/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 91 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 0 ms]
    (12) typed CpxTrs
    (13) RewriteLemmaProof [LOWER BOUND(ID), 751 ms]
    (14) BOUNDS(1, INF)
(15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(16) CpxTRS
(17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(18) CpxRelTRS
    (19) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxRelTRS
    (21) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 6 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 14 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 26 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 6 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 6 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [ComplexityIfPolyImplication, 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), 61 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (52) CdtProblem
        (53) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 82 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (58) CdtProblem
        (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (60) CdtProblem
        (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (62) CdtProblem
        (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms]
        (64) CdtProblem
        (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 104 ms]
        (66) CdtProblem
        (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (68) CdtProblem
        (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 3 ms]
        (70) CdtProblem
        (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (72) CdtProblem
        (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (74) CdtProblem
        (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 113 ms]
        (76) CdtProblem
        (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (78) CdtProblem
        (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (80) CdtProblem
        (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 37 ms]
        (82) CdtProblem
        (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms]
        (84) CdtProblem
        (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (86) CdtProblem
        (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (88) CdtProblem
        (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 149 ms]
        (90) CdtProblem
        (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 238 ms]
        (92) CdtProblem
        (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 302 ms]
        (94) CdtProblem
        (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 345 ms]
        (96) CdtProblem
        (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 250 ms]
        (98) CdtProblem
        (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 539 ms]
        (100) CdtProblem
        (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 520 ms]
        (102) CdtProblem


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

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


The TRS R consists of the following rules:

   a(a(x1)) -> b(x1)
   a(a(a(x1))) -> a(b(a(x1)))
   a(b(a(x1))) -> b(b(b(x1)))
   a(a(a(a(x1)))) -> a(a(b(a(a(x1)))))
   a(a(b(a(x1)))) -> a(b(b(a(b(x1)))))
   a(b(a(a(x1)))) -> b(a(b(b(a(x1)))))
   a(b(b(a(x1)))) -> b(b(b(b(b(x1)))))
   a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1)))))))
   a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1)))))))
   a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1)))))))
   a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1)))))))
   a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1)))))))
   a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1)))))))
   a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1)))))))
   a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1)))))))

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

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

   encArg(b(x_1)) -> b(encArg(x_1))
   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))


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

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


The TRS R consists of the following rules:

   a(a(x1)) -> b(x1)
   a(a(a(x1))) -> a(b(a(x1)))
   a(b(a(x1))) -> b(b(b(x1)))
   a(a(a(a(x1)))) -> a(a(b(a(a(x1)))))
   a(a(b(a(x1)))) -> a(b(b(a(b(x1)))))
   a(b(a(a(x1)))) -> b(a(b(b(a(x1)))))
   a(b(b(a(x1)))) -> b(b(b(b(b(x1)))))
   a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1)))))))
   a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1)))))))
   a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1)))))))
   a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1)))))))
   a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1)))))))
   a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1)))))))
   a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1)))))))
   a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1)))))))

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

   encArg(b(x_1)) -> b(encArg(x_1))
   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   a(a(x1)) -> b(x1)
   a(a(a(x1))) -> a(b(a(x1)))
   a(b(a(x1))) -> b(b(b(x1)))
   a(a(a(a(x1)))) -> a(a(b(a(a(x1)))))
   a(a(b(a(x1)))) -> a(b(b(a(b(x1)))))
   a(b(a(a(x1)))) -> b(a(b(b(a(x1)))))
   a(b(b(a(x1)))) -> b(b(b(b(b(x1)))))
   a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1)))))))
   a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1)))))))
   a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1)))))))
   a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1)))))))
   a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1)))))))
   a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1)))))))
   a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1)))))))
   a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1)))))))

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

   encArg(b(x_1)) -> b(encArg(x_1))
   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))

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

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

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

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


The TRS R consists of the following rules:

   a(a(x1)) -> b(x1)
   a(a(a(x1))) -> a(b(a(x1)))
   a(b(a(x1))) -> b(b(b(x1)))
   a(a(a(a(x1)))) -> a(a(b(a(a(x1)))))
   a(a(b(a(x1)))) -> a(b(b(a(b(x1)))))
   a(b(a(a(x1)))) -> b(a(b(b(a(x1)))))
   a(b(b(a(x1)))) -> b(b(b(b(b(x1)))))
   a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1)))))))
   a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1)))))))
   a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1)))))))
   a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1)))))))
   a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1)))))))
   a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1)))))))
   a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1)))))))
   a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1)))))))

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

   encArg(b(x_1)) -> b(encArg(x_1))
   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   a(a(x1)) -> b(x1)
   a(a(a(x1))) -> a(b(a(x1)))
   a(b(a(x1))) -> b(b(b(x1)))
   a(a(a(a(x1)))) -> a(a(b(a(a(x1)))))
   a(a(b(a(x1)))) -> a(b(b(a(b(x1)))))
   a(b(a(a(x1)))) -> b(a(b(b(a(x1)))))
   a(b(b(a(x1)))) -> b(b(b(b(b(x1)))))
   a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1)))))))
   a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1)))))))
   a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1)))))))
   a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1)))))))
   a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1)))))))
   a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1)))))))
   a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1)))))))
   a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1)))))))

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

   encArg(b(x_1)) -> b(encArg(x_1))
   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))

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

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

(10)
Obligation:
TRS:
Rules:
a(a(x1)) -> b(x1)
a(a(a(x1))) -> a(b(a(x1)))
a(b(a(x1))) -> b(b(b(x1)))
a(a(a(a(x1)))) -> a(a(b(a(a(x1)))))
a(a(b(a(x1)))) -> a(b(b(a(b(x1)))))
a(b(a(a(x1)))) -> b(a(b(b(a(x1)))))
a(b(b(a(x1)))) -> b(b(b(b(b(x1)))))
a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1)))))))
a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1)))))))
a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1)))))))
a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1)))))))
a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1)))))))
a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1)))))))
a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1)))))))
a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1)))))))
encArg(b(x_1)) -> b(encArg(x_1))
encArg(cons_a(x_1)) -> a(encArg(x_1))
encode_a(x_1) -> a(encArg(x_1))
encode_b(x_1) -> b(encArg(x_1))

Types:
a :: b:cons_a -> b:cons_a
b :: b:cons_a -> b:cons_a
encArg :: b:cons_a -> b:cons_a
cons_a :: b:cons_a -> b:cons_a
encode_a :: b:cons_a -> b:cons_a
encode_b :: b:cons_a -> b:cons_a
hole_b:cons_a1_0 :: b:cons_a
gen_b:cons_a2_0 :: Nat -> b:cons_a

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

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

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

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

(12)
Obligation:
TRS:
Rules:
a(a(x1)) -> b(x1)
a(a(a(x1))) -> a(b(a(x1)))
a(b(a(x1))) -> b(b(b(x1)))
a(a(a(a(x1)))) -> a(a(b(a(a(x1)))))
a(a(b(a(x1)))) -> a(b(b(a(b(x1)))))
a(b(a(a(x1)))) -> b(a(b(b(a(x1)))))
a(b(b(a(x1)))) -> b(b(b(b(b(x1)))))
a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1)))))))
a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1)))))))
a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1)))))))
a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1)))))))
a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1)))))))
a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1)))))))
a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1)))))))
a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1)))))))
encArg(b(x_1)) -> b(encArg(x_1))
encArg(cons_a(x_1)) -> a(encArg(x_1))
encode_a(x_1) -> a(encArg(x_1))
encode_b(x_1) -> b(encArg(x_1))

Types:
a :: b:cons_a -> b:cons_a
b :: b:cons_a -> b:cons_a
encArg :: b:cons_a -> b:cons_a
cons_a :: b:cons_a -> b:cons_a
encode_a :: b:cons_a -> b:cons_a
encode_b :: b:cons_a -> b:cons_a
hole_b:cons_a1_0 :: b:cons_a
gen_b:cons_a2_0 :: Nat -> b:cons_a


Generator Equations:
gen_b:cons_a2_0(0) <=> hole_b:cons_a1_0
gen_b:cons_a2_0(+(x, 1)) <=> b(gen_b:cons_a2_0(x))


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

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

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

(13) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_b:cons_a2_0(+(1, n7697_0))) -> *3_0, rt in Omega(0)

Induction Base:
encArg(gen_b:cons_a2_0(+(1, 0)))

Induction Step:
encArg(gen_b:cons_a2_0(+(1, +(n7697_0, 1)))) ->_R^Omega(0)
b(encArg(gen_b:cons_a2_0(+(1, n7697_0)))) ->_IH
b(*3_0)

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

(14)
BOUNDS(1, INF)

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

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

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


The TRS R consists of the following rules:

   a(a(x1)) -> b(x1)
   a(a(a(x1))) -> a(b(a(x1)))
   a(b(a(x1))) -> b(b(b(x1)))
   a(a(a(a(x1)))) -> a(a(b(a(a(x1)))))
   a(a(b(a(x1)))) -> a(b(b(a(b(x1)))))
   a(b(a(a(x1)))) -> b(a(b(b(a(x1)))))
   a(b(b(a(x1)))) -> b(b(b(b(b(x1)))))
   a(a(a(a(a(x1))))) -> a(a(a(b(a(a(a(x1)))))))
   a(a(a(b(a(x1))))) -> a(a(b(b(a(a(b(x1)))))))
   a(a(b(a(a(x1))))) -> a(b(a(b(a(b(a(x1)))))))
   a(a(b(b(a(x1))))) -> a(b(b(b(a(b(b(x1)))))))
   a(b(a(a(a(x1))))) -> b(a(a(b(b(a(a(x1)))))))
   a(b(a(b(a(x1))))) -> b(a(b(b(b(a(b(x1)))))))
   a(b(b(a(a(x1))))) -> b(b(a(b(b(b(a(x1)))))))
   a(b(b(b(a(x1))))) -> b(b(b(b(b(b(b(x1)))))))
   encArg(b(x_1)) -> b(encArg(x_1))
   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   a(c_a(c_a(c_a(c_a(x1))))) -> a(a(a(b(a(a(a(x1)))))))
   a(c_a(c_a(x1))) -> a(b(a(x1)))
   a(b(c_a(c_a(c_a(x1))))) -> b(a(a(b(b(a(a(x1)))))))
   a(b(b(c_a(x1)))) -> b(b(b(b(b(x1)))))
   a(c_a(b(c_a(x1)))) -> a(b(b(a(b(x1)))))
   a(b(b(c_a(c_a(x1))))) -> b(b(a(b(b(b(a(x1)))))))
   a(c_a(c_a(c_a(x1)))) -> a(a(b(a(a(x1)))))
   a(b(c_a(b(c_a(x1))))) -> b(a(b(b(b(a(b(x1)))))))
   a(c_a(b(b(c_a(x1))))) -> a(b(b(b(a(b(b(x1)))))))
   a(c_a(x1)) -> b(x1)
   a(c_a(b(c_a(c_a(x1))))) -> a(b(a(b(a(b(a(x1)))))))
   a(b(b(b(c_a(x1))))) -> b(b(b(b(b(b(b(x1)))))))
   a(b(c_a(c_a(x1)))) -> b(a(b(b(a(x1)))))
   a(c_a(c_a(b(c_a(x1))))) -> a(a(b(b(a(a(b(x1)))))))
   a(b(c_a(x1))) -> b(b(b(x1)))

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

   encArg(b(x_1)) -> b(encArg(x_1))
   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   a(x0) -> c_a(x0)

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

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

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

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


The TRS R consists of the following rules:

   a(c_a(c_a(c_a(c_a(x1))))) -> a(a(a(b(a(a(a(x1)))))))
   a(c_a(c_a(x1))) -> a(b(a(x1)))
   a(b(c_a(c_a(c_a(x1))))) -> b(a(a(b(b(a(a(x1)))))))
   a(b(b(c_a(x1)))) -> b(b(b(b(b(x1)))))
   a(c_a(b(c_a(x1)))) -> a(b(b(a(b(x1)))))
   a(b(b(c_a(c_a(x1))))) -> b(b(a(b(b(b(a(x1)))))))
   a(c_a(c_a(c_a(x1)))) -> a(a(b(a(a(x1)))))
   a(b(c_a(b(c_a(x1))))) -> b(a(b(b(b(a(b(x1)))))))
   a(c_a(b(b(c_a(x1))))) -> a(b(b(b(a(b(b(x1)))))))
   a(c_a(x1)) -> b(x1)
   a(c_a(b(c_a(c_a(x1))))) -> a(b(a(b(a(b(a(x1)))))))
   a(b(b(b(c_a(x1))))) -> b(b(b(b(b(b(b(x1)))))))
   a(b(c_a(c_a(x1)))) -> b(a(b(b(a(x1)))))
   a(c_a(c_a(b(c_a(x1))))) -> a(a(b(b(a(a(b(x1)))))))
   a(b(c_a(x1))) -> b(b(b(x1)))

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

   encArg(b(x_1)) -> b(encArg(x_1))
   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   a(x0) -> c_a(x0)

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

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

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


The TRS R consists of the following rules:

   a(c_a(c_a(c_a(c_a(x1))))) -> a(a(a(b(a(a(a(x1))))))) [1]
   a(c_a(c_a(x1))) -> a(b(a(x1))) [1]
   a(b(c_a(c_a(c_a(x1))))) -> b(a(a(b(b(a(a(x1))))))) [1]
   a(b(b(c_a(x1)))) -> b(b(b(b(b(x1))))) [1]
   a(c_a(b(c_a(x1)))) -> a(b(b(a(b(x1))))) [1]
   a(b(b(c_a(c_a(x1))))) -> b(b(a(b(b(b(a(x1))))))) [1]
   a(c_a(c_a(c_a(x1)))) -> a(a(b(a(a(x1))))) [1]
   a(b(c_a(b(c_a(x1))))) -> b(a(b(b(b(a(b(x1))))))) [1]
   a(c_a(b(b(c_a(x1))))) -> a(b(b(b(a(b(b(x1))))))) [1]
   a(c_a(x1)) -> b(x1) [1]
   a(c_a(b(c_a(c_a(x1))))) -> a(b(a(b(a(b(a(x1))))))) [1]
   a(b(b(b(c_a(x1))))) -> b(b(b(b(b(b(b(x1))))))) [1]
   a(b(c_a(c_a(x1)))) -> b(a(b(b(a(x1))))) [1]
   a(c_a(c_a(b(c_a(x1))))) -> a(a(b(b(a(a(b(x1))))))) [1]
   a(b(c_a(x1))) -> b(b(b(x1))) [1]
   encArg(b(x_1)) -> b(encArg(x_1)) [0]
   encArg(cons_a(x_1)) -> a(encArg(x_1)) [0]
   encode_a(x_1) -> a(encArg(x_1)) [0]
   encode_b(x_1) -> b(encArg(x_1)) [0]
   a(x0) -> c_a(x0) [0]

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

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

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

   a(c_a(c_a(c_a(c_a(x1))))) -> a(a(a(b(a(a(a(x1))))))) [1]
   a(c_a(c_a(x1))) -> a(b(a(x1))) [1]
   a(b(c_a(c_a(c_a(x1))))) -> b(a(a(b(b(a(a(x1))))))) [1]
   a(b(b(c_a(x1)))) -> b(b(b(b(b(x1))))) [1]
   a(c_a(b(c_a(x1)))) -> a(b(b(a(b(x1))))) [1]
   a(b(b(c_a(c_a(x1))))) -> b(b(a(b(b(b(a(x1))))))) [1]
   a(c_a(c_a(c_a(x1)))) -> a(a(b(a(a(x1))))) [1]
   a(b(c_a(b(c_a(x1))))) -> b(a(b(b(b(a(b(x1))))))) [1]
   a(c_a(b(b(c_a(x1))))) -> a(b(b(b(a(b(b(x1))))))) [1]
   a(c_a(x1)) -> b(x1) [1]
   a(c_a(b(c_a(c_a(x1))))) -> a(b(a(b(a(b(a(x1))))))) [1]
   a(b(b(b(c_a(x1))))) -> b(b(b(b(b(b(b(x1))))))) [1]
   a(b(c_a(c_a(x1)))) -> b(a(b(b(a(x1))))) [1]
   a(c_a(c_a(b(c_a(x1))))) -> a(a(b(b(a(a(b(x1))))))) [1]
   a(b(c_a(x1))) -> b(b(b(x1))) [1]
   encArg(b(x_1)) -> b(encArg(x_1)) [0]
   encArg(cons_a(x_1)) -> a(encArg(x_1)) [0]
   encode_a(x_1) -> a(encArg(x_1)) [0]
   encode_b(x_1) -> b(encArg(x_1)) [0]
   a(x0) -> c_a(x0) [0]

