/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


KILLED
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 35 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 0 ms]
    (10) typed CpxTrs
    (11) RewriteLemmaProof [LOWER BOUND(ID), 565 ms]
    (12) BOUNDS(1, INF)
(13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(14) TRS for Loop Detection
(15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(16) CpxTRS
(17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(18) CpxRelTRS
    (19) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxRelTRS
    (21) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 5 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 7 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 2 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms]
        (58) CdtProblem
        (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (60) CdtProblem
        (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (62) CdtProblem
        (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (64) CdtProblem
        (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms]
        (66) CdtProblem
        (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (68) CdtProblem
        (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (70) CdtProblem
        (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (72) CdtProblem
        (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (74) CdtProblem
        (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (76) CdtProblem
        (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (78) CdtProblem
        (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (80) CdtProblem
        (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (82) CdtProblem
        (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (84) CdtProblem
        (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (86) CdtProblem
        (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (88) CdtProblem
        (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (90) CdtProblem
        (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (92) CdtProblem
        (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (94) CdtProblem
        (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (96) CdtProblem
        (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (98) CdtProblem
        (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (100) CdtProblem
        (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (102) CdtProblem
        (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (104) CdtProblem
        (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (106) CdtProblem
        (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (108) CdtProblem
        (109) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (110) CdtProblem
        (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (112) CdtProblem
        (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms]
        (114) CdtProblem
        (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (116) CdtProblem
        (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (118) CdtProblem
        (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (120) CdtProblem
        (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms]
        (122) CdtProblem
        (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (124) CdtProblem
        (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (126) CdtProblem
        (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (128) CdtProblem
        (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (130) CdtProblem
        (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (132) CdtProblem
        (133) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (134) CdtProblem
        (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (136) CdtProblem
        (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (138) CdtProblem
        (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (140) CdtProblem
        (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (142) CdtProblem
        (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (144) CdtProblem
        (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (146) CdtProblem
        (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (148) CdtProblem
        (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (150) CdtProblem
        (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (152) 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(a(a(x1)))) -> b(b(x1))
   b(b(a(a(x1)))) -> a(a(b(b(x1))))
   b(b(b(b(c(c(x1)))))) -> c(c(a(a(x1))))
   b(b(b(b(x1)))) -> a(a(a(a(a(a(x1))))))
   c(c(a(a(x1)))) -> b(b(a(a(c(c(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(cons_a(x_1)) -> a(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encArg(cons_c(x_1)) -> c(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   encode_c(x_1) -> c(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(a(a(x1)))) -> b(b(x1))
   b(b(a(a(x1)))) -> a(a(b(b(x1))))
   b(b(b(b(c(c(x1)))))) -> c(c(a(a(x1))))
   b(b(b(b(x1)))) -> a(a(a(a(a(a(x1))))))
   c(c(a(a(x1)))) -> b(b(a(a(c(c(x1))))))

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

   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encArg(cons_c(x_1)) -> c(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   encode_c(x_1) -> c(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(a(a(x1)))) -> b(b(x1))
   b(b(a(a(x1)))) -> a(a(b(b(x1))))
   b(b(b(b(c(c(x1)))))) -> c(c(a(a(x1))))
   b(b(b(b(x1)))) -> a(a(a(a(a(a(x1))))))
   c(c(a(a(x1)))) -> b(b(a(a(c(c(x1))))))

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

   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encArg(cons_c(x_1)) -> c(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   encode_c(x_1) -> c(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

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

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

   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encArg(cons_c(x_1)) -> c(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   encode_c(x_1) -> c(encArg(x_1))

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

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

(8)
Obligation:
TRS:
Rules:
a(a(a(a(x1)))) -> b(b(x1))
b(b(a(a(x1)))) -> a(a(b(b(x1))))
b(b(b(b(c(c(x1)))))) -> c(c(a(a(x1))))
b(b(b(b(x1)))) -> a(a(a(a(a(a(x1))))))
c(c(a(a(x1)))) -> b(b(a(a(c(c(x1))))))
encArg(cons_a(x_1)) -> a(encArg(x_1))
encArg(cons_b(x_1)) -> b(encArg(x_1))
encArg(cons_c(x_1)) -> c(encArg(x_1))
encode_a(x_1) -> a(encArg(x_1))
encode_b(x_1) -> b(encArg(x_1))
encode_c(x_1) -> c(encArg(x_1))

Types:
a :: a:b:c:encArg:encode_a:encode_b:encode_c -> a:b:c:encArg:encode_a:encode_b:encode_c
b :: a:b:c:encArg:encode_a:encode_b:encode_c -> a:b:c:encArg:encode_a:encode_b:encode_c
c :: a:b:c:encArg:encode_a:encode_b:encode_c -> a:b:c:encArg:encode_a:encode_b:encode_c
encArg :: cons_a:cons_b:cons_c -> a:b:c:encArg:encode_a:encode_b:encode_c
cons_a :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
cons_b :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
cons_c :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
encode_a :: cons_a:cons_b:cons_c -> a:b:c:encArg:encode_a:encode_b:encode_c
encode_b :: cons_a:cons_b:cons_c -> a:b:c:encArg:encode_a:encode_b:encode_c
encode_c :: cons_a:cons_b:cons_c -> a:b:c:encArg:encode_a:encode_b:encode_c
hole_a:b:c:encArg:encode_a:encode_b:encode_c1_0 :: a:b:c:encArg:encode_a:encode_b:encode_c
hole_cons_a:cons_b:cons_c2_0 :: cons_a:cons_b:cons_c
gen_cons_a:cons_b:cons_c3_0 :: Nat -> cons_a:cons_b:cons_c

