b), encArg(x2)))
   ENCODE_F(cons_f(x0, c), x2) -> c1(F(f(encArg(x0), c), encArg(x2)))
   ENCODE_F(cons_f(x0, cons_f(z0, z1)), x2) -> c1(F(f(encArg(x0), f(encArg(z0), encArg(z1))), encArg(x2)))
   ENCODE_F(cons_f(a, x1), x2) -> c1(F(f(a, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(b, x1), x2) -> c1(F(f(b, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(c, x1), x2) -> c1(F(f(c, encArg(x1)), encArg(x2)))
   ENCODE_F(cons_f(cons_f(z0, z1), x1), x2) -> c1(F(f(f(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(c_f(a, c), f(b, z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c_f(c, b), z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c10(F(z0, c_f(c_f(y1, y2), z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, c_f(y1, y2))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, z2), z3)) -> c10(F(c_f(a, b), c_f(c, z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), z1), c_f(z2, z3)), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, y1))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, y0), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, y0)), c_f(z2, z3)), F(c_f(a, b), c_f(c, y0)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), y1)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, y0), y1)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z3)))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z3)))
   F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(a, c_f(b, c_f(c, c_f(y0, y1)))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(a, c_f(b, c_f(c, z3))) -> c10(F(c_f(a, b), c_f(c, z3)))
   F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)))
   F(a, c_f(b, c_f(c_f(c, y0), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, y0), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, y2), y3)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, y3), y4)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, y3), y4))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, y3), y4))), z3), F(z0, c_f(z1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), z3), F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, y1))), z3), F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, z2)), z3), F(c_f(a, b), c_f(c, z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), z3), F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z2)), z3), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z2)), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), z2)), z3), F(c_f(a, b), c_f(c_f(c, y0), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z2)), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), z3), F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), c_f(y2, y3)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(y2, y3))), z3), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(y2, y3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4))), z3), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(y3, y4))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(y3, y4)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(y3, y4))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(y3, y4)))), z3), F(z0, c_f(z1, c_f(y2, c_f(y3, y4)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), z3), F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4))), z3), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3))), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3))))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), c_f(y1, y2))), z3), F(c_f(a, b), c_f(c_f(c, y0), c_f(y1, y2))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4))), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5))), z3), F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4))), z3), F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, y0), y1), c_f(y2, y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(y2, y3))), z3), F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(y2, y3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5))), z3), F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, y1), y2), y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), y3))), z3), F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), y3))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3))), z3), F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3))))
   F(a, c_f(c_f(b, c_f(c, c_f(c_f(y0, y1), y2))), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))), z3), F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))))
   F(a, c_f(c_f(b, c_f(c, c_f(y0, y1))), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, c_f(y0, y1)))), z3), F(a, c_f(b, c_f(c, c_f(y0, y1)))))
   F(a, c_f(c_f(b, c_f(c, y0)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, y0))), z3), F(a, c_f(b, c_f(c, y0))))
   F(a, c_f(c_f(b, c_f(c, c_f(y0, c_f(y1, y2)))), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))), z3), F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))), z3), F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))), z3), F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3))), z3), F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, y1)), y2)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), y2))), z3), F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), y2))))
   F(a, c_f(c_f(b, c_f(c_f(c, y0), y1)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, y0), y1))), z3), F(a, c_f(b, c_f(c_f(c, y0), y1))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3))), z3), F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, y0), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(z2, c_f(y3, y4))), z4)) -> c10(F(z0, c_f(z1, c_f(z2, c_f(y3, y4)))))
   F(z0, c_f(c_f(z1, c_f(z2, c_f(c_f(y3, y4), y5))), z4)) -> c10(F(z0, c_f(z1, c_f(z2, c_f(c_f(y3, y4), y5)))))
   F(z0, c_f(c_f(z1, c_f(z2, c_f(c_f(y3, c_f(y4, y5)), y6))), z4)) -> c10(F(z0, c_f(z1, c_f(z2, c_f(c_f(y3, c_f(y4, y5)), y6)))))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), z3))))