The TRS has the following type information:
a :: c_a:b:cons_a -> c_a:b:cons_a
c_a :: c_a:b:cons_a -> c_a:b:cons_a
b :: c_a:b:cons_a -> c_a:b:cons_a
encArg :: c_a:b:cons_a -> c_a:b:cons_a
cons_a :: c_a:b:cons_a -> c_a:b:cons_a
encode_a :: c_a:b:cons_a -> c_a:b:cons_a
encode_b :: c_a:b:cons_a -> c_a:b:cons_a

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

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

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

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

(c) The following functions are completely defined:

   encArg_1
   encode_a_1
   encode_b_1
   a_1

Due to the following rules being added:

   encArg(v0) -> const [0]
   encode_a(v0) -> const [0]
   encode_b(v0) -> const [0]
   a(v0) -> const [0]

And the following fresh constants:    const

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

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

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

   a(c_a(c_a(c_a(c_a(x1))))) -> a(a(a(b(a(a(a(x1))))))) [1]
   a(c_a(c_a(x1))) -> a(b(a(x1))) [1]
   a(b(c_a(c_a(c_a(x1))))) -> b(a(a(b(b(a(a(x1))))))) [1]
   a(b(b(c_a(x1)))) -> b(b(b(b(b(x1))))) [1]
   a(c_a(b(c_a(x1)))) -> a(b(b(a(b(x1))))) [1]
   a(b(b(c_a(c_a(x1))))) -> b(b(a(b(b(b(a(x1))))))) [1]
   a(c_a(c_a(c_a(x1)))) -> a(a(b(a(a(x1))))) [1]
   a(b(c_a(b(c_a(x1))))) -> b(a(b(b(b(a(b(x1))))))) [1]
   a(c_a(b(b(c_a(x1))))) -> a(b(b(b(a(b(b(x1))))))) [1]
   a(c_a(x1)) -> b(x1) [1]
   a(c_a(b(c_a(c_a(x1))))) -> a(b(a(b(a(b(a(x1))))))) [1]
   a(b(b(b(c_a(x1))))) -> b(b(b(b(b(b(b(x1))))))) [1]
   a(b(c_a(c_a(x1)))) -> b(a(b(b(a(x1))))) [1]
   a(c_a(c_a(b(c_a(x1))))) -> a(a(b(b(a(a(b(x1))))))) [1]
   a(b(c_a(x1))) -> b(b(b(x1))) [1]
   encArg(b(x_1)) -> b(encArg(x_1)) [0]
   encArg(cons_a(x_1)) -> a(encArg(x_1)) [0]
   encode_a(x_1) -> a(encArg(x_1)) [0]
   encode_b(x_1) -> b(encArg(x_1)) [0]
   a(x0) -> c_a(x0) [0]
   encArg(v0) -> const [0]
   encode_a(v0) -> const [0]
   encode_b(v0) -> const [0]
   a(v0) -> const [0]

The TRS has the following type information:
a :: c_a:b:cons_a:const -> c_a:b:cons_a:const
c_a :: c_a:b:cons_a:const -> c_a:b:cons_a:const
b :: c_a:b:cons_a:const -> c_a:b:cons_a:const
encArg :: c_a:b:cons_a:const -> c_a:b:cons_a:const
cons_a :: c_a:b:cons_a:const -> c_a:b:cons_a:const
encode_a :: c_a:b:cons_a:const -> c_a:b:cons_a:const
encode_b :: c_a:b:cons_a:const -> c_a:b:cons_a:const
const :: c_a:b:cons_a:const