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

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

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

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

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

Types:
a :: a:b:c:encArg:encode_a:encode_b:encode_c -> a:b:c:encArg:encode_a:encode_b:encode_c
b :: a:b:c:encArg:encode_a:encode_b:encode_c -> a:b:c:encArg:encode_a:encode_b:encode_c
c :: a:b:c:encArg:encode_a:encode_b:encode_c -> a:b:c:encArg:encode_a:encode_b:encode_c
encArg :: cons_a:cons_b:cons_c -> a:b:c:encArg:encode_a:encode_b:encode_c
cons_a :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
cons_b :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
cons_c :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
encode_a :: cons_a:cons_b:cons_c -> a:b:c:encArg:encode_a:encode_b:encode_c
encode_b :: cons_a:cons_b:cons_c -> a:b:c:encArg:encode_a:encode_b:encode_c
encode_c :: cons_a:cons_b:cons_c -> a:b:c:encArg:encode_a:encode_b:encode_c
hole_a:b:c:encArg:encode_a:encode_b:encode_c1_0 :: a:b:c:encArg:encode_a:encode_b:encode_c
hole_cons_a:cons_b:cons_c2_0 :: cons_a:cons_b:cons_c
gen_cons_a:cons_b:cons_c3_0 :: Nat -> cons_a:cons_b:cons_c


Generator Equations:
gen_cons_a:cons_b:cons_c3_0(0) <=> hole_cons_a:cons_b:cons_c2_0
gen_cons_a:cons_b:cons_c3_0(+(x, 1)) <=> cons_a(gen_cons_a:cons_b:cons_c3_0(x))


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

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

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

(11) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_cons_a:cons_b:cons_c3_0(+(1, n21_0))) -> *4_0, rt in Omega(0)

Induction Base:
encArg(gen_cons_a:cons_b:cons_c3_0(+(1, 0)))

Induction Step:
encArg(gen_cons_a:cons_b:cons_c3_0(+(1, +(n21_0, 1)))) ->_R^Omega(0)
a(encArg(gen_cons_a:cons_b:cons_c3_0(+(1, n21_0)))) ->_IH
a(*4_0)

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

(12)
BOUNDS(1, INF)

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

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

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

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


The TRS R consists of the following rules:

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

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

   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encArg(cons_c(x_1)) -> c(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   encode_c(x_1) -> c(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   a(a(a(a(x1)))) -> b(b(x1))
   b(b(a(a(x1)))) -> a(a(b(b(x1))))
   b(b(b(b(c(c(x1)))))) -> c(c(a(a(x1))))
   b(b(b(b(x1)))) -> a(a(a(a(a(a(x1))))))
   c(c(a(a(x1)))) -> b(b(a(a(c(c(x1))))))
   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encArg(cons_c(x_1)) -> c(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   encode_c(x_1) -> c(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:

   b(c_b(c_b(c_b(c_c(c_c(x1)))))) -> c(c(a(a(x1))))
   b(c_b(c_b(c_b(x1)))) -> a(a(a(a(a(a(x1))))))
   a(c_a(c_a(c_a(x1)))) -> b(b(x1))
   b(c_b(c_a(c_a(x1)))) -> a(a(b(b(x1))))
   c(c_c(c_a(c_a(x1)))) -> b(b(a(a(c(c(x1))))))

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

   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encArg(cons_c(x_1)) -> c(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   encode_c(x_1) -> c(encArg(x_1))
   a(x0) -> c_a(x0)
   b(x0) -> c_b(x0)
   c(x0) -> c_c(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:

   b(c_b(c_b(c_b(c_c(c_c(x1)))))) -> c(c(a(a(x1))))
   b(c_b(c_b(c_b(x1)))) -> a(a(a(a(a(a(x1))))))
   a(c_a(c_a(c_a(x1)))) -> b(b(x1))
   b(c_b(c_a(c_a(x1)))) -> a(a(b(b(x1))))
   c(c_c(c_a(c_a(x1)))) -> b(b(a(a(c(c(x1))))))

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

   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encArg(cons_c(x_1)) -> c(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   encode_c(x_1) -> c(encArg(x_1))
   a(x0) -> c_a(x0)
   b(x0) -> c_b(x0)
   c(x0) -> c_c(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:

   b(c_b(c_b(c_b(c_c(c_c(x1)))))) -> c(c(a(a(x1)))) [1]
   b(c_b(c_b(c_b(x1)))) -> a(a(a(a(a(a(x1)))))) [1]
   a(c_a(c_a(c_a(x1)))) -> b(b(x1)) [1]
   b(c_b(c_a(c_a(x1)))) -> a(a(b(b(x1)))) [1]
   c(c_c(c_a(c_a(x1)))) -> b(b(a(a(c(c(x1)))))) [1]
   encArg(cons_a(x_1)) -> a(encArg(x_1)) [0]
   encArg(cons_b(x_1)) -> b(encArg(x_1)) [0]
   encArg(cons_c(x_1)) -> c(encArg(x_1)) [0]
   encode_a(x_1) -> a(encArg(x_1)) [0]
   encode_b(x_1) -> b(encArg(x_1)) [0]
   encode_c(x_1) -> c(encArg(x_1)) [0]
   a(x0) -> c_a(x0) [0]
   b(x0) -> c_b(x0) [0]
   c(x0) -> c_c(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:

   b(c_b(c_b(c_b(c_c(c_c(x1)))))) -> c(c(a(a(x1)))) [1]
   b(c_b(c_b(c_b(x1)))) -> a(a(a(a(a(a(x1)))))) [1]
   a(c_a(c_a(c_a(x1)))) -> b(b(x1)) [1]
   b(c_b(c_a(c_a(x1)))) -> a(a(b(b(x1)))) [1]
   c(c_c(c_a(c_a(x1)))) -> b(b(a(a(c(c(x1)))))) [1]
   encArg(cons_a(x_1)) -> a(encArg(x_1)) [0]
   encArg(cons_b(x_1)) -> b(encArg(x_1)) [0]
   encArg(cons_c(x_1)) -> c(encArg(x_1)) [0]
   encode_a(x_1) -> a(encArg(x_1)) [0]
   encode_b(x_1) -> b(encArg(x_1)) [0]
   encode_c(x_1) -> c(encArg(x_1)) [0]
   a(x0) -> c_a(x0) [0]
   b(x0) -> c_b(x0) [0]
   c(x0) -> c_c(x0) [0]