   F(z0, c_f(c_f(z1, c_f(z2, c_f(c_f(c_f(y3, y4), y5), y6))), z4)) -> c10(F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y3, y4), y5), y6)))))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), z3))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), z3))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), z3))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), z3))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), z3))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, y0), y1), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, y1), y2), z3)), z4)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), z3))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, c_f(y1, y2)), z3)), z4)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), z3))))
   F(a, c_f(c_f(b, c_f(c, c_f(c_f(y0, y1), y2))), z4)) -> c10(F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))))
   F(a, c_f(c_f(b, c_f(c, c_f(y0, y1))), z4)) -> c10(F(a, c_f(b, c_f(c, c_f(y0, y1)))))
   F(a, c_f(c_f(b, c_f(c, z3)), z4)) -> c10(F(a, c_f(b, c_f(c, z3))))
   F(a, c_f(c_f(b, c_f(c, c_f(y0, c_f(y1, y2)))), z4)) -> c10(F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)), z4)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)), z4)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)), z4)) -> c10(F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, y1)), z3)), z4)) -> c10(F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), z3))))
   F(a, c_f(c_f(b, c_f(c_f(c, y0), z3)), z4)) -> c10(F(a, c_f(b, c_f(c_f(c, y0), z3))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)), z4)) -> c10(F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, y4), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, y4), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, y5), y6))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, y5), y6)))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(y5, y6)), y7))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(y5, y6)), y7)))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, y5), y6), y7))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, y5), y6), y7)))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), c_f(y6, y7))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), c_f(y6, y7)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), c_f(y7, y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), c_f(y7, y8)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), c_f(y7, y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), c_f(y7, y8)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), c_f(y2, y3)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(y5, y6)))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(y5, y6))))))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(y3, y4))), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, c_f(y3, y4))), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), c_f(y6, y7))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), c_f(y6, y7)))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, y6), y7)))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, y6), y7))))))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), c_f(y7, y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), c_f(y7, y8)))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8))))))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), c_f(y8, y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), c_f(y8, y9)))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), c_f(y8, y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), c_f(y8, y9)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8))))))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), c_f(y8, y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), c_f(y8, y9)))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), c_f(y8, y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), c_f(y8, y9)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, y0), c_f(y1, y2)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, y0), c_f(y1, y2)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, y6), y7)), y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, y6), y7)), y8)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, y5), y6)), y7), c_f(y8, y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, y5), y6)), y7), c_f(y8, y9)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)), y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)), y9)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), y8), c_f(y9, y10))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), y8), c_f(y9, y10)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8), y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8), y9)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), y8), c_f(y9, y10))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), y8), c_f(y9, y10)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)), y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)), y9)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), y8), c_f(y9, y10))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), y8), c_f(y9, y10)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8), y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8), y9)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), y8), c_f(y9, y10))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), y8), c_f(y9, y10)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c_f(c, y0), y1), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c_f(c, y0), y1), c_f(y2, y3)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c, c_f(c_f(y0, y1), y2))), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c, c_f(y0, y1))), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c, c_f(y0, y1))), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c, y0)), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c, y0)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c, c_f(y0, c_f(y1, y2)))), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c_f(c, c_f(y0, y1)), y2)), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, y1)), y2)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c_f(c, y0), y1)), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c_f(c, y0), y1)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3))))
S tuples:
   F(x0, c_f(c_f(x1, z1), x3)) -> c10(F(c_f(f(x0, x1), z1), x3), F(x0, c_f(x1, z1)))
   F(x0, c_f(c_f(x1, c_f(z1, z2)), x3)) -> c10(F(f(f(f(x0, x1), z1), z2), x3), F(x0, c_f(x1, c_f(z1, z2))))