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

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

(28)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x1'))))))))) -> a(a(a(b(a(a(a(a(a(b(a(a(a(x1'))))))))))))) [2]
   a(c_a(c_a(c_a(c_a(c_a(c_a(x1''))))))) -> a(a(a(b(a(a(a(b(a(x1''))))))))) [2]
   a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(x11))))))))) -> a(a(a(b(a(a(b(a(a(b(b(a(a(x11))))))))))))) [2]
   a(c_a(c_a(c_a(c_a(b(b(c_a(x12)))))))) -> a(a(a(b(a(a(b(b(b(b(b(x12))))))))))) [2]
   a(c_a(c_a(c_a(c_a(c_a(b(c_a(x13)))))))) -> a(a(a(b(a(a(a(b(b(a(b(x13))))))))))) [2]
   a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(x14))))))))) -> a(a(a(b(a(a(b(b(a(b(b(b(a(x14))))))))))))) [2]
   a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x15)))))))) -> a(a(a(b(a(a(a(a(b(a(a(x15))))))))))) [2]
   a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(x16))))))))) -> a(a(a(b(a(a(b(a(b(b(b(a(b(x16))))))))))))) [2]
   a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(x17))))))))) -> a(a(a(b(a(a(a(b(b(b(a(b(b(x17))))))))))))) [2]
   a(c_a(c_a(c_a(c_a(c_a(x18)))))) -> a(a(a(b(a(a(b(x18))))))) [2]
   a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(x19))))))))) -> a(a(a(b(a(a(a(b(a(b(a(b(a(x19))))))))))))) [2]
   a(c_a(c_a(c_a(c_a(b(b(b(c_a(x110))))))))) -> a(a(a(b(a(a(b(b(b(b(b(b(b(x110))))))))))))) [2]
   a(c_a(c_a(c_a(c_a(b(c_a(c_a(x111)))))))) -> a(a(a(b(a(a(b(a(b(b(a(x111))))))))))) [2]
   a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(x112))))))))) -> a(a(a(b(a(a(a(a(b(b(a(a(b(x112))))))))))))) [2]
   a(c_a(c_a(c_a(c_a(b(c_a(x113))))))) -> a(a(a(b(a(a(b(b(b(x113))))))))) [2]
   a(c_a(c_a(c_a(c_a(x1))))) -> a(a(a(b(a(a(c_a(x1))))))) [1]
   a(c_a(c_a(c_a(c_a(x1))))) -> a(a(a(b(a(a(const)))))) [1]
   a(c_a(c_a(c_a(c_a(c_a(c_a(x114))))))) -> a(b(a(a(a(b(a(a(a(x114))))))))) [2]
   a(c_a(c_a(c_a(c_a(x115))))) -> a(b(a(b(a(x115))))) [2]
   a(c_a(c_a(b(c_a(c_a(c_a(x116))))))) -> a(b(b(a(a(b(b(a(a(x116))))))))) [2]
   a(c_a(c_a(b(b(c_a(x117)))))) -> a(b(b(b(b(b(b(x117))))))) [2]
   a(c_a(c_a(c_a(b(c_a(x118)))))) -> a(b(a(b(b(a(b(x118))))))) [2]
   a(c_a(c_a(b(b(c_a(c_a(x119))))))) -> a(b(b(b(a(b(b(b(a(x119))))))))) [2]
   a(c_a(c_a(c_a(c_a(c_a(x120)))))) -> a(b(a(a(b(a(a(x120))))))) [2]
   a(c_a(c_a(b(c_a(b(c_a(x121))))))) -> a(b(b(a(b(b(b(a(b(x121))))))))) [2]
   a(c_a(c_a(c_a(b(b(c_a(x122))))))) -> a(b(a(b(b(b(a(b(b(x122))))))))) [2]
   a(c_a(c_a(c_a(x123)))) -> a(b(b(x123))) [2]
   a(c_a(c_a(c_a(b(c_a(c_a(x124))))))) -> a(b(a(b(a(b(a(b(a(x124))))))))) [2]
   a(c_a(c_a(b(b(b(c_a(x125))))))) -> a(b(b(b(b(b(b(b(b(x125))))))))) [2]
   a(c_a(c_a(b(c_a(c_a(x126)))))) -> a(b(b(a(b(b(a(x126))))))) [2]
   a(c_a(c_a(c_a(c_a(b(c_a(x127))))))) -> a(b(a(a(b(b(a(a(b(x127))))))))) [2]
   a(c_a(c_a(b(c_a(x128))))) -> a(b(b(b(b(x128))))) [2]
   a(c_a(c_a(x1))) -> a(b(c_a(x1))) [1]
   a(c_a(c_a(x1))) -> a(b(const)) [1]
   a(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x129))))))))) -> b(a(a(b(b(a(a(a(a(b(a(a(a(x129))))))))))))) [2]
   a(b(c_a(c_a(c_a(c_a(c_a(x130))))))) -> b(a(a(b(b(a(a(b(a(x130))))))))) [2]
   a(b(c_a(c_a(c_a(b(c_a(c_a(c_a(x131))))))))) -> b(a(a(b(b(a(b(a(a(b(b(a(a(x131))))))))))))) [2]
   a(b(c_a(c_a(c_a(b(b(c_a(x132)))))))) -> b(a(a(b(b(a(b(b(b(b(b(x132))))))))))) [2]
   a(b(c_a(c_a(c_a(c_a(b(c_a(x133)))))))) -> b(a(a(b(b(a(a(b(b(a(b(x133))))))))))) [2]
   a(b(c_a(c_a(c_a(b(b(c_a(c_a(x134))))))))) -> b(a(a(b(b(a(b(b(a(b(b(b(a(x134))))))))))))) [2]
   a(b(c_a(c_a(c_a(c_a(c_a(c_a(x135)))))))) -> b(a(a(b(b(a(a(a(b(a(a(x135))))))))))) [2]
   a(b(c_a(c_a(c_a(b(c_a(b(c_a(x136))))))))) -> b(a(a(b(b(a(b(a(b(b(b(a(b(x136))))))))))))) [2]
   a(b(c_a(c_a(c_a(c_a(b(b(c_a(x137))))))))) -> b(a(a(b(b(a(a(b(b(b(a(b(b(x137))))))))))))) [2]
   a(b(c_a(c_a(c_a(c_a(x138)))))) -> b(a(a(b(b(a(b(x138))))))) [2]
   a(b(c_a(c_a(c_a(c_a(b(c_a(c_a(x139))))))))) -> b(a(a(b(b(a(a(b(a(b(a(b(a(x139))))))))))))) [2]
   a(b(c_a(c_a(c_a(b(b(b(c_a(x140))))))))) -> b(a(a(b(b(a(b(b(b(b(b(b(b(x140))))))))))))) [2]
   a(b(c_a(c_a(c_a(b(c_a(c_a(x141)))))))) -> b(a(a(b(b(a(b(a(b(b(a(x141))))))))))) [2]
   a(b(c_a(c_a(c_a(c_a(c_a(b(c_a(x142))))))))) -> b(a(a(b(b(a(a(a(b(b(a(a(b(x142))))))))))))) [2]
   a(b(c_a(c_a(c_a(b(c_a(x143))))))) -> b(a(a(b(b(a(b(b(b(x143))))))))) [2]
   a(b(c_a(c_a(c_a(x1))))) -> b(a(a(b(b(a(c_a(x1))))))) [1]
   a(b(c_a(c_a(c_a(x1))))) -> b(a(a(b(b(a(const)))))) [1]
   a(b(b(c_a(x1)))) -> b(b(b(b(b(x1))))) [1]
   a(c_a(b(c_a(c_a(c_a(c_a(x144))))))) -> a(b(b(b(a(a(b(b(a(a(x144)))))))))) [2]
   a(c_a(b(c_a(b(c_a(x145)))))) -> a(b(b(b(b(b(b(b(x145)))))))) [2]
   a(c_a(b(c_a(b(c_a(c_a(x146))))))) -> a(b(b(b(b(a(b(b(b(a(x146)))))))))) [2]
   a(c_a(b(c_a(c_a(b(c_a(x147))))))) -> a(b(b(b(a(b(b(b(a(b(x147)))))))))) [2]
   a(c_a(b(c_a(b(b(c_a(x148))))))) -> a(b(b(b(b(b(b(b(b(b(x148)))))))))) [2]
   a(c_a(b(c_a(c_a(c_a(x149)))))) -> a(b(b(b(a(b(b(a(x149)))))))) [2]
   a(c_a(b(c_a(c_a(x150))))) -> a(b(b(b(b(b(x150)))))) [2]
   a(c_a(b(c_a(x1)))) -> a(b(b(c_a(b(x1))))) [1]
   a(c_a(b(c_a(x1)))) -> a(b(b(const))) [1]
   a(b(b(c_a(c_a(c_a(c_a(c_a(c_a(x151))))))))) -> b(b(a(b(b(b(a(a(a(b(a(a(a(x151))))))))))))) [2]
   a(b(b(c_a(c_a(c_a(c_a(x152))))))) -> b(b(a(b(b(b(a(b(a(x152))))))))) [2]
   a(b(b(c_a(c_a(b(c_a(c_a(c_a(x153))))))))) -> b(b(a(b(b(b(b(a(a(b(b(a(a(x153))))))))))))) [2]
   a(b(b(c_a(c_a(b(b(c_a(x154)))))))) -> b(b(a(b(b(b(b(b(b(b(b(x154))))))))))) [2]
   a(b(b(c_a(c_a(c_a(b(c_a(x155)))))))) -> b(b(a(b(b(b(a(b(b(a(b(x155))))))))))) [2]
   a(b(b(c_a(c_a(b(b(c_a(c_a(x156))))))))) -> b(b(a(b(b(b(b(b(a(b(b(b(a(x156))))))))))))) [2]
   a(b(b(c_a(c_a(c_a(c_a(c_a(x157)))))))) -> b(b(a(b(b(b(a(a(b(a(a(x157))))))))))) [2]
   a(b(b(c_a(c_a(b(c_a(b(c_a(x158))))))))) -> b(b(a(b(b(b(b(a(b(b(b(a(b(x158))))))))))))) [2]
   a(b(b(c_a(c_a(c_a(b(b(c_a(x159))))))))) -> b(b(a(b(b(b(a(b(b(b(a(b(b(x159))))))))))))) [2]
   a(b(b(c_a(c_a(c_a(x160)))))) -> b(b(a(b(b(b(b(x160))))))) [2]
   a(b(b(c_a(c_a(c_a(b(c_a(c_a(x161))))))))) -> b(b(a(b(b(b(a(b(a(b(a(b(a(x161))))))))))))) [2]
   a(b(b(c_a(c_a(b(b(b(c_a(x162))))))))) -> b(b(a(b(b(b(b(b(b(b(b(b(b(x162))))))))))))) [2]
   a(b(b(c_a(c_a(b(c_a(c_a(x163)))))))) -> b(b(a(b(b(b(b(a(b(b(a(x163))))))))))) [2]
   a(b(b(c_a(c_a(c_a(c_a(b(c_a(x164))))))))) -> b(b(a(b(b(b(a(a(b(b(a(a(b(x164))))))))))))) [2]
   a(b(b(c_a(c_a(b(c_a(x165))))))) -> b(b(a(b(b(b(b(b(b(x165))))))))) [2]
   a(b(b(c_a(c_a(x1))))) -> b(b(a(b(b(b(c_a(x1))))))) [1]
   a(b(b(c_a(c_a(x1))))) -> b(b(a(b(b(b(const)))))) [1]
   a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x166)))))))) -> a(a(b(a(a(a(a(b(a(a(a(x166))))))))))) [2]
   a(c_a(c_a(c_a(c_a(c_a(x167)))))) -> a(a(b(a(a(b(a(x167))))))) [2]
   a(c_a(c_a(c_a(b(c_a(c_a(c_a(x168)))))))) -> a(a(b(a(b(a(a(b(b(a(a(x168))))))))))) [2]
   a(c_a(c_a(c_a(b(b(c_a(x169))))))) -> a(a(b(a(b(b(b(b(b(x169))))))))) [2]
   a(c_a(c_a(c_a(c_a(b(c_a(x170))))))) -> a(a(b(a(a(b(b(a(b(x170))))))))) [2]
   a(c_a(c_a(c_a(b(b(c_a(c_a(x171)))))))) -> a(a(b(a(b(b(a(b(b(b(a(x171))))))))))) [2]
   a(c_a(c_a(c_a(c_a(c_a(c_a(x172))))))) -> a(a(b(a(a(a(b(a(a(x172))))))))) [2]
   a(c_a(c_a(c_a(b(c_a(b(c_a(x173)))))))) -> a(a(b(a(b(a(b(b(b(a(b(x173))))))))))) [2]
   a(c_a(c_a(c_a(c_a(b(b(c_a(x174)))))))) -> a(a(b(a(a(b(b(b(a(b(b(x174))))))))))) [2]
   a(c_a(c_a(c_a(c_a(x175))))) -> a(a(b(a(b(x175))))) [2]
   a(c_a(c_a(c_a(c_a(b(c_a(c_a(x176)))))))) -> a(a(b(a(a(b(a(b(a(b(a(x176))))))))))) [2]
   a(c_a(c_a(c_a(b(b(b(c_a(x177)))))))) -> a(a(b(a(b(b(b(b(b(b(b(x177))))))))))) [2]
   a(c_a(c_a(c_a(b(c_a(c_a(x178))))))) -> a(a(b(a(b(a(b(b(a(x178))))))))) [2]
   a(c_a(c_a(c_a(c_a(c_a(b(c_a(x179)))))))) -> a(a(b(a(a(a(b(b(a(a(b(x179))))))))))) [2]
   a(c_a(c_a(c_a(b(c_a(x180)))))) -> a(a(b(a(b(b(b(x180))))))) [2]
   a(c_a(c_a(c_a(x1)))) -> a(a(b(a(c_a(x1))))) [1]
   a(c_a(c_a(c_a(x1)))) -> a(a(b(a(const)))) [1]
   a(b(c_a(b(c_a(c_a(c_a(c_a(x181)))))))) -> b(a(b(b(b(b(a(a(b(b(a(a(x181)))))))))))) [2]
   a(b(c_a(b(c_a(b(c_a(x182))))))) -> b(a(b(b(b(b(b(b(b(b(x182)))))))))) [2]
   a(b(c_a(b(c_a(b(c_a(c_a(x183)))))))) -> b(a(b(b(b(b(b(a(b(b(b(a(x183)))))))))))) [2]
   a(b(c_a(b(c_a(c_a(b(c_a(x184)))))))) -> b(a(b(b(b(b(a(b(b(b(a(b(x184)))))))))))) [2]
   a(b(c_a(b(c_a(b(b(c_a(x185)))))))) -> b(a(b(b(b(b(b(b(b(b(b(b(x185)))))))))))) [2]
   a(b(c_a(b(c_a(c_a(c_a(x186))))))) -> b(a(b(b(b(b(a(b(b(a(x186)))))))))) [2]
   a(b(c_a(b(c_a(c_a(x187)))))) -> b(a(b(b(b(b(b(b(x187)))))))) [2]
   a(b(c_a(b(c_a(x1))))) -> b(a(b(b(b(c_a(b(x1))))))) [1]
   a(b(c_a(b(c_a(x1))))) -> b(a(b(b(b(const))))) [1]
   a(c_a(b(b(c_a(c_a(x188)))))) -> a(b(b(b(b(b(b(b(b(x188))))))))) [2]
   a(c_a(b(b(c_a(c_a(c_a(x189))))))) -> a(b(b(b(b(b(a(b(b(b(a(x189))))))))))) [2]
   a(c_a(b(b(c_a(b(c_a(x190))))))) -> a(b(b(b(b(b(b(b(b(b(b(x190))))))))))) [2]
   a(c_a(b(b(c_a(x1))))) -> a(b(b(b(c_a(b(b(x1))))))) [1]
   a(c_a(b(b(c_a(x1))))) -> a(b(b(b(const)))) [1]
   a(c_a(x1)) -> b(x1) [1]
   a(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(x191))))))))) -> a(b(a(b(a(b(a(a(a(b(a(a(a(x191))))))))))))) [2]
   a(c_a(b(c_a(c_a(c_a(c_a(x192))))))) -> a(b(a(b(a(b(a(b(a(x192))))))))) [2]
   a(c_a(b(c_a(c_a(b(c_a(c_a(c_a(x193))))))))) -> a(b(a(b(a(b(b(a(a(b(b(a(a(x193))))))))))))) [2]
   a(c_a(b(c_a(c_a(b(b(c_a(x194)))))))) -> a(b(a(b(a(b(b(b(b(b(b(x194))))))))))) [2]
   a(c_a(b(c_a(c_a(c_a(b(c_a(x195)))))))) -> a(b(a(b(a(b(a(b(b(a(b(x195))))))))))) [2]
   a(c_a(b(c_a(c_a(b(b(c_a(c_a(x196))))))))) -> a(b(a(b(a(b(b(b(a(b(b(b(a(x196))))))))))))) [2]
   a(c_a(b(c_a(c_a(c_a(c_a(c_a(x197)))))))) -> a(b(a(b(a(b(a(a(b(a(a(x197))))))))))) [2]
   a(c_a(b(c_a(c_a(b(c_a(b(c_a(x198))))))))) -> a(b(a(b(a(b(b(a(b(b(b(a(b(x198))))))))))))) [2]
   a(c_a(b(c_a(c_a(c_a(b(b(c_a(x199))))))))) -> a(b(a(b(a(b(a(b(b(b(a(b(b(x199))))))))))))) [2]
   a(c_a(b(c_a(c_a(c_a(x1100)))))) -> a(b(a(b(a(b(b(x1100))))))) [2]
   a(c_a(b(c_a(c_a(c_a(b(c_a(c_a(x1101))))))))) -> a(b(a(b(a(b(a(b(a(b(a(b(a(x1101))))))))))))) [2]
   a(c_a(b(c_a(c_a(b(b(b(c_a(x1102))))))))) -> a(b(a(b(a(b(b(b(b(b(b(b(b(x1102))))))))))))) [2]
   a(c_a(b(c_a(c_a(b(c_a(c_a(x1103)))))))) -> a(b(a(b(a(b(b(a(b(b(a(x1103))))))))))) [2]
   a(c_a(b(c_a(c_a(c_a(c_a(b(c_a(x1104))))))))) -> a(b(a(b(a(b(a(a(b(b(a(a(b(x1104))))))))))))) [2]
   a(c_a(b(c_a(c_a(b(c_a(x1105))))))) -> a(b(a(b(a(b(b(b(b(x1105))))))))) [2]
   a(c_a(b(c_a(c_a(x1))))) -> a(b(a(b(a(b(c_a(x1))))))) [1]
   a(c_a(b(c_a(c_a(x1))))) -> a(b(a(b(a(b(const)))))) [1]
   a(b(b(b(c_a(x1))))) -> b(b(b(b(b(b(b(x1))))))) [1]
   a(b(c_a(c_a(c_a(c_a(c_a(c_a(x1106)))))))) -> b(a(b(b(a(a(a(b(a(a(a(x1106))))))))))) [2]
   a(b(c_a(c_a(c_a(c_a(x1107)))))) -> b(a(b(b(a(b(a(x1107))))))) [2]
   a(b(c_a(c_a(b(c_a(c_a(c_a(x1108)))))))) -> b(a(b(b(b(a(a(b(b(a(a(x1108))))))))))) [2]
   a(b(c_a(c_a(b(b(c_a(x1109))))))) -> b(a(b(b(b(b(b(b(b(x1109))))))))) [2]
   a(b(c_a(c_a(c_a(b(c_a(x1110))))))) -> b(a(b(b(a(b(b(a(b(x1110))))))))) [2]
   a(b(c_a(c_a(b(b(c_a(c_a(x1111)))))))) -> b(a(b(b(b(b(a(b(b(b(a(x1111))))))))))) [2]
   a(b(c_a(c_a(c_a(c_a(c_a(x1112))))))) -> b(a(b(b(a(a(b(a(a(x1112))))))))) [2]
   a(b(c_a(c_a(b(c_a(b(c_a(x1113)))))))) -> b(a(b(b(b(a(b(b(b(a(b(x1113))))))))))) [2]
   a(b(c_a(c_a(c_a(b(b(c_a(x1114)))))))) -> b(a(b(b(a(b(b(b(a(b(b(x1114))))))))))) [2]
   a(b(c_a(c_a(c_a(x1115))))) -> b(a(b(b(b(x1115))))) [2]
   a(b(c_a(c_a(c_a(b(c_a(c_a(x1116)))))))) -> b(a(b(b(a(b(a(b(a(b(a(x1116))))))))))) [2]
   a(b(c_a(c_a(b(b(b(c_a(x1117)))))))) -> b(a(b(b(b(b(b(b(b(b(b(x1117))))))))))) [2]
   a(b(c_a(c_a(b(c_a(c_a(x1118))))))) -> b(a(b(b(b(a(b(b(a(x1118))))))))) [2]
   a(b(c_a(c_a(c_a(c_a(b(c_a(x1119)))))))) -> b(a(b(b(a(a(b(b(a(a(b(x1119))))))))))) [2]
   a(b(c_a(c_a(b(c_a(x1120)))))) -> b(a(b(b(b(b(b(x1120))))))) [2]
   a(b(c_a(c_a(x1)))) -> b(a(b(b(c_a(x1))))) [1]
   a(b(c_a(c_a(x1)))) -> b(a(b(b(const)))) [1]
   a(c_a(c_a(b(c_a(c_a(c_a(c_a(x1121)))))))) -> a(a(b(b(a(b(a(a(b(b(a(a(x1121)))))))))))) [2]
   a(c_a(c_a(b(c_a(b(c_a(x1122))))))) -> a(a(b(b(a(b(b(b(b(b(x1122)))))))))) [2]
   a(c_a(c_a(b(c_a(b(c_a(c_a(x1123)))))))) -> a(a(b(b(a(b(b(a(b(b(b(a(x1123)))))))))))) [2]
   a(c_a(c_a(b(c_a(c_a(b(c_a(x1124)))))))) -> a(a(b(b(a(b(a(b(b(b(a(b(x1124)))))))))))) [2]
   a(c_a(c_a(b(c_a(b(b(c_a(x1125)))))))) -> a(a(b(b(a(b(b(b(b(b(b(b(x1125)))))))))))) [2]
   a(c_a(c_a(b(c_a(c_a(c_a(x1126))))))) -> a(a(b(b(a(b(a(b(b(a(x1126)))))))))) [2]
   a(c_a(c_a(b(c_a(c_a(x1127)))))) -> a(a(b(b(a(b(b(b(x1127)))))))) [2]
   a(c_a(c_a(b(c_a(x1))))) -> a(a(b(b(a(c_a(b(x1))))))) [1]
   a(c_a(c_a(b(c_a(x1))))) -> a(a(b(b(a(const))))) [1]
   a(b(c_a(x1))) -> b(b(b(x1))) [1]
   encArg(b(x_1)) -> b(encArg(x_1)) [0]
   encArg(cons_a(b(x_1'))) -> a(b(encArg(x_1'))) [0]
   encArg(cons_a(cons_a(x_1''))) -> a(a(encArg(x_1''))) [0]
   encArg(cons_a(x_1)) -> a(const) [0]
   encode_a(b(x_11)) -> a(b(encArg(x_11))) [0]
   encode_a(cons_a(x_12)) -> a(a(encArg(x_12))) [0]
   encode_a(x_1) -> a(const) [0]
   encode_b(x_1) -> b(encArg(x_1)) [0]
   a(x0) -> c_a(x0) [0]
   encArg(v0) -> const [0]
   encode_a(v0) -> const [0]
   encode_b(v0) -> const [0]
   a(v0) -> const [0]

The TRS has the following type information:
a :: c_a:b:cons_a:const -> c_a:b:cons_a:const
c_a :: c_a:b:cons_a:const -> c_a:b:cons_a:const
b :: c_a:b:cons_a:const -> c_a:b:cons_a:const
encArg :: c_a:b:cons_a:const -> c_a:b:cons_a:const
cons_a :: c_a:b:cons_a:const -> c_a:b:cons_a:const
encode_a :: c_a:b:cons_a:const -> c_a:b:cons_a:const
encode_b :: c_a:b:cons_a:const -> c_a:b:cons_a:const
const :: c_a:b:cons_a:const