The TRS has the following type information:
b :: c_c:c_b:c_a -> c_c:c_b:c_a
c_b :: c_c:c_b:c_a -> c_c:c_b:c_a
c_c :: c_c:c_b:c_a -> c_c:c_b:c_a
c :: c_c:c_b:c_a -> c_c:c_b:c_a
a :: c_c:c_b:c_a -> c_c:c_b:c_a
c_a :: c_c:c_b:c_a -> c_c:c_b:c_a
encArg :: cons_a:cons_b:cons_c -> c_c:c_b:c_a
cons_a :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
cons_b :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
cons_c :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
encode_a :: cons_a:cons_b:cons_c -> c_c:c_b:c_a
encode_b :: cons_a:cons_b:cons_c -> c_c:c_b:c_a
encode_c :: cons_a:cons_b:cons_c -> c_c:c_b:c_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
   encode_c_1
   a_1
   b_1
   c_1

Due to the following rules being added:

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

And the following fresh constants:    const, const1

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

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

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

   b(c_b(c_b(c_b(c_c(c_c(x1)))))) -> c(c(a(a(x1)))) [1]
   b(c_b(c_b(c_b(x1)))) -> a(a(a(a(a(a(x1)))))) [1]
   a(c_a(c_a(c_a(x1)))) -> b(b(x1)) [1]
   b(c_b(c_a(c_a(x1)))) -> a(a(b(b(x1)))) [1]
   c(c_c(c_a(c_a(x1)))) -> b(b(a(a(c(c(x1)))))) [1]
   encArg(cons_a(x_1)) -> a(encArg(x_1)) [0]
   encArg(cons_b(x_1)) -> b(encArg(x_1)) [0]
   encArg(cons_c(x_1)) -> c(encArg(x_1)) [0]
   encode_a(x_1) -> a(encArg(x_1)) [0]
   encode_b(x_1) -> b(encArg(x_1)) [0]
   encode_c(x_1) -> c(encArg(x_1)) [0]
   a(x0) -> c_a(x0) [0]
   b(x0) -> c_b(x0) [0]
   c(x0) -> c_c(x0) [0]
   encArg(v0) -> const [0]
   encode_a(v0) -> const [0]
   encode_b(v0) -> const [0]
   encode_c(v0) -> const [0]
   a(v0) -> const [0]
   b(v0) -> const [0]
   c(v0) -> const [0]

The TRS has the following type information:
b :: c_c:c_b:c_a:const -> c_c:c_b:c_a:const
c_b :: c_c:c_b:c_a:const -> c_c:c_b:c_a:const
c_c :: c_c:c_b:c_a:const -> c_c:c_b:c_a:const
c :: c_c:c_b:c_a:const -> c_c:c_b:c_a:const
a :: c_c:c_b:c_a:const -> c_c:c_b:c_a:const
c_a :: c_c:c_b:c_a:const -> c_c:c_b:c_a:const
encArg :: cons_a:cons_b:cons_c -> c_c:c_b:c_a:const
cons_a :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
cons_b :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
cons_c :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
encode_a :: cons_a:cons_b:cons_c -> c_c:c_b:c_a:const
encode_b :: cons_a:cons_b:cons_c -> c_c:c_b:c_a:const
encode_c :: cons_a:cons_b:cons_c -> c_c:c_b:c_a:const
const :: c_c:c_b:c_a:const
const1 :: cons_a:cons_b:cons_c

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:

   b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x1'))))))))) -> c(c(a(b(b(x1'))))) [2]
   b(c_b(c_b(c_b(c_c(c_c(x1)))))) -> c(c(a(c_a(x1)))) [1]
   b(c_b(c_b(c_b(c_c(c_c(x1)))))) -> c(c(a(const))) [1]
   b(c_b(c_b(c_b(c_a(c_a(c_a(x1''))))))) -> a(a(a(a(a(b(b(x1''))))))) [2]
   b(c_b(c_b(c_b(x1)))) -> a(a(a(a(a(c_a(x1)))))) [1]
   b(c_b(c_b(c_b(x1)))) -> a(a(a(a(a(const))))) [1]
   a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x11))))))))) -> b(c(c(a(a(x11))))) [2]
   a(c_a(c_a(c_a(c_b(c_b(c_b(x12))))))) -> b(a(a(a(a(a(a(x12))))))) [2]
   a(c_a(c_a(c_a(c_b(c_a(c_a(x13))))))) -> b(a(a(b(b(x13))))) [2]
   a(c_a(c_a(c_a(x1)))) -> b(c_b(x1)) [1]
   a(c_a(c_a(c_a(x1)))) -> b(const) [1]
   b(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x14))))))))) -> a(a(b(c(c(a(a(x14))))))) [2]
   b(c_b(c_a(c_a(c_b(c_b(c_b(x15))))))) -> a(a(b(a(a(a(a(a(a(x15))))))))) [2]
   b(c_b(c_a(c_a(c_b(c_a(c_a(x16))))))) -> a(a(b(a(a(b(b(x16))))))) [2]
   b(c_b(c_a(c_a(x1)))) -> a(a(b(c_b(x1)))) [1]
   b(c_b(c_a(c_a(x1)))) -> a(a(b(const))) [1]
   c(c_c(c_a(c_a(c_c(c_a(c_a(x17))))))) -> b(b(a(a(c(b(b(a(a(c(c(x17))))))))))) [2]
   c(c_c(c_a(c_a(x1)))) -> b(b(a(a(c(c_c(x1)))))) [1]
   c(c_c(c_a(c_a(x1)))) -> b(b(a(a(c(const))))) [1]
   encArg(cons_a(cons_a(x_1'))) -> a(a(encArg(x_1'))) [0]
   encArg(cons_a(cons_b(x_1''))) -> a(b(encArg(x_1''))) [0]
   encArg(cons_a(cons_c(x_11))) -> a(c(encArg(x_11))) [0]
   encArg(cons_a(x_1)) -> a(const) [0]
   encArg(cons_b(cons_a(x_12))) -> b(a(encArg(x_12))) [0]
   encArg(cons_b(cons_b(x_13))) -> b(b(encArg(x_13))) [0]
   encArg(cons_b(cons_c(x_14))) -> b(c(encArg(x_14))) [0]
   encArg(cons_b(x_1)) -> b(const) [0]
   encArg(cons_c(cons_a(x_15))) -> c(a(encArg(x_15))) [0]
   encArg(cons_c(cons_b(x_16))) -> c(b(encArg(x_16))) [0]
   encArg(cons_c(cons_c(x_17))) -> c(c(encArg(x_17))) [0]
   encArg(cons_c(x_1)) -> c(const) [0]
   encode_a(cons_a(x_18)) -> a(a(encArg(x_18))) [0]
   encode_a(cons_b(x_19)) -> a(b(encArg(x_19))) [0]
   encode_a(cons_c(x_110)) -> a(c(encArg(x_110))) [0]
   encode_a(x_1) -> a(const) [0]
   encode_b(cons_a(x_111)) -> b(a(encArg(x_111))) [0]
   encode_b(cons_b(x_112)) -> b(b(encArg(x_112))) [0]
   encode_b(cons_c(x_113)) -> b(c(encArg(x_113))) [0]
   encode_b(x_1) -> b(const) [0]
   encode_c(cons_a(x_114)) -> c(a(encArg(x_114))) [0]
   encode_c(cons_b(x_115)) -> c(b(encArg(x_115))) [0]
   encode_c(cons_c(x_116)) -> c(c(encArg(x_116))) [0]
   encode_c(x_1) -> c(const) [0]
   a(x0) -> c_a(x0) [0]
   b(x0) -> c_b(x0) [0]
   c(x0) -> c_c(x0) [0]
   encArg(v0) -> const [0]
   encode_a(v0) -> const [0]
   encode_b(v0) -> const [0]
   encode_c(v0) -> const [0]
   a(v0) -> const [0]
   b(v0) -> const [0]
   c(v0) -> const [0]

The TRS has the following type information:
b :: c_c:c_b:c_a:const -> c_c:c_b:c_a:const
c_b :: c_c:c_b:c_a:const -> c_c:c_b:c_a:const
c_c :: c_c:c_b:c_a:const -> c_c:c_b:c_a:const
c :: c_c:c_b:c_a:const -> c_c:c_b:c_a:const
a :: c_c:c_b:c_a:const -> c_c:c_b:c_a:const
c_a :: c_c:c_b:c_a:const -> c_c:c_b:c_a:const
encArg :: cons_a:cons_b:cons_c -> c_c:c_b:c_a:const
cons_a :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
cons_b :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
cons_c :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
encode_a :: cons_a:cons_b:cons_c -> c_c:c_b:c_a:const
encode_b :: cons_a:cons_b:cons_c -> c_c:c_b:c_a:const
encode_c :: cons_a:cons_b:cons_c -> c_c:c_b:c_a:const
const :: c_c:c_b:c_a:const
const1 :: cons_a:cons_b:cons_c