   F(z0, c_f(c_f(z1, x2), x3)) -> c10(F(f(c_f(z0, z1), x2), x3), F(z0, c_f(z1, x2)))
   F(z0, c_f(c_f(c_f(z1, z2), x2), x3)) -> c10(F(f(f(f(z0, z1), z2), x2), x3), F(z0, c_f(c_f(z1, z2), x2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z0, x2), x3)) -> c10(F(f(f(b, f(a, f(c, f(b, z0)))), x2), x3), F(c_f(c_f(a, b), c), c_f(z0, x2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(b, f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, c_f(a, f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(f(b, f(a, c_f(c, f(b, x0)))), x1), F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c10(F(f(b, f(a, f(c, c_f(b, z1)))), x1), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c10(F(f(b, f(a, f(c, f(f(b, z1), z2)))), x1), F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c10(F(c_f(c_f(a, b), c), x0))
   F(c_f(c_f(a, b), c), x0) -> c11(F(b, c_f(a, c_f(c, f(b, x0)))), F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, c_f(a, f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, c_f(a, f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), z1) -> c11(F(b, f(a, c_f(c, c_f(b, z1)))), F(a, f(c, f(b, z1))), F(c, f(b, z1)), F(b, z1))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c11(F(b, f(a, c_f(c, f(f(b, z1), z2)))), F(a, f(c, f(b, c_f(z1, z2)))), F(c, f(b, c_f(z1, z2))), F(b, c_f(z1, z2)))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))))
   F(c_f(c_f(a, b), c), x0) -> c11(F(a, f(c, f(b, x0))), F(c, f(b, x0)), F(b, x0))
   F(c_f(c_f(a, b), c), c_f(x0, z1)) -> c11(F(b, f(a, f(c, c_f(f(b, x0), z1)))), F(a, f(c, f(b, c_f(x0, z1)))), F(c, f(b, c_f(x0, z1))), F(b, c_f(x0, z1)))
   F(c_f(c_f(a, b), c), c_f(x0, c_f(z1, z2))) -> c11(F(b, f(a, f(c, f(f(f(b, x0), z1), z2)))), F(a, f(c, f(b, c_f(x0, c_f(z1, z2))))), F(c, f(b, c_f(x0, c_f(z1, z2)))), F(b, c_f(x0, c_f(z1, z2))))
   F(c_f(c_f(a, b), c), c_f(z1, x1)) -> c11(F(b, f(a, f(c, f(c_f(b, z1), x1)))), F(a, f(c, f(b, c_f(z1, x1)))), F(c, f(b, c_f(z1, x1))), F(b, c_f(z1, x1)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), x1)) -> c11(F(b, f(a, f(c, f(f(f(b, z1), z2), x1)))), F(a, f(c, f(b, c_f(c_f(z1, z2), x1)))), F(c, f(b, c_f(c_f(z1, z2), x1))), F(b, c_f(c_f(z1, z2), x1)))
   F(c_f(c_f(a, b), c), c_f(x0, x1)) -> c11(F(a, f(c, f(b, c_f(x0, x1)))), F(c, f(b, c_f(x0, x1))))
   F(z0, c_f(z1, c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, y2), y3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, y2), y3), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), z2), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), z2), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), z2), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), z2), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), z2), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, z2)) -> c10(F(c_f(c_f(c_f(a, b), c), z1), z2), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), z2), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(a, b), c_f(c, c_f(y0, y1))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(a, b), c_f(c, z2)) -> c10(F(c_f(c_f(a, b), c), z2))
   F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))) -> c10(F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(c_f(a, c), f(b, z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(c_f(c_f(a, b), c), z0) -> c11(F(b, f(a, f(c_f(c, b), z0))), F(a, f(c, f(b, z0))), F(c, f(b, z0)), F(b, z0))
   F(z0, c_f(c_f(c_f(y1, y2), z2), z3)) -> c10(F(z0, c_f(c_f(y1, y2), z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), z2), z3)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, y3)), z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(z1, c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(z1, c_f(y1, y2))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, z2), z3)) -> c10(F(c_f(a, b), c_f(c, z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, y2), y3)), c_f(z2, z3)), F(z0, c_f(c_f(y1, y2), y3)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), y4)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(y2, y3)), y4)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), y4)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), y2)))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, y1)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, y1)))
   F(c_f(c_f(a, b), c), c_f(z1, c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), z1), c_f(z2, z3)), F(c_f(c_f(a, b), c), z1))
   F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(y0, c_f(y1, y2))))
   F(z0, c_f(z1, c_f(z2, c_f(y2, y3)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(y2, y3))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(y2, y3))), c_f(z2, z3)), F(z0, c_f(y1, c_f(y2, y3))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, y3), y4)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, y3), y4))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, y3), y4))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)))
   F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c10(F(c_f(z0, z1), c_f(z2, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, z1))
   F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), c_f(z2, z3)), F(z0, c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, y2), y3), y4), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), y3)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), y3)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, y1))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, y0), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, y0)), c_f(z2, z3)), F(c_f(a, b), c_f(c, y0)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)))
   F(z0, c_f(z1, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), c_f(z2, z3)), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)))
   F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3))) -> c10(F(c_f(z0, z1), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z3)), F(z0, z1))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), c_f(z2, z3)), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), y2)))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), y1)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, y0), y1)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z3)))