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

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

   const => 0

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

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

   a(z) -{ 2 }-> a(a(a(1 + a(a(a(a(a(1 + a(a(a(x1'))))))))))) :|: x1' >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1')))))))
   a(z) -{ 2 }-> a(a(a(1 + a(a(a(a(1 + a(a(x15))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x15)))))), x15 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(a(a(1 + (1 + a(a(1 + x112)))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x112))))))), x112 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(a(1 + a(x1''))))))) :|: x1'' >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x1'')))))
   a(z) -{ 2 }-> a(a(a(1 + a(a(a(1 + a(1 + a(1 + a(x19))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x19))))))), x19 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(a(1 + (1 + a(1 + x13)))))))) :|: x13 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x13))))))
   a(z) -{ 2 }-> a(a(a(1 + a(a(a(1 + (1 + (1 + a(1 + (1 + x17)))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x17))))))), x17 >= 0
   a(z) -{ 1 }-> a(a(a(1 + a(a(0))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 1 }-> a(a(a(1 + a(a(1 + x1))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 2 }-> a(a(a(1 + a(a(1 + x18))))) :|: x18 >= 0, z = 1 + (1 + (1 + (1 + (1 + x18))))
   a(z) -{ 2 }-> a(a(a(1 + a(a(1 + a(a(1 + (1 + a(a(x11)))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x11))))))), x11 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(1 + a(1 + (1 + a(x111)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x111)))))), x111 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(1 + a(1 + (1 + (1 + a(1 + x16))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x16))))))), x16 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(1 + (1 + a(1 + (1 + (1 + a(x14)))))))))) :|: x14 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x14)))))))
   a(z) -{ 2 }-> a(a(a(1 + a(a(1 + (1 + (1 + x113))))))) :|: x113 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x113)))))
   a(z) -{ 2 }-> a(a(a(1 + a(a(1 + (1 + (1 + (1 + (1 + x12))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x12)))))), x12 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(1 + (1 + (1 + (1 + (1 + (1 + (1 + x110))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x110))))))), x110 >= 0
   a(z) -{ 2 }-> a(a(1 + a(a(a(a(1 + a(a(a(x166))))))))) :|: x166 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x166))))))
   a(z) -{ 2 }-> a(a(1 + a(a(a(1 + a(a(x172))))))) :|: x172 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x172)))))
   a(z) -{ 2 }-> a(a(1 + a(a(a(1 + (1 + a(a(1 + x179)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x179)))))), x179 >= 0
   a(z) -{ 2 }-> a(a(1 + a(a(1 + a(x167))))) :|: z = 1 + (1 + (1 + (1 + (1 + x167)))), x167 >= 0
   a(z) -{ 2 }-> a(a(1 + a(a(1 + a(1 + a(1 + a(x176))))))) :|: x176 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x176))))))
   a(z) -{ 2 }-> a(a(1 + a(a(1 + (1 + a(1 + x170)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x170))))), x170 >= 0
   a(z) -{ 2 }-> a(a(1 + a(a(1 + (1 + (1 + a(1 + (1 + x174)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x174)))))), x174 >= 0
   a(z) -{ 1 }-> a(a(1 + a(0))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   a(z) -{ 1 }-> a(a(1 + a(1 + x1))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   a(z) -{ 2 }-> a(a(1 + a(1 + x175))) :|: x175 >= 0, z = 1 + (1 + (1 + (1 + x175)))
   a(z) -{ 2 }-> a(a(1 + a(1 + a(a(1 + (1 + a(a(x168)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x168)))))), x168 >= 0
   a(z) -{ 2 }-> a(a(1 + a(1 + a(1 + (1 + a(x178)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x178))))), x178 >= 0
   a(z) -{ 2 }-> a(a(1 + a(1 + a(1 + (1 + (1 + a(1 + x173))))))) :|: x173 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x173))))))
   a(z) -{ 2 }-> a(a(1 + a(1 + (1 + a(1 + (1 + (1 + a(x171)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x171)))))), x171 >= 0
   a(z) -{ 2 }-> a(a(1 + a(1 + (1 + (1 + x180))))) :|: z = 1 + (1 + (1 + (1 + (1 + x180)))), x180 >= 0
   a(z) -{ 2 }-> a(a(1 + a(1 + (1 + (1 + (1 + (1 + x169))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x169))))), x169 >= 0
   a(z) -{ 2 }-> a(a(1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + x177))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x177)))))), x177 >= 0
   a(z) -{ 1 }-> a(a(1 + (1 + a(0)))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 2 }-> a(a(1 + (1 + a(1 + a(a(1 + (1 + a(a(x1121))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1121)))))), x1121 >= 0
   a(z) -{ 2 }-> a(a(1 + (1 + a(1 + a(1 + (1 + a(x1126))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x1126))))), x1126 >= 0
   a(z) -{ 2 }-> a(a(1 + (1 + a(1 + a(1 + (1 + (1 + a(1 + x1124)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1124)))))), x1124 >= 0
   a(z) -{ 1 }-> a(a(1 + (1 + a(1 + (1 + x1))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 2 }-> a(a(1 + (1 + a(1 + (1 + a(1 + (1 + (1 + a(x1123))))))))) :|: x1123 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1123))))))
   a(z) -{ 2 }-> a(a(1 + (1 + a(1 + (1 + (1 + x1127)))))) :|: z = 1 + (1 + (1 + (1 + (1 + x1127)))), x1127 >= 0
   a(z) -{ 2 }-> a(a(1 + (1 + a(1 + (1 + (1 + (1 + (1 + x1122)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x1122))))), x1122 >= 0
   a(z) -{ 2 }-> a(a(1 + (1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + x1125)))))))))) :|: x1125 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1125))))))
   a(z) -{ 2 }-> a(1 + a(a(a(1 + a(a(a(x114))))))) :|: x114 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x114)))))
   a(z) -{ 2 }-> a(1 + a(a(1 + a(a(x120))))) :|: x120 >= 0, z = 1 + (1 + (1 + (1 + (1 + x120))))
   a(z) -{ 2 }-> a(1 + a(a(1 + (1 + a(a(1 + x127)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x127))))), x127 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(x115))) :|: x115 >= 0, z = 1 + (1 + (1 + (1 + x115)))
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + a(a(a(1 + a(a(a(x191))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x191))))))), x191 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + a(a(1 + a(a(x197))))))) :|: x197 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x197))))))
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + a(a(1 + (1 + a(a(1 + x1104)))))))) :|: x1104 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1104)))))))
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + a(1 + a(x124))))) :|: x124 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x124)))))
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + a(1 + a(x192))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x192))))), x192 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + a(1 + a(1 + a(1 + a(x1101))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1101))))))), x1101 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + a(1 + (1 + a(1 + x195)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x195)))))), x195 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + a(1 + (1 + (1 + a(1 + (1 + x199)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x199))))))), x199 >= 0
   a(z) -{ 1 }-> a(1 + a(1 + a(1 + 0))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 1 }-> a(1 + a(1 + a(1 + (1 + x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + (1 + x1100)))) :|: z = 1 + (1 + (1 + (1 + (1 + x1100)))), x1100 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + (1 + a(a(1 + (1 + a(a(x193))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x193))))))), x193 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + (1 + a(1 + (1 + a(x1103))))))) :|: x1103 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1103))))))
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + (1 + a(1 + (1 + (1 + a(1 + x198)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x198))))))), x198 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + (1 + (1 + a(1 + (1 + (1 + a(x196))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x196))))))), x196 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + (1 + (1 + (1 + x1105)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x1105))))), x1105 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + (1 + (1 + (1 + (1 + (1 + x194)))))))) :|: x194 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x194))))))
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1102)))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1102))))))), x1102 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + (1 + a(1 + x118)))) :|: z = 1 + (1 + (1 + (1 + (1 + x118)))), x118 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + (1 + (1 + a(1 + (1 + x122)))))) :|: x122 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x122)))))
   a(z) -{ 1 }-> a(1 + 0) :|: z = 1 + (1 + x1), x1 >= 0
   a(z) -{ 1 }-> a(1 + (1 + x1)) :|: z = 1 + (1 + x1), x1 >= 0
   a(z) -{ 2 }-> a(1 + (1 + x123)) :|: x123 >= 0, z = 1 + (1 + (1 + x123))
   a(z) -{ 2 }-> a(1 + (1 + a(a(1 + (1 + a(a(x116))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x116))))), x116 >= 0
   a(z) -{ 2 }-> a(1 + (1 + a(1 + (1 + a(x126))))) :|: z = 1 + (1 + (1 + (1 + (1 + x126)))), x126 >= 0
   a(z) -{ 2 }-> a(1 + (1 + a(1 + (1 + (1 + a(1 + x121)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x121))))), x121 >= 0
   a(z) -{ 1 }-> a(1 + (1 + 0)) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   a(z) -{ 2 }-> a(1 + (1 + (1 + a(a(1 + (1 + a(a(x144)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x144))))), x144 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + a(1 + (1 + a(x149)))))) :|: x149 >= 0, z = 1 + (1 + (1 + (1 + (1 + x149))))
   a(z) -{ 2 }-> a(1 + (1 + (1 + a(1 + (1 + (1 + a(x119))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x119))))), x119 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + a(1 + (1 + (1 + a(1 + x147))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x147))))), x147 >= 0
   a(z) -{ 1 }-> a(1 + (1 + (1 + 0))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 1 }-> a(1 + (1 + (1 + (1 + x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + x128)))) :|: z = 1 + (1 + (1 + (1 + x128))), x128 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + a(1 + (1 + (1 + a(x146)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x146))))), x146 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (1 + x150))))) :|: x150 >= 0, z = 1 + (1 + (1 + (1 + x150)))
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (1 + a(1 + (1 + (1 + a(x189))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x189))))), x189 >= 0
   a(z) -{ 1 }-> a(1 + (1 + (1 + (1 + (1 + (1 + x1)))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (1 + (1 + x117)))))) :|: x117 >= 0, z = 1 + (1 + (1 + (1 + (1 + x117))))
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (1 + (1 + (1 + x145))))))) :|: x145 >= 0, z = 1 + (1 + (1 + (1 + (1 + x145))))
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x125)))))))) :|: x125 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x125)))))
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x188)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + x188)))), x188 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x148))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x148))))), x148 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x190)))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x190))))), x190 >= 0
   a(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   a(z) -{ 1 }-> 1 + x1 :|: x1 >= 0, z = 1 + x1
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(a(a(a(1 + a(a(a(x129)))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x129))))))), x129 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(a(a(1 + a(a(x135)))))))) :|: x135 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x135))))))
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(a(a(1 + (1 + a(a(1 + x142))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x142))))))), x142 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(a(1 + a(x130)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x130))))), x130 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(a(1 + a(1 + a(1 + a(x139)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x139))))))), x139 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(a(1 + (1 + a(1 + x133))))))) :|: x133 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x133))))))
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(a(1 + (1 + (1 + a(1 + (1 + x137))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x137))))))), x137 >= 0
   a(z) -{ 1 }-> 1 + a(a(1 + (1 + a(0)))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 1 }-> 1 + a(a(1 + (1 + a(1 + x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(1 + x138)))) :|: z = 1 + (1 + (1 + (1 + (1 + x138)))), x138 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(1 + a(a(1 + (1 + a(a(x131))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x131))))))), x131 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(1 + a(1 + (1 + a(x141))))))) :|: x141 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x141))))))
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(1 + a(1 + (1 + (1 + a(1 + x136)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x136))))))), x136 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(1 + (1 + a(1 + (1 + (1 + a(x134))))))))) :|: x134 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x134)))))))
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(1 + (1 + (1 + x143)))))) :|: x143 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x143)))))
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(1 + (1 + (1 + (1 + (1 + x132)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x132)))))), x132 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + x140)))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x140))))))), x140 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + a(a(a(1 + a(a(a(x1106)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1106)))))), x1106 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + a(a(1 + a(a(x1112)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x1112))))), x1112 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + a(a(1 + (1 + a(a(1 + x1119))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1119)))))), x1119 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + a(1 + a(x1107)))) :|: x1107 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1107))))
   a(z) -{ 2 }-> 1 + a(1 + (1 + a(1 + a(1 + a(1 + a(x1116)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1116)))))), x1116 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + a(1 + (1 + a(1 + x1110))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x1110))))), x1110 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + a(1 + (1 + (1 + a(1 + (1 + x1114))))))) :|: x1114 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1114))))))
   a(z) -{ 1 }-> 1 + a(1 + (1 + 0)) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   a(z) -{ 1 }-> 1 + a(1 + (1 + (1 + x1))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + x1115))) :|: x1115 >= 0, z = 1 + (1 + (1 + (1 + x1115)))
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + a(a(1 + (1 + a(a(x1108)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1108)))))), x1108 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + a(1 + (1 + a(x1118)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x1118))))), x1118 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + a(1 + (1 + (1 + a(1 + x1113))))))) :|: x1113 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1113))))))
   a(z) -{ 1 }-> 1 + a(1 + (1 + (1 + 0))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + a(a(1 + (1 + a(a(x181))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x181)))))), x181 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + a(1 + (1 + a(x186))))))) :|: x186 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x186)))))
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + a(1 + (1 + (1 + a(x1111)))))))) :|: x1111 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1111))))))
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + a(1 + (1 + (1 + a(1 + x184)))))))) :|: x184 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x184))))))
   a(z) -{ 1 }-> 1 + a(1 + (1 + (1 + (1 + (1 + x1))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + (1 + x1120))))) :|: z = 1 + (1 + (1 + (1 + (1 + x1120)))), x1120 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + (1 + a(1 + (1 + (1 + a(x183))))))))) :|: x183 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x183))))))
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + (1 + (1 + x187)))))) :|: x187 >= 0, z = 1 + (1 + (1 + (1 + (1 + x187))))
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + x1109))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x1109))))), x1109 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x182)))))))) :|: x182 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x182)))))
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1117))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1117)))))), x1117 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x185)))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x185)))))), x185 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + a(a(a(1 + a(a(a(x151)))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x151))))))), x151 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + a(a(1 + a(a(x157)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x157)))))), x157 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + a(a(1 + (1 + a(a(1 + x164))))))))) :|: x164 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x164)))))))
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + a(1 + a(x152)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x152))))), x152 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + a(1 + a(1 + a(1 + a(x161)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x161))))))), x161 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + a(1 + (1 + a(1 + x155))))))) :|: x155 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x155))))))
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + a(1 + (1 + (1 + a(1 + (1 + x159))))))))) :|: x159 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x159)))))))
   a(z) -{ 1 }-> 1 + (1 + a(1 + (1 + (1 + 0)))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 1 }-> 1 + (1 + a(1 + (1 + (1 + (1 + x1))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + (1 + x160))))) :|: z = 1 + (1 + (1 + (1 + (1 + x160)))), x160 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + (1 + a(a(1 + (1 + a(a(x153)))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x153))))))), x153 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + (1 + a(1 + (1 + a(x163)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x163)))))), x163 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + (1 + a(1 + (1 + (1 + a(1 + x158))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x158))))))), x158 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + (1 + (1 + a(1 + (1 + (1 + a(x156)))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x156))))))), x156 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + (1 + (1 + (1 + x165))))))) :|: x165 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x165)))))
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x154))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x154)))))), x154 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x162))))))))))) :|: x162 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x162)))))))
   a(z) -{ 1 }-> 1 + (1 + (1 + x1)) :|: z = 1 + (1 + x1), x1 >= 0
   a(z) -{ 1 }-> 1 + (1 + (1 + (1 + (1 + x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   a(z) -{ 1 }-> 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   encArg(z) -{ 0 }-> a(a(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0
   encArg(z) -{ 0 }-> a(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> a(1 + encArg(x_1')) :|: z = 1 + (1 + x_1'), x_1' >= 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_a(z) -{ 0 }-> a(a(encArg(x_12))) :|: z = 1 + x_12, x_12 >= 0
   encode_a(z) -{ 0 }-> a(0) :|: x_1 >= 0, z = x_1
   encode_a(z) -{ 0 }-> a(1 + encArg(x_11)) :|: x_11 >= 0, z = 1 + x_11
   encode_a(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_b(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_b(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1