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

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

   const => 0
   const1 => 0

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

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

   a(z) -{ 2 }-> b(c(c(a(a(x11))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x11))))))), x11 >= 0
   a(z) -{ 2 }-> b(a(a(b(b(x13))))) :|: x13 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x13)))))
   a(z) -{ 2 }-> b(a(a(a(a(a(a(x12))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x12))))), x12 >= 0
   a(z) -{ 1 }-> b(0) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   a(z) -{ 1 }-> b(1 + x1) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   a(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   b(z) -{ 2 }-> c(c(a(b(b(x1'))))) :|: x1' >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1')))))))
   b(z) -{ 1 }-> c(c(a(0))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1))))
   b(z) -{ 1 }-> c(c(a(1 + x1))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1))))
   b(z) -{ 2 }-> a(a(b(c(c(a(a(x14))))))) :|: x14 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x14)))))))
   b(z) -{ 2 }-> a(a(b(a(a(b(b(x16))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x16))))), x16 >= 0
   b(z) -{ 2 }-> a(a(b(a(a(a(a(a(a(x15))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x15))))), x15 >= 0
   b(z) -{ 1 }-> a(a(b(0))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   b(z) -{ 1 }-> a(a(b(1 + x1))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   b(z) -{ 2 }-> a(a(a(a(a(b(b(x1''))))))) :|: x1'' >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x1'')))))
   b(z) -{ 1 }-> a(a(a(a(a(0))))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   b(z) -{ 1 }-> a(a(a(a(a(1 + x1))))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   b(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   b(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   c(z) -{ 2 }-> b(b(a(a(c(b(b(a(a(c(c(x17))))))))))) :|: x17 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x17)))))
   c(z) -{ 1 }-> b(b(a(a(c(0))))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   c(z) -{ 1 }-> b(b(a(a(c(1 + x1))))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   c(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   c(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   encArg(z) -{ 0 }-> c(c(encArg(x_17))) :|: x_17 >= 0, z = 1 + (1 + x_17)
   encArg(z) -{ 0 }-> c(b(encArg(x_16))) :|: x_16 >= 0, z = 1 + (1 + x_16)
   encArg(z) -{ 0 }-> c(a(encArg(x_15))) :|: x_15 >= 0, z = 1 + (1 + x_15)
   encArg(z) -{ 0 }-> c(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> b(c(encArg(x_14))) :|: x_14 >= 0, z = 1 + (1 + x_14)
   encArg(z) -{ 0 }-> b(b(encArg(x_13))) :|: z = 1 + (1 + x_13), x_13 >= 0
   encArg(z) -{ 0 }-> b(a(encArg(x_12))) :|: z = 1 + (1 + x_12), x_12 >= 0
   encArg(z) -{ 0 }-> b(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> a(c(encArg(x_11))) :|: x_11 >= 0, z = 1 + (1 + x_11)
   encArg(z) -{ 0 }-> a(b(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0
   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 }-> 0 :|: v0 >= 0, z = v0
   encode_a(z) -{ 0 }-> a(c(encArg(x_110))) :|: z = 1 + x_110, x_110 >= 0
   encode_a(z) -{ 0 }-> a(b(encArg(x_19))) :|: z = 1 + x_19, x_19 >= 0
   encode_a(z) -{ 0 }-> a(a(encArg(x_18))) :|: z = 1 + x_18, x_18 >= 0
   encode_a(z) -{ 0 }-> a(0) :|: x_1 >= 0, z = x_1
   encode_a(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_b(z) -{ 0 }-> b(c(encArg(x_113))) :|: z = 1 + x_113, x_113 >= 0
   encode_b(z) -{ 0 }-> b(b(encArg(x_112))) :|: z = 1 + x_112, x_112 >= 0
   encode_b(z) -{ 0 }-> b(a(encArg(x_111))) :|: z = 1 + x_111, x_111 >= 0
   encode_b(z) -{ 0 }-> b(0) :|: x_1 >= 0, z = x_1
   encode_b(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_c(z) -{ 0 }-> c(c(encArg(x_116))) :|: x_116 >= 0, z = 1 + x_116
   encode_c(z) -{ 0 }-> c(b(encArg(x_115))) :|: x_115 >= 0, z = 1 + x_115
   encode_c(z) -{ 0 }-> c(a(encArg(x_114))) :|: x_114 >= 0, z = 1 + x_114
   encode_c(z) -{ 0 }-> c(0) :|: x_1 >= 0, z = x_1
   encode_c(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


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

(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 }-> b(c(c(a(a(z - 8))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> b(a(a(b(b(z - 6))))) :|: z - 6 >= 0
   a(z) -{ 2 }-> b(a(a(a(a(a(a(z - 6))))))) :|: z - 6 >= 0
   a(z) -{ 1 }-> b(0) :|: z - 3 >= 0
   a(z) -{ 1 }-> b(1 + (z - 3)) :|: z - 3 >= 0
   a(z) -{ 0 }-> 0 :|: z >= 0
   a(z) -{ 0 }-> 1 + z :|: z >= 0
   b(z) -{ 2 }-> c(c(a(b(b(z - 8))))) :|: z - 8 >= 0
   b(z) -{ 1 }-> c(c(a(0))) :|: z - 5 >= 0
   b(z) -{ 1 }-> c(c(a(1 + (z - 5)))) :|: z - 5 >= 0
   b(z) -{ 2 }-> a(a(b(c(c(a(a(z - 8))))))) :|: z - 8 >= 0
   b(z) -{ 2 }-> a(a(b(a(a(b(b(z - 6))))))) :|: z - 6 >= 0
   b(z) -{ 2 }-> a(a(b(a(a(a(a(a(a(z - 6))))))))) :|: z - 6 >= 0
   b(z) -{ 1 }-> a(a(b(0))) :|: z - 3 >= 0
   b(z) -{ 1 }-> a(a(b(1 + (z - 3)))) :|: z - 3 >= 0
   b(z) -{ 2 }-> a(a(a(a(a(b(b(z - 6))))))) :|: z - 6 >= 0
   b(z) -{ 1 }-> a(a(a(a(a(0))))) :|: z - 3 >= 0
   b(z) -{ 1 }-> a(a(a(a(a(1 + (z - 3)))))) :|: z - 3 >= 0
   b(z) -{ 0 }-> 0 :|: z >= 0
   b(z) -{ 0 }-> 1 + z :|: z >= 0
   c(z) -{ 2 }-> b(b(a(a(c(b(b(a(a(c(c(z - 6))))))))))) :|: z - 6 >= 0
   c(z) -{ 1 }-> b(b(a(a(c(0))))) :|: z - 3 >= 0
   c(z) -{ 1 }-> b(b(a(a(c(1 + (z - 3)))))) :|: z - 3 >= 0
   c(z) -{ 0 }-> 0 :|: z >= 0
   c(z) -{ 0 }-> 1 + z :|: z >= 0
   encArg(z) -{ 0 }-> c(c(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> c(b(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> c(a(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> c(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> b(c(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> b(b(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> b(a(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> b(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> a(c(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> a(b(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> a(a(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> a(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_a(z) -{ 0 }-> a(c(encArg(z - 1))) :|: z - 1 >= 0
   encode_a(z) -{ 0 }-> a(b(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 }-> 0 :|: z >= 0
   encode_b(z) -{ 0 }-> b(c(encArg(z - 1))) :|: z - 1 >= 0
   encode_b(z) -{ 0 }-> b(b(encArg(z - 1))) :|: z - 1 >= 0
   encode_b(z) -{ 0 }-> b(a(encArg(z - 1))) :|: z - 1 >= 0
   encode_b(z) -{ 0 }-> b(0) :|: z >= 0
   encode_b(z) -{ 0 }-> 0 :|: z >= 0
   encode_c(z) -{ 0 }-> c(c(encArg(z - 1))) :|: z - 1 >= 0
   encode_c(z) -{ 0 }-> c(b(encArg(z - 1))) :|: z - 1 >= 0
   encode_c(z) -{ 0 }-> c(a(encArg(z - 1))) :|: z - 1 >= 0
   encode_c(z) -{ 0 }-> c(0) :|: z >= 0
   encode_c(z) -{ 0 }-> 0 :|: 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]
   encode_c(v0) -> null_encode_c [0]
   a(v0) -> null_a [0]
   b(v0) -> null_b [0]
   c(v0) -> null_c [0]