   F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z3)))
   F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(a, c_f(b, c_f(c, c_f(y0, y1)))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(a, c_f(b, c_f(c, z3))) -> c10(F(c_f(a, b), c_f(c, z3)))
   F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))) -> c10(F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)))
   F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)))
   F(a, c_f(b, c_f(c_f(c, y0), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, y0), z3)))
   F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3))) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, y2), y3))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, y2), y3)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), y4))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), y4)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), y4))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), y4)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, y3), y4)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, y3), y4))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, y3), y4)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, y3), y4))), z3), F(z0, c_f(z1, c_f(c_f(y2, y3), y4))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(y3, y4)), y5))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, y3), y4), y5))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))), z3), F(c_f(a, b), c_f(c, c_f(c_f(y0, y1), y2))))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, y1))), z3), F(c_f(a, b), c_f(c, c_f(y0, y1))))
   F(c_f(a, b), c_f(c_f(c, z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, z2)), z3), F(c_f(a, b), c_f(c, z2)))
   F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))), z3), F(c_f(a, b), c_f(c, c_f(y0, c_f(y1, y2)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2)), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6)), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2)), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), z2)))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2)), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z2)), z3), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z2)), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), z2)), z3), F(c_f(a, b), c_f(c_f(c, y0), z2)))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), z2), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z2)), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), z2)))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))), z3), F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))), z3), F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), c_f(y2, y3)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(y2, y3))), z3), F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(y2, y3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4))), z3), F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(y3, y4))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(y3, y4)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(y3, y4))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(y3, y4)))), z3), F(z0, c_f(z1, c_f(y2, c_f(y3, y4)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))), z3), F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, y4), y5)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))), z3), F(z0, c_f(z1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))), z3), F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4))), z3), F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3))), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3))))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), c_f(y1, y2)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, y0), c_f(y1, y2))), z3), F(c_f(a, b), c_f(c_f(c, y0), c_f(y1, y2))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4))), z3), F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))), z3), F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8))))
   F(z0, c_f(c_f(z1, z2), c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), z3)) -> c10(F(c_f(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))), z3), F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7))))
   F(z0, c_f(c_f(z1, z2), c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)))) -> c10(F(c_f(z0, c_f(z1, z2)), c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))), F(z0, c_f(z1, z2)))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), z3)) -> c10(F(c_f(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))), z3), F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), z3)) -> c10(F(c_f(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6))), z3), F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5))), z3), F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4))), z3), F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, y0), y1), c_f(y2, y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(y2, y3))), z3), F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(y2, y3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5))), z3), F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, y1), y2), y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), y3))), z3), F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), y3))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3))), z3), F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3))))
   F(a, c_f(c_f(b, c_f(c, c_f(c_f(y0, y1), y2))), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))), z3), F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))))
   F(a, c_f(c_f(b, c_f(c, c_f(y0, y1))), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, c_f(y0, y1)))), z3), F(a, c_f(b, c_f(c, c_f(y0, y1)))))
   F(a, c_f(c_f(b, c_f(c, y0)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, y0))), z3), F(a, c_f(b, c_f(c, y0))))
   F(a, c_f(c_f(b, c_f(c, c_f(y0, c_f(y1, y2)))), z3)) -> c10(F(c_f(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))), z3), F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))), z3), F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), z3)) -> c10(F(c_f(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))), z3), F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3))), z3), F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, y1)), y2)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), y2))), z3), F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), y2))))