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

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

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

   a(z) -{ 2 }-> a(a(a(1 + a(a(a(a(a(1 + a(a(a(z - 8))))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(a(a(1 + a(a(z - 7))))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(a(a(1 + (1 + a(a(1 + (z - 8))))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(a(1 + a(z - 6))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(a(1 + a(1 + a(1 + a(z - 8))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(a(1 + (1 + a(1 + (z - 7))))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(a(1 + (1 + (1 + a(1 + (1 + (z - 8))))))))))) :|: z - 8 >= 0
   a(z) -{ 1 }-> a(a(a(1 + a(a(0))))) :|: z - 4 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(1 + a(a(1 + (1 + a(a(z - 8)))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(1 + a(1 + (1 + a(z - 7)))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(1 + a(1 + (1 + (1 + a(1 + (z - 8)))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(1 + (z - 5)))))) :|: z - 5 >= 0
   a(z) -{ 1 }-> a(a(a(1 + a(a(1 + (z - 4)))))) :|: z - 4 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(1 + (1 + a(1 + (1 + (1 + a(z - 8)))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(1 + (1 + (1 + (z - 6)))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(1 + (1 + (1 + (1 + (1 + (z - 7)))))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(a(a(1 + a(a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 8)))))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> a(a(1 + a(a(a(a(1 + a(a(a(z - 7))))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(a(1 + a(a(a(1 + a(a(z - 6))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(a(1 + a(a(a(1 + (1 + a(a(1 + (z - 7))))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(a(1 + a(a(1 + a(z - 5))))) :|: z - 5 >= 0
   a(z) -{ 2 }-> a(a(1 + a(a(1 + a(1 + a(1 + a(z - 7))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(a(1 + a(a(1 + (1 + a(1 + (z - 6))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(a(1 + a(a(1 + (1 + (1 + a(1 + (1 + (z - 7))))))))) :|: z - 7 >= 0
   a(z) -{ 1 }-> a(a(1 + a(0))) :|: z - 3 >= 0
   a(z) -{ 2 }-> a(a(1 + a(1 + a(a(1 + (1 + a(a(z - 7)))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(a(1 + a(1 + a(1 + (1 + a(z - 6)))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(a(1 + a(1 + a(1 + (1 + (1 + a(1 + (z - 7)))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(a(1 + a(1 + (z - 4)))) :|: z - 4 >= 0
   a(z) -{ 1 }-> a(a(1 + a(1 + (z - 3)))) :|: z - 3 >= 0
   a(z) -{ 2 }-> a(a(1 + a(1 + (1 + a(1 + (1 + (1 + a(z - 7)))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(a(1 + a(1 + (1 + (1 + (z - 5)))))) :|: z - 5 >= 0
   a(z) -{ 2 }-> a(a(1 + a(1 + (1 + (1 + (1 + (1 + (z - 6)))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(a(1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 7)))))))))) :|: z - 7 >= 0
   a(z) -{ 1 }-> a(a(1 + (1 + a(0)))) :|: z - 4 >= 0
   a(z) -{ 2 }-> a(a(1 + (1 + a(1 + a(a(1 + (1 + a(a(z - 7))))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(a(1 + (1 + a(1 + a(1 + (1 + a(z - 6))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(a(1 + (1 + a(1 + a(1 + (1 + (1 + a(1 + (z - 7))))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(a(1 + (1 + a(1 + (1 + a(1 + (1 + (1 + a(z - 7))))))))) :|: z - 7 >= 0
   a(z) -{ 1 }-> a(a(1 + (1 + a(1 + (1 + (z - 4)))))) :|: z - 4 >= 0
   a(z) -{ 2 }-> a(a(1 + (1 + a(1 + (1 + (1 + (z - 5))))))) :|: z - 5 >= 0
   a(z) -{ 2 }-> a(a(1 + (1 + a(1 + (1 + (1 + (1 + (1 + (z - 6))))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(a(1 + (1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 7))))))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(1 + a(a(a(1 + a(a(a(z - 6))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(1 + a(a(1 + a(a(z - 5))))) :|: z - 5 >= 0
   a(z) -{ 2 }-> a(1 + a(a(1 + (1 + a(a(1 + (z - 6))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(z - 4))) :|: z - 4 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + a(a(a(1 + a(a(a(z - 8))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + a(a(1 + a(a(z - 7))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + a(a(1 + (1 + a(a(1 + (z - 8))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + a(1 + a(z - 6))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + a(1 + a(1 + a(1 + a(z - 8))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + a(1 + (1 + a(1 + (z - 7))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + a(1 + (1 + (1 + a(1 + (1 + (z - 8))))))))) :|: z - 8 >= 0
   a(z) -{ 1 }-> a(1 + a(1 + a(1 + 0))) :|: z - 4 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + (1 + a(a(1 + (1 + a(a(z - 8))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + (1 + a(1 + (1 + a(z - 7))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + (1 + a(1 + (1 + (1 + a(1 + (z - 8))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + (1 + (z - 5))))) :|: z - 5 >= 0
   a(z) -{ 1 }-> a(1 + a(1 + a(1 + (1 + (z - 4))))) :|: z - 4 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + (1 + (1 + a(1 + (1 + (1 + a(z - 8))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + (1 + (1 + (1 + (z - 6))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + (1 + (1 + (1 + (1 + (1 + (z - 7))))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 8))))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + (1 + a(1 + (z - 5))))) :|: z - 5 >= 0
   a(z) -{ 2 }-> a(1 + a(1 + (1 + (1 + a(1 + (1 + (z - 6))))))) :|: z - 6 >= 0
   a(z) -{ 1 }-> a(1 + 0) :|: z - 2 >= 0
   a(z) -{ 2 }-> a(1 + (1 + a(a(1 + (1 + a(a(z - 6))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(1 + (1 + a(1 + (1 + a(z - 5))))) :|: z - 5 >= 0
   a(z) -{ 2 }-> a(1 + (1 + a(1 + (1 + (1 + a(1 + (z - 6))))))) :|: z - 6 >= 0
   a(z) -{ 1 }-> a(1 + (1 + 0)) :|: z - 3 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (z - 3))) :|: z - 3 >= 0
   a(z) -{ 1 }-> a(1 + (1 + (z - 2))) :|: z - 2 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + a(a(1 + (1 + a(a(z - 6)))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + a(1 + (1 + a(z - 5)))))) :|: z - 5 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + a(1 + (1 + (1 + a(z - 6))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + a(1 + (1 + (1 + a(1 + (z - 6)))))))) :|: z - 6 >= 0
   a(z) -{ 1 }-> a(1 + (1 + (1 + 0))) :|: z - 4 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + a(1 + (1 + (1 + a(z - 6)))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (z - 4))))) :|: z - 4 >= 0
   a(z) -{ 1 }-> a(1 + (1 + (1 + (1 + (z - 3))))) :|: z - 3 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (1 + a(1 + (1 + (1 + a(z - 6))))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (1 + (z - 4)))))) :|: z - 4 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (1 + (1 + (z - 5))))))) :|: z - 5 >= 0
   a(z) -{ 1 }-> a(1 + (1 + (1 + (1 + (1 + (1 + (z - 4))))))) :|: z - 4 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 5)))))))) :|: z - 5 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 6))))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 5))))))))) :|: z - 5 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 6)))))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 6))))))))))) :|: z - 6 >= 0
   a(z) -{ 0 }-> 0 :|: z >= 0
   a(z) -{ 0 }-> 1 + z :|: z >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(a(a(a(1 + a(a(a(z - 8)))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(a(a(1 + a(a(z - 7)))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(a(a(1 + (1 + a(a(1 + (z - 8)))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(a(1 + a(z - 6)))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(a(1 + a(1 + a(1 + a(z - 8)))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(a(1 + (1 + a(1 + (z - 7)))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(a(1 + (1 + (1 + a(1 + (1 + (z - 8)))))))))) :|: z - 8 >= 0
   a(z) -{ 1 }-> 1 + a(a(1 + (1 + a(0)))) :|: z - 4 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(1 + a(a(1 + (1 + a(a(z - 8))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(1 + a(1 + (1 + a(z - 7))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(1 + a(1 + (1 + (1 + a(1 + (z - 8))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(1 + (z - 5))))) :|: z - 5 >= 0
   a(z) -{ 1 }-> 1 + a(a(1 + (1 + a(1 + (z - 4))))) :|: z - 4 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(1 + (1 + a(1 + (1 + (1 + a(z - 8))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(1 + (1 + (1 + (z - 6))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(1 + (1 + (1 + (1 + (1 + (z - 7))))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + a(a(1 + (1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 8))))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + a(a(a(1 + a(a(a(z - 7)))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + a(a(1 + a(a(z - 6)))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + a(a(1 + (1 + a(a(1 + (z - 7)))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + a(1 + a(z - 5)))) :|: z - 5 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + a(1 + a(1 + a(1 + a(z - 7)))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + a(1 + (1 + a(1 + (z - 6)))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + a(1 + (1 + (1 + a(1 + (1 + (z - 7)))))))) :|: z - 7 >= 0
   a(z) -{ 1 }-> 1 + a(1 + (1 + 0)) :|: z - 3 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + a(a(1 + (1 + a(a(z - 7)))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + a(1 + (1 + a(z - 6)))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + a(1 + (1 + (1 + a(1 + (z - 7)))))))) :|: z - 7 >= 0
   a(z) -{ 1 }-> 1 + a(1 + (1 + (1 + 0))) :|: z - 4 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (z - 4)))) :|: z - 4 >= 0
   a(z) -{ 1 }-> 1 + a(1 + (1 + (1 + (z - 3)))) :|: z - 3 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + a(a(1 + (1 + a(a(z - 7))))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + a(1 + (1 + a(z - 6))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + a(1 + (1 + (1 + a(z - 7)))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + a(1 + (1 + (1 + a(1 + (z - 7))))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + (1 + a(1 + (1 + (1 + a(z - 7))))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + (1 + (z - 5)))))) :|: z - 5 >= 0
   a(z) -{ 1 }-> 1 + a(1 + (1 + (1 + (1 + (1 + (z - 4)))))) :|: z - 4 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + (1 + (1 + (z - 5))))))) :|: z - 5 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 6)))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 6))))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 7)))))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 7))))))))))) :|: z - 7 >= 0
   a(z) -{ 1 }-> 1 + (z - 1) :|: z - 1 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + a(a(a(1 + a(a(a(z - 8)))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + a(a(1 + a(a(z - 7)))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + a(a(1 + (1 + a(a(1 + (z - 8)))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + a(1 + a(z - 6)))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + a(1 + a(1 + a(1 + a(z - 8)))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + a(1 + (1 + a(1 + (z - 7)))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + a(1 + (1 + (1 + a(1 + (1 + (z - 8)))))))))) :|: z - 8 >= 0
   a(z) -{ 1 }-> 1 + (1 + a(1 + (1 + (1 + 0)))) :|: z - 4 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + (1 + a(a(1 + (1 + a(a(z - 8)))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + (1 + a(1 + (1 + a(z - 7)))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + (1 + a(1 + (1 + (1 + a(1 + (z - 8)))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + (1 + (z - 5)))))) :|: z - 5 >= 0
   a(z) -{ 1 }-> 1 + (1 + a(1 + (1 + (1 + (1 + (z - 4)))))) :|: z - 4 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + (1 + (1 + a(1 + (1 + (1 + a(z - 8)))))))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + (1 + (1 + (1 + (z - 6)))))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 7)))))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> 1 + (1 + a(1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 8)))))))))))) :|: z - 8 >= 0
   a(z) -{ 1 }-> 1 + (1 + (1 + (z - 2))) :|: z - 2 >= 0
   a(z) -{ 1 }-> 1 + (1 + (1 + (1 + (1 + (z - 3))))) :|: z - 3 >= 0
   a(z) -{ 1 }-> 1 + (1 + (1 + (1 + (1 + (1 + (1 + (z - 4))))))) :|: z - 4 >= 0
   encArg(z) -{ 0 }-> a(a(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> a(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> a(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_a(z) -{ 0 }-> a(a(encArg(z - 1))) :|: z - 1 >= 0
   encode_a(z) -{ 0 }-> a(0) :|: z >= 0
   encode_a(z) -{ 0 }-> a(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_a(z) -{ 0 }-> 0 :|: z >= 0
   encode_b(z) -{ 0 }-> 0 :|: z >= 0
   encode_b(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0


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

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

   encArg(v0) -> null_encArg [0]
   encode_a(v0) -> null_encode_a [0]
   encode_b(v0) -> null_encode_b [0]
   a(v0) -> null_a [0]

And the following fresh constants:    null_encArg, null_encode_a, null_encode_b, null_a

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

(34)
Obligation:
Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is:

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

   a(c_a(c_a(c_a(c_a(x1))))) -> a(a(a(b(a(a(a(x1))))))) [1]
   a(c_a(c_a(x1))) -> a(b(a(x1))) [1]
   a(b(c_a(c_a(c_a(x1))))) -> b(a(a(b(b(a(a(x1))))))) [1]
   a(b(b(c_a(x1)))) -> b(b(b(b(b(x1))))) [1]
   a(c_a(b(c_a(x1)))) -> a(b(b(a(b(x1))))) [1]
   a(b(b(c_a(c_a(x1))))) -> b(b(a(b(b(b(a(x1))))))) [1]
   a(c_a(c_a(c_a(x1)))) -> a(a(b(a(a(x1))))) [1]
   a(b(c_a(b(c_a(x1))))) -> b(a(b(b(b(a(b(x1))))))) [1]
   a(c_a(b(b(c_a(x1))))) -> a(b(b(b(a(b(b(x1))))))) [1]
   a(c_a(x1)) -> b(x1) [1]
   a(c_a(b(c_a(c_a(x1))))) -> a(b(a(b(a(b(a(x1))))))) [1]
   a(b(b(b(c_a(x1))))) -> b(b(b(b(b(b(b(x1))))))) [1]
   a(b(c_a(c_a(x1)))) -> b(a(b(b(a(x1))))) [1]
   a(c_a(c_a(b(c_a(x1))))) -> a(a(b(b(a(a(b(x1))))))) [1]
   a(b(c_a(x1))) -> b(b(b(x1))) [1]
   encArg(b(x_1)) -> b(encArg(x_1)) [0]
   encArg(cons_a(x_1)) -> a(encArg(x_1)) [0]
   encode_a(x_1) -> a(encArg(x_1)) [0]
   encode_b(x_1) -> b(encArg(x_1)) [0]
   a(x0) -> c_a(x0) [0]
   encArg(v0) -> null_encArg [0]
   encode_a(v0) -> null_encode_a [0]
   encode_b(v0) -> null_encode_b [0]
   a(v0) -> null_a [0]

The TRS has the following type information:
a :: c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a -> c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a
c_a :: c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a -> c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a
b :: c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a -> c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a
encArg :: c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a -> c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a
cons_a :: c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a -> c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a
encode_a :: c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a -> c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a
encode_b :: c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a -> c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a
null_encArg :: c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a
null_encode_a :: c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a
null_encode_b :: c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a
null_a :: c_a:b:cons_a:null_encArg:null_encode_a:null_encode_b:null_a

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

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

   null_encArg => 0
   null_encode_a => 0
   null_encode_b => 0
   null_a => 0

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

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

   a(z) -{ 1 }-> a(a(a(1 + a(a(a(x1)))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 1 }-> a(a(1 + a(a(x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   a(z) -{ 1 }-> a(a(1 + (1 + a(a(1 + x1))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 1 }-> a(1 + a(x1)) :|: z = 1 + (1 + x1), x1 >= 0
   a(z) -{ 1 }-> a(1 + a(1 + a(1 + a(x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 1 }-> a(1 + (1 + a(1 + x1))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   a(z) -{ 1 }-> a(1 + (1 + (1 + a(1 + (1 + x1))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   a(z) -{ 1 }-> 1 + x1 :|: x1 >= 0, z = 1 + x1
   a(z) -{ 1 }-> 1 + a(a(1 + (1 + a(a(x1))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 1 }-> 1 + a(1 + (1 + a(x1))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   a(z) -{ 1 }-> 1 + a(1 + (1 + (1 + a(1 + x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 1 }-> 1 + (1 + a(1 + (1 + (1 + a(x1))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 1 }-> 1 + (1 + (1 + x1)) :|: z = 1 + (1 + x1), x1 >= 0
   a(z) -{ 1 }-> 1 + (1 + (1 + (1 + (1 + x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   a(z) -{ 1 }-> 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   encArg(z) -{ 0 }-> a(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_a(z) -{ 0 }-> a(encArg(x_1)) :|: x_1 >= 0, z = x_1
   encode_a(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_b(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_b(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1

Only complete derivations are relevant for the runtime complexity.