And the following fresh constants:    null_encArg, null_encode_a, null_encode_b, null_encode_c, null_a, null_b, null_c, const

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

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

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

   b(c_b(c_b(c_b(c_c(c_c(x1)))))) -> c(c(a(a(x1)))) [1]
   b(c_b(c_b(c_b(x1)))) -> a(a(a(a(a(a(x1)))))) [1]
   a(c_a(c_a(c_a(x1)))) -> b(b(x1)) [1]
   b(c_b(c_a(c_a(x1)))) -> a(a(b(b(x1)))) [1]
   c(c_c(c_a(c_a(x1)))) -> b(b(a(a(c(c(x1)))))) [1]
   encArg(cons_a(x_1)) -> a(encArg(x_1)) [0]
   encArg(cons_b(x_1)) -> b(encArg(x_1)) [0]
   encArg(cons_c(x_1)) -> c(encArg(x_1)) [0]
   encode_a(x_1) -> a(encArg(x_1)) [0]
   encode_b(x_1) -> b(encArg(x_1)) [0]
   encode_c(x_1) -> c(encArg(x_1)) [0]
   a(x0) -> c_a(x0) [0]
   b(x0) -> c_b(x0) [0]
   c(x0) -> c_c(x0) [0]
   encArg(v0) -> null_encArg [0]
   encode_a(v0) -> null_encode_a [0]
   encode_b(v0) -> null_encode_b [0]
   encode_c(v0) -> null_encode_c [0]
   a(v0) -> null_a [0]
   b(v0) -> null_b [0]
   c(v0) -> null_c [0]

The TRS has the following type information:
b :: c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c -> c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
c_b :: c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c -> c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
c_c :: c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c -> c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
c :: c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c -> c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
a :: c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c -> c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
c_a :: c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c -> c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
encArg :: cons_a:cons_b:cons_c -> c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
cons_a :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
cons_b :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
cons_c :: cons_a:cons_b:cons_c -> cons_a:cons_b:cons_c
encode_a :: cons_a:cons_b:cons_c -> c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
encode_b :: cons_a:cons_b:cons_c -> c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
encode_c :: cons_a:cons_b:cons_c -> c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
null_encArg :: c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
null_encode_a :: c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
null_encode_b :: c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
null_encode_c :: c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
null_a :: c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
null_b :: c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
null_c :: c_c:c_b:c_a:null_encArg:null_encode_a:null_encode_b:null_encode_c:null_a:null_b:null_c
const :: cons_a:cons_b:cons_c

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_encode_c => 0
   null_a => 0
   null_b => 0
   null_c => 0
   const => 0

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

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

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

Only complete derivations are relevant for the runtime complexity.

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

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0))
   ENCARG(cons_b(z0)) -> c2(B(encArg(z0)), ENCARG(z0))
   ENCARG(cons_c(z0)) -> c3(C(encArg(z0)), ENCARG(z0))
   ENCODE_A(z0) -> c4(A(encArg(z0)), ENCARG(z0))
   ENCODE_B(z0) -> c5(B(encArg(z0)), ENCARG(z0))
   ENCODE_C(z0) -> c6(C(encArg(z0)), ENCARG(z0))
   A(z0) -> c7
   A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0))
   B(z0) -> c9
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(z0) -> c13
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
K tuples:none
Defined Rule Symbols:   b_1, a_1, c_1, encArg_1, encode_a_1, encode_b_1, encode_c_1

Defined Pair Symbols:   ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, A_1, B_1, C_1

Compound Symbols:   c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c7, c8_2, c9, c10_4, c11_6, c12_4, c13, c14_6


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

(39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 3 trailing nodes:
   B(z0) -> c9
   A(z0) -> c7
   C(z0) -> c13

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0))
   ENCARG(cons_b(z0)) -> c2(B(encArg(z0)), ENCARG(z0))
   ENCARG(cons_c(z0)) -> c3(C(encArg(z0)), ENCARG(z0))
   ENCODE_A(z0) -> c4(A(encArg(z0)), ENCARG(z0))
   ENCODE_B(z0) -> c5(B(encArg(z0)), ENCARG(z0))
   ENCODE_C(z0) -> c6(C(encArg(z0)), ENCARG(z0))
   A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
K tuples:none
Defined Rule Symbols:   b_1, a_1, c_1, encArg_1, encode_a_1, encode_b_1, encode_c_1

Defined Pair Symbols:   ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, A_1, B_1, C_1

Compound Symbols:   c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c8_2, c10_4, c11_6, c12_4, c14_6