   F(a, c_f(c_f(b, c_f(c_f(c, y0), y1)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, y0), y1))), z3), F(a, c_f(b, c_f(c_f(c, y0), y1))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), z3)) -> c10(F(c_f(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3))), z3), F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, y3)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, y2), y3), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, y1), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), y2), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(y0, c_f(y1, y2)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, y1)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, y0), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, y0), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(z2, c_f(y3, y4))), z4)) -> c10(F(z0, c_f(z1, c_f(z2, c_f(y3, y4)))))
   F(z0, c_f(c_f(z1, c_f(z2, c_f(c_f(y3, y4), y5))), z4)) -> c10(F(z0, c_f(z1, c_f(z2, c_f(c_f(y3, y4), y5)))))
   F(z0, c_f(c_f(z1, c_f(z2, c_f(c_f(y3, c_f(y4, y5)), y6))), z4)) -> c10(F(z0, c_f(z1, c_f(z2, c_f(c_f(y3, c_f(y4, y5)), y6)))))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), z3))))
   F(z0, c_f(c_f(z1, c_f(z2, c_f(c_f(c_f(y3, y4), y5), y6))), z4)) -> c10(F(z0, c_f(z1, c_f(z2, c_f(c_f(c_f(y3, y4), y5), y6)))))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), z3))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), z3))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), z3))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), z3))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(z2, z3))))
   F(z0, c_f(c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), z3)), z4)) -> c10(F(z0, c_f(z1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), z3))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, y0), y1), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, y0), y1), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, y1), y2), z3)), z4)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, y1), y2), z3))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, c_f(y1, y2)), z3)), z4)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(y0, c_f(y1, y2)), z3))))
   F(a, c_f(c_f(b, c_f(c, c_f(c_f(y0, y1), y2))), z4)) -> c10(F(a, c_f(b, c_f(c, c_f(c_f(y0, y1), y2)))))
   F(a, c_f(c_f(b, c_f(c, c_f(y0, y1))), z4)) -> c10(F(a, c_f(b, c_f(c, c_f(y0, y1)))))
   F(a, c_f(c_f(b, c_f(c, z3)), z4)) -> c10(F(a, c_f(b, c_f(c, z3))))
   F(a, c_f(c_f(b, c_f(c, c_f(y0, c_f(y1, y2)))), z4)) -> c10(F(a, c_f(b, c_f(c, c_f(y0, c_f(y1, y2))))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3)), z4)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), z3))))
   F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3)), z4)) -> c10(F(c_f(a, b), c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), z3))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3)), z4)) -> c10(F(a, c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), z3))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, y1)), z3)), z4)) -> c10(F(a, c_f(b, c_f(c_f(c, c_f(y0, y1)), z3))))
   F(a, c_f(c_f(b, c_f(c_f(c, y0), z3)), z4)) -> c10(F(a, c_f(b, c_f(c_f(c, y0), z3))))
   F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3)), z4)) -> c10(F(a, c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, y4), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, y4), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, y5), y6))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, y5), y6)))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(y5, y6)), y7))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(y5, y6)), y7)))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, y5), y6), y7))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, y5), y6), y7)))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), z3)), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), c_f(y6, y7))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, y4), y5), c_f(y6, y7)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, y2), y3), c_f(y4, y5)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), c_f(y7, y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(y4, y5)), y6), c_f(y7, y8)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), c_f(y5, y6)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), c_f(y7, y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, y4), y5), y6), c_f(y7, y8)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), c_f(y5, y6)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), y2), c_f(y3, y4)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, y1), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, y1), c_f(y2, y3)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(y0, c_f(y1, y2)), c_f(y3, y4)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(y5, y6)))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(y5, y6))))))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(y3, y4))), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, c_f(y3, y4))), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), c_f(y6, y7))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(y4, y5)), c_f(y6, y7)))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(y2, y3)), c_f(y4, y5)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, y6), y7)))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, y6), y7))))))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(y3, y4), y5))), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), c_f(y7, y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, y5), y6)), c_f(y7, y8)))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), c_f(y5, y6)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8))))))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6))), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), c_f(y8, y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), c_f(y8, y9)))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), c_f(y6, y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), c_f(y8, y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), c_f(y8, y9)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), c_f(y6, y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8))))))