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

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0))
   ENCODE_A(z0) -> c2(A(encArg(z0)), ENCARG(z0))
   ENCODE_B(z0) -> c3(ENCARG(z0))
   A(z0) -> c4
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(z0))) -> c6(A(b(a(z0))), A(z0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
S tuples:
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(z0))) -> c6(A(b(a(z0))), A(z0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
K tuples:none
Defined Rule Symbols:   a_1, encArg_1, encode_a_1, encode_b_1

Defined Pair Symbols:   ENCARG_1, ENCODE_A_1, ENCODE_B_1, A_1

Compound Symbols:   c_1, c1_2, c2_2, c3_1, c4, c5_6, c6_2, c7_4, c8, c9_2, c10_2, c11_4, c12_2, c13_2, c14, c15_4, c16, c17_2, c18_4, c19


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

(39) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   ENCODE_B(z0) -> c3(ENCARG(z0))
Removed 1 trailing nodes:
   A(z0) -> c4

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0))
   ENCODE_A(z0) -> c2(A(encArg(z0)), ENCARG(z0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(z0))) -> c6(A(b(a(z0))), A(z0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
S tuples:
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(z0))) -> c6(A(b(a(z0))), A(z0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
K tuples:none
Defined Rule Symbols:   a_1, encArg_1, encode_a_1, encode_b_1

Defined Pair Symbols:   ENCARG_1, ENCODE_A_1, A_1

Compound Symbols:   c_1, c1_2, c2_2, c5_6, c6_2, c7_4, c8, c9_2, c10_2, c11_4, c12_2, c13_2, c14, c15_4, c16, c17_2, c18_4, c19


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

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(z0))) -> c6(A(b(a(z0))), A(z0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCODE_A(z0) -> c3(ENCARG(z0))
S tuples:
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(z0))) -> c6(A(b(a(z0))), A(z0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
K tuples:none
Defined Rule Symbols:   a_1, encArg_1, encode_a_1, encode_b_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c1_2, c5_6, c6_2, c7_4, c8, c9_2, c10_2, c11_4, c12_2, c13_2, c14, c15_4, c16, c17_2, c18_4, c19, c3_1


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

(43) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   ENCODE_A(z0) -> c3(ENCARG(z0))

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(z0))) -> c6(A(b(a(z0))), A(z0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
S tuples:
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(z0))) -> c6(A(b(a(z0))), A(z0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
K tuples:none
Defined Rule Symbols:   a_1, encArg_1, encode_a_1, encode_b_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c1_2, c5_6, c6_2, c7_4, c8, c9_2, c10_2, c11_4, c12_2, c13_2, c14, c15_4, c16, c17_2, c18_4, c19, c3_1


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

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

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(z0))) -> c6(A(b(a(z0))), A(z0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
S tuples:
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(z0))) -> c6(A(b(a(z0))), A(z0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c1_2, c5_6, c6_2, c7_4, c8, c9_2, c10_2, c11_4, c12_2, c13_2, c14, c15_4, c16, c17_2, c18_4, c19, c3_1


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

(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(z0))) -> c6(A(b(a(z0))), A(z0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
S tuples:
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(z0))) -> c6(A(b(a(z0))), A(z0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c5_6, c6_2, c7_4, c8, c9_2, c10_2, c11_4, c12_2, c13_2, c14, c15_4, c16, c17_2, c18_4, c19, c3_1, c1_2


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

(49) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0)) by 
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(c_a(c_a(z0))) -> c6(A(b(a(z0))), A(z0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
S tuples:
   A(c_a(c_a(z0))) -> c6(A(b(a(z0))), A(z0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c6_2, c7_4, c8, c9_2, c10_2, c11_4, c12_2, c13_2, c14, c15_4, c16, c17_2, c18_4, c19, c3_1, c1_2, c5_6


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(c_a(z0))) -> c6(A(b(a(z0))), A(z0)) by 
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(b(b(b(b(z0))))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(b(b(b(b(b(z0))))))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(b(b(b(z0))))), A(b(c_a(z0))))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(b(b(b(b(z0))))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(b(b(b(b(b(z0))))))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(b(b(b(z0))))), A(b(c_a(z0))))
S tuples:
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(b(b(b(b(z0))))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(b(b(b(b(b(z0))))))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(b(b(b(z0))))), A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c7_4, c8, c9_2, c10_2, c11_4, c12_2, c13_2, c14, c15_4, c16, c17_2, c18_4, c19, c3_1, c1_2, c5_6, c6_2


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

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
S tuples:
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c7_4, c8, c9_2, c10_2, c11_4, c12_2, c13_2, c14, c15_4, c16, c17_2, c18_4, c19, c3_1, c1_2, c5_6, c6_2, c6_1


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0)) by 
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0)))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c9_2, c10_2, c11_4, c12_2, c13_2, c14, c15_4, c16, c17_2, c18_4, c19, c3_1, c1_2, c5_6, c6_2, c6_1, c7_4


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

(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(b(c_a(z0)))) -> c9(A(b(b(a(b(z0))))), A(b(z0))) by 
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(b(b(b(b(b(z0)))))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(b(b(a(b(b(b(a(z0)))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(b(b(b(b(b(b(z0)))))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(b(b(b(b(z0)))))), A(b(c_a(z0))))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(b(b(b(b(b(z0)))))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(b(b(a(b(b(b(a(z0)))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(b(b(b(b(b(b(z0)))))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(b(b(b(b(z0)))))), A(b(c_a(z0))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(b(b(b(b(b(z0)))))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(b(b(a(b(b(b(a(z0)))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(b(b(b(b(b(b(z0)))))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(b(b(b(b(z0)))))), A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c10_2, c11_4, c12_2, c13_2, c14, c15_4, c16, c17_2, c18_4, c19, c3_1, c1_2, c5_6, c6_2, c6_1, c7_4, c9_2


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

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c10_2, c11_4, c12_2, c13_2, c14, c15_4, c16, c17_2, c18_4, c19, c3_1, c1_2, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1


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

(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(a(z0))))), A(z0)) by 
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(b(a(a(b(b(a(a(z0))))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(b(b(b(b(b(b(z0))))))))), A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(b(b(a(b(b(b(a(z0))))))))))), A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(b(a(b(b(b(a(b(z0))))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(b(b(b(b(z0))))), A(c_a(z0)))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(b(b(b(b(b(b(b(z0))))))))))), A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(b(b(b(a(b(b(a(z0))))))))), A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(b(b(b(b(b(z0))))))), A(b(c_a(z0))))

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(b(a(a(b(b(a(a(z0))))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(b(b(b(b(b(b(z0))))))))), A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(b(b(a(b(b(b(a(z0))))))))))), A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(b(a(b(b(b(a(b(z0))))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(b(b(b(b(z0))))), A(c_a(z0)))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(b(b(b(b(b(b(b(z0))))))))))), A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(b(b(b(a(b(b(a(z0))))))))), A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(b(b(b(b(b(z0))))))), A(b(c_a(z0))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(b(a(a(b(b(a(a(z0))))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(b(b(b(b(b(b(z0))))))))), A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(b(b(a(b(b(b(a(z0))))))))))), A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(b(a(b(b(b(a(b(z0))))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(b(b(b(b(z0))))), A(c_a(z0)))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(b(b(b(b(b(b(b(z0))))))))))), A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(b(b(b(a(b(b(a(z0))))))))), A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(b(b(b(b(b(z0))))))), A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c11_4, c12_2, c13_2, c14, c15_4, c16, c17_2, c18_4, c19, c3_1, c1_2, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2


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

(63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 8 trailing tuple parts
----------------------------------------

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c11_4, c12_2, c13_2, c14, c15_4, c16, c17_2, c18_4, c19, c3_1, c1_2, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1


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

(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0)) by 
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0)))
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c12_2, c13_2, c14, c15_4, c16, c17_2, c18_4, c19, c3_1, c1_2, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4


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

(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(b(c_a(b(c_a(z0))))) -> c12(A(b(b(b(a(b(z0)))))), A(b(z0))) by 
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(b(b(b(a(a(b(b(a(a(z0))))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(b(b(b(b(b(b(z0))))))))), A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(b(b(b(a(b(b(b(a(z0))))))))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(b(b(b(a(b(b(b(a(b(z0))))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(b(b(b(b(b(b(b(z0))))))))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(b(b(b(a(b(b(a(z0))))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(b(b(b(b(b(z0))))))), A(b(c_a(z0))))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(b(b(b(a(a(b(b(a(a(z0))))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(b(b(b(b(b(b(z0))))))))), A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(b(b(b(a(b(b(b(a(z0))))))))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(b(b(b(a(b(b(b(a(b(z0))))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(b(b(b(b(b(b(b(z0))))))))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(b(b(b(a(b(b(a(z0))))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(b(b(b(b(b(z0))))))), A(b(c_a(z0))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(b(b(b(a(a(b(b(a(a(z0))))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(b(b(b(b(b(b(z0))))))))), A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(b(b(b(a(b(b(b(a(z0))))))))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(b(b(b(a(b(b(b(a(b(z0))))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(b(b(b(b(b(b(b(z0))))))))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(b(b(b(a(b(b(a(z0))))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(b(b(b(b(b(z0))))))), A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c13_2, c14, c15_4, c16, c17_2, c18_4, c19, c3_1, c1_2, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2


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

(69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 7 trailing tuple parts
----------------------------------------

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0))))
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c13_2, c14, c15_4, c16, c17_2, c18_4, c19, c3_1, c1_2, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(b(b(c_a(z0))))) -> c13(A(b(b(b(a(b(b(z0))))))), A(b(b(z0)))) by 
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(b(b(b(b(b(b(z0))))))))), A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(b(b(b(a(b(b(b(a(z0))))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(b(b(b(b(b(b(b(z0))))))))))), A(b(b(b(c_a(z0))))))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(b(b(b(b(b(b(z0))))))))), A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(b(b(b(a(b(b(b(a(z0))))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(b(b(b(b(b(b(b(z0))))))))))), A(b(b(b(c_a(z0))))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(b(b(b(b(b(b(z0))))))))), A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(b(b(b(a(b(b(b(a(z0))))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(b(b(b(b(b(b(b(z0))))))))))), A(b(b(b(c_a(z0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c14, c15_4, c16, c17_2, c18_4, c19, c3_1, c1_2, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1, c13_2


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

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c14, c15_4, c16, c17_2, c18_4, c19, c3_1, c1_2, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1, c13_2, c13_1


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0)) by 
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0))
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c14, c16, c17_2, c18_4, c19, c3_1, c1_2, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1, c13_2, c13_1, c15_4


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

(77) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(b(c_a(c_a(z0)))) -> c17(A(b(b(a(z0)))), A(z0)) by 
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(b(b(b(b(b(z0)))))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(b(b(a(b(b(b(a(z0)))))))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(b(b(b(b(b(b(z0)))))))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(b(b(b(b(z0)))))), A(b(c_a(z0))))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(b(b(b(b(b(z0)))))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(b(b(a(b(b(b(a(z0)))))))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(b(b(b(b(b(b(z0)))))))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(b(b(b(b(z0)))))), A(b(c_a(z0))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(b(b(b(b(b(z0)))))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(b(b(a(b(b(b(a(z0)))))))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(b(b(b(b(b(b(z0)))))))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(b(b(b(b(z0)))))), A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c14, c16, c18_4, c19, c3_1, c1_2, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1, c13_2, c13_1, c15_4, c17_2


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

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0)))
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c14, c16, c18_4, c19, c3_1, c1_2, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1, c13_2, c13_1, c15_4, c17_2, c17_1


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

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(c_a(b(c_a(z0))))) -> c18(A(a(b(b(a(a(b(z0))))))), A(b(b(a(a(b(z0)))))), A(a(b(z0))), A(b(z0))) by 
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   ENCODE_A(z0) -> c3(A(encArg(z0)))
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c14, c16, c19, c3_1, c1_2, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1, c13_2, c13_1, c15_4, c17_2, c17_1, c18_4


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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_A(z0) -> c3(A(encArg(z0))) by 
   ENCODE_A(b(z0)) -> c3(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0))))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   ENCODE_A(b(z0)) -> c3(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c14, c16, c19, c1_2, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1, c13_2, c13_1, c15_4, c17_2, c17_1, c18_4, c3_1


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

(85) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_a(b(z0))) -> c1(A(b(encArg(z0))), ENCARG(b(z0))) by 
   ENCARG(cons_a(b(b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(b(b(z0))))
   ENCARG(cons_a(b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(b(cons_a(z0))))
   ENCARG(cons_a(b(x0))) -> c1(ENCARG(b(x0)))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   ENCODE_A(b(z0)) -> c3(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0))))
   ENCARG(cons_a(b(b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(b(b(z0))))
   ENCARG(cons_a(b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(b(cons_a(z0))))
   ENCARG(cons_a(b(x0))) -> c1(ENCARG(b(x0)))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c14, c16, c19, c1_2, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1, c13_2, c13_1, c15_4, c17_2, c17_1, c18_4, c3_1, c1_1


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0))) by 
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   ENCODE_A(b(z0)) -> c3(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0))))
   ENCARG(cons_a(b(b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(b(b(z0))))
   ENCARG(cons_a(b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(b(cons_a(z0))))
   ENCARG(cons_a(b(x0))) -> c1(ENCARG(b(x0)))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c14, c16, c19, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1, c13_2, c13_1, c15_4, c17_2, c17_1, c18_4, c3_1, c1_2, c1_1


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

(89) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0)) by 
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(c_a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(c_a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   ENCODE_A(b(z0)) -> c3(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0))))
   ENCARG(cons_a(b(b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(b(b(z0))))
   ENCARG(cons_a(b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(b(cons_a(z0))))
   ENCARG(cons_a(b(x0))) -> c1(ENCARG(b(x0)))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(c_a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(c_a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(c_a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(c_a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c14, c16, c19, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1, c13_2, c13_1, c15_4, c17_2, c17_1, c18_4, c3_1, c1_2, c1_1


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0)) by 
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(b(b(a(a(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(c_a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(c_a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   ENCODE_A(b(z0)) -> c3(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0))))
   ENCARG(cons_a(b(b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(b(b(z0))))
   ENCARG(cons_a(b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(b(cons_a(z0))))
   ENCARG(cons_a(b(x0))) -> c1(ENCARG(b(x0)))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(c_a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(c_a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(b(b(a(a(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(c_a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(c_a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(c_a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(c_a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(b(b(a(a(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(c_a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(c_a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c14, c16, c19, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1, c13_2, c13_1, c15_4, c17_2, c17_1, c18_4, c3_1, c1_2, c1_1


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(93) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0)) by 
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(b(b(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(c_a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(c_a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   ENCODE_A(b(z0)) -> c3(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0))))
   ENCARG(cons_a(b(b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(b(b(z0))))
   ENCARG(cons_a(b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(b(cons_a(z0))))
   ENCARG(cons_a(b(x0))) -> c1(ENCARG(b(x0)))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(c_a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(c_a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(b(b(a(a(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(c_a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(c_a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(b(b(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(c_a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(c_a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(c_a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(c_a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(b(b(a(a(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(c_a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(c_a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(b(b(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(c_a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(c_a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c14, c16, c19, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1, c13_2, c13_1, c15_4, c17_2, c17_1, c18_4, c3_1, c1_2, c1_1, c5_1


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

(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0)) by 
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(b(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(c_a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(c_a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   ENCODE_A(b(z0)) -> c3(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0))))
   ENCARG(cons_a(b(b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(b(b(z0))))
   ENCARG(cons_a(b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(b(cons_a(z0))))
   ENCARG(cons_a(b(x0))) -> c1(ENCARG(b(x0)))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(c_a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(c_a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(b(b(a(a(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(c_a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(c_a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(b(b(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(c_a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(c_a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(b(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(c_a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(c_a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(c_a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(c_a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(b(b(a(a(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(c_a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(c_a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(b(b(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(c_a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(c_a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(b(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(c_a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(c_a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c14, c16, c19, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1, c13_2, c13_1, c15_4, c17_2, c17_1, c18_4, c3_1, c1_2, c1_1, c5_1


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

(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0)) by 
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(a(c_a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(a(c_a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(a(c_a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(a(c_a(c_a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(a(z0)))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(a(b(z0)))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(a(z0)))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(b(z0)))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   ENCODE_A(b(z0)) -> c3(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0))))
   ENCARG(cons_a(b(b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(b(b(z0))))
   ENCARG(cons_a(b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(b(cons_a(z0))))
   ENCARG(cons_a(b(x0))) -> c1(ENCARG(b(x0)))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(c_a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(c_a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(b(b(a(a(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(c_a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(c_a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(b(b(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(c_a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(c_a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(b(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(c_a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(c_a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(a(z0)))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(a(b(z0)))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(a(z0)))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(b(z0)))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(c_a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(c_a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(b(b(a(a(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(c_a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(c_a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(b(b(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(c_a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(c_a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(b(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(c_a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(c_a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(a(z0)))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(a(b(z0)))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(a(z0)))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(b(z0)))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c14, c16, c19, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1, c13_2, c13_1, c15_4, c17_2, c17_1, c18_4, c3_1, c1_2, c1_1, c5_1, c5_3