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

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0))
   ENCARG(cons_b(z0)) -> c2(B(encArg(z0)), ENCARG(z0))
   ENCARG(cons_c(z0)) -> c3(C(encArg(z0)), ENCARG(z0))
   A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   ENCODE_A(z0) -> c7(ENCARG(z0))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_B(z0) -> c7(ENCARG(z0))
   ENCODE_C(z0) -> c7(C(encArg(z0)))
   ENCODE_C(z0) -> c7(ENCARG(z0))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
K tuples:none
Defined Rule Symbols:   b_1, a_1, c_1, encArg_1, encode_a_1, encode_b_1, encode_c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c1_2, c2_2, c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1


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

(43) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 3 leading nodes:
   ENCODE_A(z0) -> c7(ENCARG(z0))
   ENCODE_B(z0) -> c7(ENCARG(z0))
   ENCODE_C(z0) -> c7(ENCARG(z0))

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0))
   ENCARG(cons_b(z0)) -> c2(B(encArg(z0)), ENCARG(z0))
   ENCARG(cons_c(z0)) -> c3(C(encArg(z0)), ENCARG(z0))
   A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_C(z0) -> c7(C(encArg(z0)))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
K tuples:none
Defined Rule Symbols:   b_1, a_1, c_1, encArg_1, encode_a_1, encode_b_1, encode_c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c1_2, c2_2, c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_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))
   encode_c(z0) -> c(encArg(z0))

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_a(z0)) -> c1(A(encArg(z0)), ENCARG(z0))
   ENCARG(cons_b(z0)) -> c2(B(encArg(z0)), ENCARG(z0))
   ENCARG(cons_c(z0)) -> c3(C(encArg(z0)), ENCARG(z0))
   A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_C(z0) -> c7(C(encArg(z0)))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c1_2, c2_2, c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_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(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c1(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_c(z0))) -> c1(A(c(encArg(z0))), ENCARG(cons_c(z0)))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_b(z0)) -> c2(B(encArg(z0)), ENCARG(z0))
   ENCARG(cons_c(z0)) -> c3(C(encArg(z0)), ENCARG(z0))
   A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_C(z0) -> c7(C(encArg(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c1(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_c(z0))) -> c1(A(c(encArg(z0))), ENCARG(cons_c(z0)))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c2_2, c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2


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

(49) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_b(z0)) -> c2(B(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_c(z0)) -> c3(C(encArg(z0)), ENCARG(z0))
   A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_C(z0) -> c7(C(encArg(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c1(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_c(z0))) -> c1(A(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c2_2


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_c(z0)) -> c3(C(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_C(z0) -> c7(C(encArg(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c1(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_c(z0))) -> c1(A(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c2_2, c3_2


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

(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(c_a(c_a(z0)))) -> c8(B(b(z0)), B(z0)) by 
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_C(z0) -> c7(C(encArg(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c1(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_c(z0))) -> c1(A(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
S tuples:
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1, A_1

Compound Symbols:   c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c2_2, c3_2, c8_2


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(a(z0)))), C(a(a(z0))), A(a(z0)), A(z0)) by 
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_C(z0) -> c7(C(encArg(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c1(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_c(z0))) -> c1(A(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
S tuples:
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1, A_1

Compound Symbols:   c11_6, c12_4, c14_6, c7_1, c1_2, c2_2, c3_2, c8_2, c10_4


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

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

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_C(z0) -> c7(C(encArg(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c1(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_c(z0))) -> c1(A(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
S tuples:
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1, A_1

Compound Symbols:   c12_4, c14_6, c7_1, c1_2, c2_2, c3_2, c8_2, c10_4, c11_6


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(b(z0)))), A(b(b(z0))), B(b(z0)), B(z0)) by 
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_C(z0) -> c7(C(encArg(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c1(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_c(z0))) -> c1(A(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
S tuples:
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1, A_1, B_1

Compound Symbols:   c14_6, c7_1, c1_2, c2_2, c3_2, c8_2, c10_4, c11_6, c12_4


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

(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0)) by 
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_C(z0) -> c7(C(encArg(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c1(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_c(z0))) -> c1(A(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1, A_1, B_1, C_1

Compound Symbols:   c7_1, c1_2, c2_2, c3_2, c8_2, c10_4, c11_6, c12_4, c14_6


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_A(z0) -> c7(A(encArg(z0))) by 
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_C(z0) -> c7(C(encArg(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c1(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_c(z0))) -> c1(A(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCODE_B_1, ENCODE_C_1, ENCARG_1, A_1, B_1, C_1, ENCODE_A_1

Compound Symbols:   c7_1, c1_2, c2_2, c3_2, c8_2, c10_4, c11_6, c12_4, c14_6


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

(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_B(z0) -> c7(B(encArg(z0))) by 
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCODE_C(z0) -> c7(C(encArg(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c1(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_c(z0))) -> c1(A(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCODE_C_1, ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1

Compound Symbols:   c7_1, c1_2, c2_2, c3_2, c8_2, c10_4, c11_6, c12_4, c14_6


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

(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_C(z0) -> c7(C(encArg(z0))) by 
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_a(cons_a(z0))) -> c1(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c1(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_c(z0))) -> c1(A(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c1_2, c2_2, c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1


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

(69) 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(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_a(cons_b(z0))) -> c1(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_c(z0))) -> c1(A(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c1_2, c2_2, c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_a(cons_b(z0))) -> c1(A(b(encArg(z0))), ENCARG(cons_b(z0))) by 
   ENCARG(cons_a(cons_b(x0))) -> c1(A(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_a(cons_c(z0))) -> c1(A(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(A(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c1_2, c2_2, c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1


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

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_a(cons_c(z0))) -> c1(A(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c1_2, c2_2, c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_1


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_a(cons_c(z0))) -> c1(A(c(encArg(z0))), ENCARG(cons_c(z0))) by 
   ENCARG(cons_a(cons_c(x0))) -> c1(A(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(x0))) -> c1(A(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c2_2, c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1