   F(z0, c_f(c_f(c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6))), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), c_f(y8, y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), c_f(y8, y9)))))
   F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), c_f(y6, y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), c_f(y8, y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), c_f(y8, y9)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), c_f(y6, y7)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), c_f(y4, y5)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), c_f(y4, y5)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), c_f(y3, y4)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, y1)), c_f(y2, y3)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, y0), c_f(y1, y2)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, y0), c_f(y1, y2)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), c_f(y3, y4)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, y6), y7)), y8))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, y6), y7)), y8)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, y4), y5)), y6)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, y5), y6)), y7), c_f(y8, y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, y5), y6)), y7), c_f(y8, y9)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, y3), y4)), y5), c_f(y6, y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)), y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(y5, c_f(y6, y7)), y8)), y9)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(y3, c_f(y4, y5)), y6)), y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), y8), c_f(y9, y10))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(y4, c_f(y5, y6)), y7)), y8), c_f(y9, y10)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(y3, y4)), y5)), y6), c_f(y7, y8)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8), y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(y4, c_f(y5, y6)), y7), y8), y9)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(y2, c_f(y3, y4)), y5), y6), y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), y8), c_f(y9, y10))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(y3, c_f(y4, y5)), y6), y7), y8), c_f(y9, y10)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(y1, c_f(y2, y3)), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)), y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(y4, c_f(c_f(c_f(y5, y6), y7), y8)), y9)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(y2, c_f(c_f(c_f(y3, y4), y5), y6)), y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), y8), c_f(y9, y10))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(y3, c_f(c_f(c_f(y4, y5), y6), y7)), y8), c_f(y9, y10)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(y1, c_f(c_f(c_f(y2, y3), y4), y5)), y6), c_f(y7, y8)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8), y9))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(z2, c_f(c_f(c_f(c_f(c_f(y4, y5), y6), y7), y8), y9)))))
   F(z0, c_f(c_f(c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(y1, c_f(c_f(c_f(c_f(c_f(y2, y3), y4), y5), y6), y7)), c_f(z2, z3))))
   F(z0, c_f(c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), y8), c_f(y9, y10))), z4)) -> c10(F(z0, c_f(c_f(y1, y2), c_f(c_f(c_f(c_f(c_f(c_f(y3, y4), y5), y6), y7), y8), c_f(y9, y10)))))
   F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3)), z4)) -> c10(F(z0, c_f(c_f(c_f(c_f(c_f(c_f(c_f(y1, y2), y3), y4), y5), y6), c_f(y7, y8)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4), c_f(y5, y6)), c_f(z2, z3))))
   F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), c_f(z2, z3)), z4)) -> c10(F(c_f(c_f(a, b), c), c_f(c_f(c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4), c_f(y5, y6)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3), c_f(y4, y5)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, y1)), y2), c_f(y3, y4)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c_f(c, y0), y1), c_f(y2, y3)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c_f(c, y0), y1), c_f(y2, y3)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3), c_f(y4, y5)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, y1), y2), y3)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(y0, c_f(y1, y2)), y3)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c, c_f(c_f(y0, y1), y2))), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c, c_f(c_f(y0, y1), y2))), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c, c_f(y0, y1))), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c, c_f(y0, y1))), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c, y0)), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c, y0)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c, c_f(y0, c_f(y1, y2)))), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c, c_f(y0, c_f(y1, y2)))), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(c_f(y0, y1), y2), y3), y4)), c_f(z2, z3))))
   F(c_f(a, b), c_f(c_f(c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3)), z4)) -> c10(F(c_f(a, b), c_f(c_f(c, c_f(c_f(c_f(y0, c_f(y1, y2)), y3), y4)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c_f(c, c_f(c_f(y0, y1), y2)), y3)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c_f(c, c_f(y0, y1)), y2)), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, y1)), y2)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c_f(c, y0), y1)), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c_f(c, y0), y1)), c_f(z2, z3))))
   F(a, c_f(c_f(c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3)), z4)) -> c10(F(a, c_f(c_f(b, c_f(c_f(c, c_f(y0, c_f(y1, y2))), y3)), c_f(z2, z3))))
K tuples:none
Defined Rule Symbols:   encArg_1, f_2

Defined Pair Symbols:   ENCARG_1, F_2, ENCODE_F_2

Compound Symbols:   c4_3, c4_2, c10_2, c10_1, c11_4, c11_1, c11_3, c11_2, c1_1