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

(99) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0)))))) by 
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(c_a(a(b(a(a(a(a(a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(c_a(b(a(a(a(a(a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(c_a(a(a(a(a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(c_a(a(a(a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(c_a(a(a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(c_a(a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(a(c_a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(c_a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(c_a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(c_a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(b(b(b(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(b(a(b(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(a(b(a(a(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(a(b(b(a(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))), A(c_a(c_a(c_a(c_a(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   ENCODE_A(b(z0)) -> c3(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0))))
   ENCARG(cons_a(b(b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(b(b(z0))))
   ENCARG(cons_a(b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(b(cons_a(z0))))
   ENCARG(cons_a(b(x0))) -> c1(ENCARG(b(x0)))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(c_a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(c_a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(b(b(a(a(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(c_a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(c_a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(b(b(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(c_a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(c_a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(b(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(c_a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(c_a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(a(z0)))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(a(b(z0)))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(a(z0)))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(b(z0)))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(c_a(a(a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(c_a(a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(a(c_a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(c_a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(c_a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(c_a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(b(b(b(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(b(a(b(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(a(b(a(a(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(a(b(b(a(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))), A(c_a(c_a(c_a(c_a(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(c_a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(c_a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(b(b(a(a(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(c_a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(c_a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(b(b(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(c_a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(c_a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(b(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(c_a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(c_a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(a(z0)))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(a(b(z0)))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(a(z0)))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(b(z0)))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(c_a(a(a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(c_a(a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(a(c_a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(c_a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(c_a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(c_a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(b(b(b(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(b(a(b(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(a(b(a(a(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(a(b(b(a(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))), A(c_a(c_a(c_a(c_a(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c14, c16, c19, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1, c13_2, c13_1, c15_4, c17_2, c17_1, c18_4, c3_1, c1_2, c1_1, c5_1, c5_3, c5_5


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

(101) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0)))) by 
   A(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))) -> c5(A(c_a(a(b(a(a(a(b(a(x0))))))))), A(a(b(a(a(a(c_a(c_a(x0)))))))), A(b(a(a(a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(x0))))), A(a(c_a(c_a(x0)))), A(c_a(c_a(x0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))) -> c5(A(a(c_a(b(a(a(a(b(a(x0))))))))), A(a(b(a(a(a(c_a(c_a(x0)))))))), A(b(a(a(a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(x0))))), A(a(c_a(c_a(x0)))), A(c_a(c_a(x0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))) -> c5(A(a(a(b(c_a(a(a(b(a(x0))))))))), A(a(b(a(a(a(c_a(c_a(x0)))))))), A(b(a(a(a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(x0))))), A(a(c_a(c_a(x0)))), A(c_a(c_a(x0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))) -> c5(A(a(a(b(a(c_a(a(b(a(x0))))))))), A(a(b(a(a(a(c_a(c_a(x0)))))))), A(b(a(a(a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(x0))))), A(a(c_a(c_a(x0)))), A(c_a(c_a(x0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))) -> c5(A(a(a(b(a(a(c_a(b(a(x0))))))))), A(a(b(a(a(a(c_a(c_a(x0)))))))), A(b(a(a(a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(x0))))), A(a(c_a(c_a(x0)))), A(c_a(c_a(x0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(c_a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(a(a(a(b(a(a(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(b(a(a(b(b(a(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))), A(c_a(c_a(b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(b(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(b(b(c_a(z0)))))))))), A(a(a(c_a(c_a(b(b(c_a(z0)))))))), A(a(c_a(c_a(b(b(c_a(z0))))))), A(c_a(c_a(b(b(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(b(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(c_a(b(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(c_a(b(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(b(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(b(b(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(b(b(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(b(b(c_a(c_a(z0))))))))), A(a(c_a(c_a(b(b(c_a(c_a(z0)))))))), A(c_a(c_a(b(b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(b(a(a(b(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(b(b(a(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(b(c_a(b(c_a(z0))))))))))), A(a(a(c_a(c_a(b(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(b(c_a(z0)))))))), A(c_a(c_a(b(c_a(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(b(b(a(b(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(b(b(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(b(b(c_a(z0))))))))), A(a(c_a(c_a(c_a(b(b(c_a(z0)))))))), A(c_a(c_a(c_a(b(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(z0))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(b(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(b(b(b(b(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(b(b(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(b(b(b(c_a(z0))))))))))), A(a(a(c_a(c_a(b(b(b(c_a(z0))))))))), A(a(c_a(c_a(b(b(b(c_a(z0)))))))), A(c_a(c_a(b(b(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(c_a(z0))))))), A(c_a(c_a(b(c_a(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(a(a(b(b(a(a(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))), A(c_a(c_a(c_a(c_a(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(b(z0))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))) -> c5(A(a(b(a(a(a(c_a(c_a(x0)))))))), A(b(a(a(a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(x0))))), A(a(c_a(c_a(x0)))), A(c_a(c_a(x0))))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> a(a(a(b(a(a(a(z0)))))))
   a(c_a(c_a(z0))) -> a(b(a(z0)))
   a(b(c_a(c_a(c_a(z0))))) -> b(a(a(b(b(a(a(z0)))))))
   a(b(b(c_a(z0)))) -> b(b(b(b(b(z0)))))
   a(c_a(b(c_a(z0)))) -> a(b(b(a(b(z0)))))
   a(b(b(c_a(c_a(z0))))) -> b(b(a(b(b(b(a(z0)))))))
   a(c_a(c_a(c_a(z0)))) -> a(a(b(a(a(z0)))))
   a(b(c_a(b(c_a(z0))))) -> b(a(b(b(b(a(b(z0)))))))
   a(c_a(b(b(c_a(z0))))) -> a(b(b(b(a(b(b(z0)))))))
   a(c_a(z0)) -> b(z0)
   a(c_a(b(c_a(c_a(z0))))) -> a(b(a(b(a(b(a(z0)))))))
   a(b(b(b(c_a(z0))))) -> b(b(b(b(b(b(b(z0)))))))
   a(b(c_a(c_a(z0)))) -> b(a(b(b(a(z0)))))
   a(c_a(c_a(b(c_a(z0))))) -> a(a(b(b(a(a(b(z0)))))))
   a(b(c_a(z0))) -> b(b(b(z0)))
Tuples:
   ENCARG(b(z0)) -> c(ENCARG(z0))
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   ENCODE_A(b(z0)) -> c3(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c3(A(a(encArg(z0))))
   ENCARG(cons_a(b(b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(b(b(z0))))
   ENCARG(cons_a(b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(b(cons_a(z0))))
   ENCARG(cons_a(b(x0))) -> c1(ENCARG(b(x0)))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(c_a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(c_a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(b(b(a(a(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(c_a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(c_a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(b(b(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(c_a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(c_a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(b(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(c_a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(c_a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(a(z0)))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(a(b(z0)))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(a(z0)))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(b(z0)))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(c_a(a(a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(c_a(a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(a(c_a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(c_a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(c_a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(c_a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(b(b(b(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(b(a(b(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(a(b(a(a(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(a(b(b(a(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))), A(c_a(c_a(c_a(c_a(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))) -> c5(A(a(a(b(a(a(c_a(b(a(x0))))))))), A(a(b(a(a(a(c_a(c_a(x0)))))))), A(b(a(a(a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(x0))))), A(a(c_a(c_a(x0)))), A(c_a(c_a(x0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(c_a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(a(a(a(b(a(a(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(b(a(a(b(b(a(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))), A(c_a(c_a(b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(b(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(b(b(c_a(z0)))))))))), A(a(a(c_a(c_a(b(b(c_a(z0)))))))), A(a(c_a(c_a(b(b(c_a(z0))))))), A(c_a(c_a(b(b(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(b(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(c_a(b(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(c_a(b(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(b(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(b(b(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(b(b(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(b(b(c_a(c_a(z0))))))))), A(a(c_a(c_a(b(b(c_a(c_a(z0)))))))), A(c_a(c_a(b(b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(b(a(a(b(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(b(b(a(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(b(c_a(b(c_a(z0))))))))))), A(a(a(c_a(c_a(b(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(b(c_a(z0)))))))), A(c_a(c_a(b(c_a(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(b(b(a(b(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(b(b(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(b(b(c_a(z0))))))))), A(a(c_a(c_a(c_a(b(b(c_a(z0)))))))), A(c_a(c_a(c_a(b(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(z0))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(b(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(b(b(b(b(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(b(b(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(b(b(b(c_a(z0))))))))))), A(a(a(c_a(c_a(b(b(b(c_a(z0))))))))), A(a(c_a(c_a(b(b(b(c_a(z0)))))))), A(c_a(c_a(b(b(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(c_a(z0))))))), A(c_a(c_a(b(c_a(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(a(a(b(b(a(a(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))), A(c_a(c_a(c_a(c_a(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(b(z0))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))) -> c5(A(a(b(a(a(a(c_a(c_a(x0)))))))), A(b(a(a(a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(x0))))), A(a(c_a(c_a(x0)))), A(c_a(c_a(x0))))
S tuples:
   A(b(b(c_a(z0)))) -> c8
   A(c_a(z0)) -> c14
   A(b(b(b(c_a(z0))))) -> c16
   A(b(c_a(z0))) -> c19
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(z0))) -> c6(A(b(c_a(z0))), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c6(A(b(a(a(a(b(a(a(a(z0))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c6(A(b(a(b(a(z0))))), A(c_a(c_a(z0))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c6(A(b(b(a(a(b(b(a(a(z0))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c6(A(b(a(b(b(a(b(z0))))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(b(b(c_a(c_a(z0))))))) -> c6(A(b(b(b(a(b(b(b(a(z0))))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c6(A(b(a(a(b(a(a(z0))))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c6(A(b(b(a(b(b(b(a(b(z0))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c6(A(b(a(b(b(b(a(b(b(z0))))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(z0)))) -> c6(A(b(b(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c6(A(b(a(b(a(b(a(b(a(z0))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c6(A(b(b(a(b(b(a(z0))))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c6(A(b(a(a(b(b(a(a(b(z0))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(b(c_a(z0)))))) -> c6(A(b(b(c_a(z0)))))
   A(c_a(c_a(b(b(b(c_a(z0))))))) -> c6(A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(z0))))) -> c6(A(b(c_a(z0))))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(c_a(b(b(a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(x0))))) -> c7(A(a(b(b(c_a(a(x0)))))), A(b(b(a(a(x0))))), A(a(x0)), A(x0))
   A(b(c_a(c_a(c_a(z0))))) -> c7(A(a(b(b(a(c_a(z0)))))), A(b(b(a(a(z0))))), A(a(z0)), A(z0))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c7(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(b(b(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c7(A(a(b(b(a(a(b(a(z0)))))))), A(b(b(a(a(c_a(c_a(z0))))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c7(A(a(b(b(a(a(b(b(a(b(z0)))))))))), A(b(b(a(a(c_a(b(c_a(z0)))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(a(a(b(a(a(z0)))))))))), A(b(b(a(a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(b(b(a(a(c_a(b(b(c_a(z0))))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c7(A(a(b(b(a(b(z0)))))), A(b(b(a(a(c_a(z0)))))), A(a(c_a(z0))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c7(A(a(b(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(b(b(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c7(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c7(A(a(b(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(b(b(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c7(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(b(c_a(x0)))) -> c9(A(b(b(c_a(b(x0))))), A(b(x0)))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c9(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c9(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c9(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(z0)))))) -> c9(A(b(b(c_a(z0)))))
   A(c_a(b(c_a(b(c_a(c_a(z0))))))) -> c9(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(b(b(c_a(z0))))))) -> c9(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(z0))))) -> c9(A(b(c_a(z0))))
   A(b(b(c_a(c_a(z0))))) -> c10(A(b(b(b(c_a(z0))))), A(z0))
   A(b(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(a(a(b(a(a(a(z0))))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(z0))))))) -> c10(A(b(b(b(a(b(a(z0))))))), A(c_a(c_a(z0))))
   A(b(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c10(A(b(b(b(a(b(b(a(b(z0))))))))), A(c_a(b(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c10(A(b(b(b(a(a(b(a(a(z0))))))))), A(c_a(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c10(A(b(b(b(a(b(b(b(a(b(b(z0))))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c10(A(b(b(b(a(b(a(b(a(b(a(z0))))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c10(A(b(b(b(a(a(b(b(a(a(b(z0))))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c10(A(b(c_a(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(b(c_a(z0)))))))) -> c10(A(b(b(c_a(z0)))))
   A(b(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c10(A(b(b(c_a(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c10(A(b(c_a(b(c_a(z0))))))
   A(b(b(c_a(c_a(c_a(z0)))))) -> c10(A(c_a(z0)))
   A(b(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c10(A(b(b(b(c_a(z0))))))
   A(b(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c10(A(b(c_a(c_a(z0)))))
   A(b(b(c_a(c_a(b(c_a(z0))))))) -> c10(A(b(c_a(z0))))
   A(c_a(c_a(c_a(x0)))) -> c11(A(c_a(b(a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(x0)))) -> c11(A(a(b(c_a(a(x0))))), A(b(a(a(x0)))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(z0)))) -> c11(A(a(b(a(c_a(z0))))), A(b(a(a(z0)))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(a(a(b(b(a(a(z0))))))))))), A(b(a(a(b(c_a(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(c_a(z0))))))) -> c11(A(a(b(a(b(b(b(b(b(z0))))))))), A(b(a(a(b(b(c_a(z0))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(b(b(a(b(b(b(a(z0))))))))))), A(b(a(a(b(b(c_a(c_a(z0)))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(b(a(b(b(b(a(b(z0))))))))))), A(b(a(a(b(c_a(b(c_a(z0)))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(b(b(c_a(z0)))))))) -> c11(A(a(b(a(b(b(b(b(b(b(b(z0))))))))))), A(b(a(a(b(b(b(c_a(z0)))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(b(c_a(c_a(z0))))))) -> c11(A(a(b(a(b(a(b(b(a(z0))))))))), A(b(a(a(b(c_a(c_a(z0))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(b(c_a(z0)))))) -> c11(A(a(b(a(b(b(b(z0))))))), A(b(a(a(b(c_a(z0)))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(a(a(b(a(a(a(z0))))))))))), A(b(a(a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c11(A(a(b(a(a(b(a(z0))))))), A(b(a(a(c_a(c_a(z0)))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c11(A(a(b(a(a(b(b(a(b(z0))))))))), A(b(a(a(c_a(b(c_a(z0))))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c11(A(a(b(a(a(a(b(a(a(z0))))))))), A(b(a(a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c11(A(a(b(a(a(b(b(b(a(b(b(z0))))))))))), A(b(a(a(c_a(b(b(c_a(z0)))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c11(A(a(b(a(b(z0))))), A(b(a(a(c_a(z0))))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c11(A(a(b(a(a(b(a(b(a(b(a(z0))))))))))), A(b(a(a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c11(A(a(b(a(a(a(b(b(a(a(b(z0))))))))))), A(b(a(a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(x0))))) -> c12(A(b(b(b(c_a(b(x0)))))), A(b(x0)))
   A(b(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c12(A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(b(c_a(z0))))))) -> c12(A(b(b(c_a(z0)))))
   A(b(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c12(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c12(A(b(c_a(b(c_a(z0))))))
   A(b(c_a(b(c_a(b(b(c_a(z0)))))))) -> c12(A(b(b(b(c_a(z0))))))
   A(b(c_a(b(c_a(c_a(c_a(z0))))))) -> c12(A(b(c_a(c_a(z0)))))
   A(b(c_a(b(c_a(c_a(z0)))))) -> c12(A(b(c_a(z0))))
   A(c_a(b(b(c_a(x0))))) -> c13(A(b(b(b(c_a(b(b(x0))))))), A(b(b(x0))))
   A(c_a(b(b(c_a(c_a(z0)))))) -> c13(A(b(b(c_a(z0)))))
   A(c_a(b(b(c_a(c_a(c_a(z0))))))) -> c13(A(b(b(c_a(c_a(z0))))))
   A(c_a(b(b(c_a(b(c_a(z0))))))) -> c13(A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(c_a(b(a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(x0))))) -> c15(A(b(a(b(c_a(b(a(x0))))))), A(b(a(b(a(x0))))), A(b(a(x0))), A(x0))
   A(c_a(b(c_a(c_a(z0))))) -> c15(A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(a(z0))))), A(b(a(z0))), A(z0))
   A(c_a(b(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(a(b(b(a(a(z0))))))))))))), A(b(a(b(a(b(c_a(c_a(c_a(z0))))))))), A(b(a(b(c_a(c_a(c_a(z0))))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(z0))))))))))), A(b(a(b(a(b(b(c_a(z0)))))))), A(b(a(b(b(c_a(z0)))))), A(b(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(a(b(b(b(a(z0))))))))))))), A(b(a(b(a(b(b(c_a(c_a(z0))))))))), A(b(a(b(b(c_a(c_a(z0))))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(a(b(b(b(a(b(z0))))))))))))), A(b(a(b(a(b(c_a(b(c_a(z0))))))))), A(b(a(b(c_a(b(c_a(z0))))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(b(b(b(b(b(b(b(z0))))))))))))), A(b(a(b(a(b(b(b(c_a(z0))))))))), A(b(a(b(b(b(c_a(z0))))))), A(b(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(b(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(b(a(b(b(a(z0))))))))))), A(b(a(b(a(b(c_a(c_a(z0)))))))), A(b(a(b(c_a(c_a(z0)))))), A(b(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(b(c_a(z0))))))) -> c15(A(b(a(b(a(b(b(b(b(z0))))))))), A(b(a(b(a(b(c_a(z0))))))), A(b(a(b(c_a(z0))))), A(b(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(a(b(a(a(a(z0))))))))))))), A(b(a(b(a(c_a(c_a(c_a(c_a(z0))))))))), A(b(a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(z0))))))) -> c15(A(b(a(b(a(b(a(b(a(z0))))))))), A(b(a(b(a(c_a(c_a(z0))))))), A(b(a(c_a(c_a(z0))))), A(c_a(c_a(z0))))
   A(c_a(b(c_a(c_a(c_a(b(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(b(b(a(b(z0))))))))))), A(b(a(b(a(c_a(b(c_a(z0)))))))), A(b(a(c_a(b(c_a(z0)))))), A(c_a(b(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c15(A(b(a(b(a(b(a(a(b(a(a(z0))))))))))), A(b(a(b(a(c_a(c_a(c_a(z0)))))))), A(b(a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(b(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(b(b(a(b(b(z0))))))))))))), A(b(a(b(a(c_a(b(b(c_a(z0))))))))), A(b(a(c_a(b(b(c_a(z0))))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(z0)))))) -> c15(A(b(a(b(a(b(b(z0))))))), A(b(a(b(a(c_a(z0)))))), A(b(a(c_a(z0)))), A(c_a(z0)))
   A(c_a(b(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(b(a(b(a(b(a(z0))))))))))))), A(b(a(b(a(c_a(b(c_a(c_a(z0))))))))), A(b(a(c_a(b(c_a(c_a(z0))))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(b(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c15(A(b(a(b(a(b(a(a(b(b(a(a(b(z0))))))))))))), A(b(a(b(a(c_a(c_a(b(c_a(z0))))))))), A(b(a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(z0)))) -> c17(A(b(b(c_a(z0)))), A(z0))
   A(b(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(a(a(a(b(a(a(a(z0)))))))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(c_a(z0)))))) -> c17(A(b(b(a(b(a(z0)))))), A(c_a(c_a(z0))))
   A(b(c_a(c_a(b(c_a(c_a(c_a(z0)))))))) -> c17(A(b(b(b(a(a(b(b(a(a(z0)))))))))), A(b(c_a(c_a(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(c_a(z0))))))) -> c17(A(b(b(a(b(b(a(b(z0)))))))), A(c_a(b(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c17(A(b(b(a(a(b(a(a(z0)))))))), A(c_a(c_a(c_a(z0)))))
   A(b(c_a(c_a(b(c_a(b(c_a(z0)))))))) -> c17(A(b(b(b(a(b(b(b(a(b(z0)))))))))), A(b(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c17(A(b(b(a(b(b(b(a(b(b(z0)))))))))), A(c_a(b(b(c_a(z0))))))
   A(b(c_a(c_a(c_a(z0))))) -> c17(A(b(b(b(z0)))), A(c_a(z0)))
   A(b(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c17(A(b(b(a(b(a(b(a(b(a(z0)))))))))), A(c_a(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(c_a(z0))))))) -> c17(A(b(b(b(a(b(b(a(z0)))))))), A(b(c_a(c_a(z0)))))
   A(b(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c17(A(b(b(a(a(b(b(a(a(b(z0)))))))))), A(c_a(c_a(b(c_a(z0))))))
   A(b(c_a(c_a(b(b(c_a(z0))))))) -> c17(A(b(b(c_a(z0)))))
   A(b(c_a(c_a(b(b(c_a(c_a(z0)))))))) -> c17(A(b(b(c_a(c_a(z0))))))
   A(b(c_a(c_a(b(b(b(c_a(z0)))))))) -> c17(A(b(b(b(c_a(z0))))))
   A(b(c_a(c_a(b(c_a(z0)))))) -> c17(A(b(c_a(z0))))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(c_a(b(b(a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(c_a(a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(x0))))) -> c18(A(a(b(b(a(c_a(b(x0))))))), A(b(b(a(a(b(x0)))))), A(a(b(x0))), A(b(x0)))
   A(c_a(c_a(b(c_a(b(c_a(z0))))))) -> c18(A(a(b(b(a(b(b(b(b(b(z0)))))))))), A(b(b(a(a(b(b(c_a(z0)))))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(b(c_a(b(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(a(b(b(b(a(z0)))))))))))), A(b(b(a(a(b(b(c_a(c_a(z0))))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(b(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(b(b(b(b(b(b(z0)))))))))))), A(b(b(a(a(b(b(b(c_a(z0))))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(a(b(b(a(a(z0)))))))))))), A(b(b(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(b(c_a(z0)))))))) -> c18(A(a(b(b(a(b(a(b(b(b(a(b(z0)))))))))))), A(b(b(a(a(b(c_a(b(c_a(z0))))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(b(c_a(c_a(c_a(z0))))))) -> c18(A(a(b(b(a(b(a(b(b(a(z0)))))))))), A(b(b(a(a(b(c_a(c_a(z0)))))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(b(c_a(c_a(z0)))))) -> c18(A(a(b(b(a(b(b(b(z0)))))))), A(b(b(a(a(b(c_a(z0))))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(c_a(b(a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(c_a(a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(c_a(a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(c_a(a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(c_a(a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(c_a(a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(c_a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(b(b(a(a(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(c_a(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(c_a(b(a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(c_a(b(a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(c_a(b(a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(c_a(b(a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(c_a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(c_a(b(a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(b(b(a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(c_a(c_a(a(x0))))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(c_a(a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(c_a(a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(c_a(a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(c_a(a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(c_a(a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(a(b(b(a(x0)))))), A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))), A(a(x0)), A(x0))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(c_a(c_a(z0))))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(a(b(a(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(a(b(a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(a(b(b(a(a(z0))))))))))))), A(a(b(a(a(a(b(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(b(c_a(c_a(c_a(z0))))))))), A(a(a(b(c_a(c_a(c_a(z0))))))), A(a(b(c_a(c_a(c_a(z0)))))), A(b(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(z0))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(b(b(a(b(z0))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(a(b(b(b(a(z0))))))))))))), A(a(b(a(a(a(b(b(c_a(c_a(z0)))))))))), A(b(a(a(a(b(b(c_a(c_a(z0))))))))), A(a(a(b(b(c_a(c_a(z0))))))), A(a(b(b(c_a(c_a(z0)))))), A(b(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(a(a(b(a(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(b(c_a(b(c_a(z0)))))))))), A(b(a(a(a(b(c_a(b(c_a(z0))))))))), A(a(a(b(c_a(b(c_a(z0))))))), A(a(b(c_a(b(c_a(z0)))))), A(b(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(b(b(a(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(b(b(c_a(z0)))))))))), A(b(a(a(a(c_a(b(b(c_a(z0))))))))), A(a(a(c_a(b(b(c_a(z0))))))), A(a(c_a(b(b(c_a(z0)))))), A(c_a(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(c_a(b(z0))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(b(a(b(a(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(b(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(b(c_a(c_a(z0))))))))), A(a(a(c_a(b(c_a(c_a(z0))))))), A(a(c_a(b(c_a(c_a(z0)))))), A(c_a(b(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(b(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(b(b(b(c_a(z0)))))))))), A(b(a(a(a(b(b(b(c_a(z0))))))))), A(a(a(b(b(b(c_a(z0))))))), A(a(b(b(b(c_a(z0)))))), A(b(b(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(c_a(b(a(b(b(a(z0))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(c_a(a(a(b(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(c_a(b(b(b(z0))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(a(b(a(a(a(z0)))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c5(A(a(a(b(a(a(b(a(z0)))))))), A(a(b(a(a(a(c_a(z0))))))), A(b(a(a(a(c_a(z0)))))), A(a(a(c_a(z0)))), A(a(c_a(z0))), A(c_a(z0)))
   A(c_a(c_a(c_a(c_a(b(c_a(z0))))))) -> c5(A(a(a(b(a(a(b(b(a(b(z0)))))))))), A(a(b(a(a(a(b(c_a(z0)))))))), A(b(a(a(a(b(c_a(z0))))))), A(a(a(b(c_a(z0))))), A(a(b(c_a(z0)))), A(b(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(a(a(z0)))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(b(b(a(b(b(z0)))))))))))), A(a(b(a(a(a(b(b(c_a(z0))))))))), A(b(a(a(a(b(b(c_a(z0)))))))), A(a(a(b(b(c_a(z0)))))), A(a(b(b(c_a(z0))))), A(b(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(z0))))) -> c5(A(a(a(b(a(b(z0)))))), A(a(b(a(a(a(z0)))))), A(b(a(a(a(z0))))), A(a(a(z0))), A(a(z0)), A(z0))
   A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(b(a(b(a(b(a(z0)))))))))))), A(a(b(a(a(a(b(c_a(c_a(z0))))))))), A(b(a(a(a(b(c_a(c_a(z0)))))))), A(a(a(b(c_a(c_a(z0)))))), A(a(b(c_a(c_a(z0))))), A(b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), A(a(b(a(a(a(c_a(b(c_a(z0))))))))), A(b(a(a(a(c_a(b(c_a(z0)))))))), A(a(a(c_a(b(c_a(z0)))))), A(a(c_a(b(c_a(z0))))), A(c_a(b(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(x0))))) -> c5(A(a(b(a(a(a(x0)))))), A(b(a(a(a(x0))))), A(a(a(x0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(c_a(a(a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(c_a(a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(a(c_a(b(a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(c_a(a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(c_a(a(x0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(c_a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(a(a(b(a(a(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(a(a(b(b(a(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(b(b(b(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(b(a(b(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(a(b(b(b(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(a(b(a(a(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(a(b(b(b(a(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(b(b(a(b(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(b(a(b(a(b(a(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(b(b(b(b(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(a(b(b(a(z0))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))), A(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(a(a(b(b(a(a(b(z0))))))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(a(a(b(a(a(b(b(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))), A(c_a(c_a(c_a(c_a(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))))) -> c5(A(a(b(a(a(a(c_a(c_a(c_a(c_a(x0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(x0))))))))), A(a(a(c_a(c_a(c_a(c_a(x0))))))), A(a(c_a(c_a(c_a(c_a(x0)))))), A(c_a(c_a(c_a(c_a(x0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))) -> c5(A(a(a(b(a(a(c_a(b(a(x0))))))))), A(a(b(a(a(a(c_a(c_a(x0)))))))), A(b(a(a(a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(x0))))), A(a(c_a(c_a(x0)))), A(c_a(c_a(x0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))) -> c5(A(a(a(b(a(a(a(b(c_a(z0))))))))), A(a(b(a(a(a(c_a(c_a(z0)))))))), A(b(a(a(a(c_a(c_a(z0))))))), A(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(a(a(a(b(a(a(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(z0))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(z0))))))))), A(a(a(c_a(c_a(c_a(c_a(z0))))))), A(a(c_a(c_a(c_a(c_a(z0)))))), A(c_a(c_a(c_a(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(b(a(a(b(b(a(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(b(c_a(c_a(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(c_a(c_a(z0)))))))), A(c_a(c_a(b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(b(b(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(b(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(b(b(c_a(z0)))))))))), A(a(a(c_a(c_a(b(b(c_a(z0)))))))), A(a(c_a(c_a(b(b(c_a(z0))))))), A(c_a(c_a(b(b(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(b(a(b(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(b(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(c_a(b(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(b(c_a(z0)))))))), A(a(c_a(c_a(c_a(b(c_a(z0))))))), A(c_a(c_a(c_a(b(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(a(b(b(b(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(b(b(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(b(b(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(b(b(c_a(c_a(z0))))))))), A(a(c_a(c_a(b(b(c_a(c_a(z0)))))))), A(c_a(c_a(b(b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(b(a(a(b(a(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_a(c_a(z0)))))))), A(a(c_a(c_a(c_a(c_a(c_a(z0))))))), A(c_a(c_a(c_a(c_a(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(b(b(a(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(b(c_a(b(c_a(z0))))))))))), A(a(a(c_a(c_a(b(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(b(c_a(b(c_a(z0)))))))), A(c_a(c_a(b(c_a(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(b(b(a(b(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(b(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(b(b(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(b(b(c_a(z0))))))))), A(a(c_a(c_a(c_a(b(b(c_a(z0)))))))), A(c_a(c_a(c_a(b(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c5(A(a(a(b(a(a(a(b(b(z0))))))))), A(a(b(a(a(a(c_a(c_a(c_a(z0))))))))), A(b(a(a(a(c_a(c_a(c_a(z0)))))))), A(a(a(c_a(c_a(c_a(z0)))))), A(a(c_a(c_a(c_a(z0))))), A(c_a(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(a(b(a(b(a(b(a(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(b(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(b(b(b(b(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(b(b(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(b(b(b(c_a(z0))))))))))), A(a(a(c_a(c_a(b(b(b(c_a(z0))))))))), A(a(c_a(c_a(b(b(b(c_a(z0)))))))), A(c_a(c_a(b(b(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(c_a(z0)))))))))) -> c5(A(a(a(b(a(a(a(b(b(a(b(b(a(z0))))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(c_a(z0))))))))))), A(b(a(a(a(c_a(c_a(b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(b(c_a(c_a(z0)))))))), A(a(c_a(c_a(b(c_a(c_a(z0))))))), A(c_a(c_a(b(c_a(c_a(z0)))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))) -> c5(A(a(a(b(a(a(a(b(a(a(b(b(a(a(b(z0))))))))))))))), A(a(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))))))), A(b(a(a(a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))))), A(a(a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_a(b(c_a(z0)))))))), A(c_a(c_a(c_a(c_a(b(c_a(z0))))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(b(c_a(z0))))))))) -> c5(A(a(a(b(a(a(a(b(b(b(b(z0))))))))))), A(a(b(a(a(a(c_a(c_a(b(c_a(z0)))))))))), A(b(a(a(a(c_a(c_a(b(c_a(z0))))))))), A(a(a(c_a(c_a(b(c_a(z0))))))), A(a(c_a(c_a(b(c_a(z0)))))), A(c_a(c_a(b(c_a(z0))))))
   A(c_a(c_a(c_a(c_a(c_a(c_a(x0))))))) -> c5(A(a(b(a(a(a(c_a(c_a(x0)))))))), A(b(a(a(a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(x0))))), A(a(c_a(c_a(x0)))), A(c_a(c_a(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1

Defined Pair Symbols:   ENCARG_1, A_1, ENCODE_A_1

Compound Symbols:   c_1, c8, c14, c16, c19, c5_6, c6_2, c6_1, c7_4, c9_2, c9_1, c10_2, c10_1, c11_4, c12_2, c12_1, c13_2, c13_1, c15_4, c17_2, c17_1, c18_4, c3_1, c1_2, c1_1, c5_1, c5_3, c5_5