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

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c2_2, c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0))) by 
   ENCARG(cons_b(cons_a(x0))) -> c2(B(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(x0))) -> c2(B(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c2_2, c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1


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

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c2_2, c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_1


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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_b(cons_b(z0))) -> c2(B(b(encArg(z0))), ENCARG(cons_b(z0))) by 
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c2_2, c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_1


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

(85) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_b(cons_c(z0))) -> c2(B(c(encArg(z0))), ENCARG(cons_c(z0))) by 
   ENCARG(cons_b(cons_c(x0))) -> c2(B(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(B(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1


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

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1


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

(89) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_c(cons_a(z0))) -> c3(C(a(encArg(z0))), ENCARG(cons_a(z0))) by 
   ENCARG(cons_c(cons_a(x0))) -> c3(C(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(x0))) -> c3(C(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1


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

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_1


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

(93) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_c(cons_b(z0))) -> c3(C(b(encArg(z0))), ENCARG(cons_b(z0))) by 
   ENCARG(cons_c(cons_b(x0))) -> c3(C(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(x0))) -> c3(C(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_1


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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0)))
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   ENCARG_1, A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c3_2, c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_1


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

(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_c(cons_c(z0))) -> c3(C(c(encArg(z0))), ENCARG(cons_c(z0))) by 
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1


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

(99) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0))))))) by 
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_c(c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_c(c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_c(c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1


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

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1


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

(103) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(a(z0))))))), B(c_b(c_b(c_b(z0))))) by 
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_a(a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_a(a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_a(a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1


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

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1


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

(107) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(b(z0))))), B(c_b(c_a(c_a(z0))))) by 
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_a(a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_a(a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_a(a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1


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

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1


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

(111) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0)) by 
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1


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

(113) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0)) by 
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_1


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

(115) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0)) by 
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(a(c_a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c(c_a(c_a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c10_4, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_1, c10_2


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

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(b(z0))))), C(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))))) by 
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c_c(a(b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(c_a(b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2


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

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

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2


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

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

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2


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

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

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2


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

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

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2, c11_3


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

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

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c11_6, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2, c11_3, c11_4


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

(129) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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))))) by 
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(c_a(a(a(a(b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(c_a(a(a(b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(c_a(a(b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(c_a(b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2, c11_6, c11_3, c11_4


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

(131) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0)) by 
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2, c11_6, c11_3, c11_4


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

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2, c11_6, c11_3, c11_4, c12_3


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

(135) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0)) by 
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(c_b(b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2, c11_6, c11_3, c11_4, c12_3, c12_1


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

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2, c11_6, c11_3, c11_4, c12_3, c12_1


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

(139) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(c_b(c_a(c_a(z0)))) -> c12(A(a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0)) by 
   B(c_b(c_a(c_a(x0)))) -> c12(A(c_a(b(c_b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(x0)))) -> c12(A(a(c_b(c_b(x0)))), A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(c_b(c_b(c_c(c_c(z0)))))))) -> c12(A(a(c(c(a(a(z0)))))), A(b(b(c_b(c_b(c_c(c_c(z0))))))), B(b(c_b(c_b(c_c(c_c(z0)))))), B(c_b(c_b(c_c(c_c(z0))))))
   B(c_b(c_a(c_a(c_b(c_b(z0)))))) -> c12(A(a(a(a(a(a(a(a(z0)))))))), A(b(b(c_b(c_b(z0))))), B(b(c_b(c_b(z0)))), B(c_b(c_b(z0))))
   B(c_b(c_a(c_a(c_a(c_a(z0)))))) -> c12(A(a(a(a(b(b(z0)))))), A(b(b(c_a(c_a(z0))))), B(b(c_a(c_a(z0)))), B(c_a(c_a(z0))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
   B(c_b(c_a(c_a(c_b(c_b(c_c(c_c(z0)))))))) -> c12(A(a(c(c(a(a(z0)))))), A(b(b(c_b(c_b(c_c(c_c(z0))))))), B(b(c_b(c_b(c_c(c_c(z0)))))), B(c_b(c_b(c_c(c_c(z0))))))
   B(c_b(c_a(c_a(c_b(c_b(z0)))))) -> c12(A(a(a(a(a(a(a(a(z0)))))))), A(b(b(c_b(c_b(z0))))), B(b(c_b(c_b(z0)))), B(c_b(c_b(z0))))
   B(c_b(c_a(c_a(c_a(c_a(z0)))))) -> c12(A(a(a(a(b(b(z0)))))), A(b(b(c_a(c_a(z0))))), B(b(c_a(c_a(z0)))), B(c_a(c_a(z0))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
   B(c_b(c_a(c_a(c_b(c_b(c_c(c_c(z0)))))))) -> c12(A(a(c(c(a(a(z0)))))), A(b(b(c_b(c_b(c_c(c_c(z0))))))), B(b(c_b(c_b(c_c(c_c(z0)))))), B(c_b(c_b(c_c(c_c(z0))))))
   B(c_b(c_a(c_a(c_b(c_b(z0)))))) -> c12(A(a(a(a(a(a(a(a(z0)))))))), A(b(b(c_b(c_b(z0))))), B(b(c_b(c_b(z0)))), B(c_b(c_b(z0))))
   B(c_b(c_a(c_a(c_a(c_a(z0)))))) -> c12(A(a(a(a(b(b(z0)))))), A(b(b(c_a(c_a(z0))))), B(b(c_a(c_a(z0)))), B(c_a(c_a(z0))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2, c11_6, c11_3, c11_4, c12_3, c12_1


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

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
   B(c_b(c_a(c_a(c_b(c_b(z0)))))) -> c12(A(a(a(a(a(a(a(a(z0)))))))), A(b(b(c_b(c_b(z0))))), B(b(c_b(c_b(z0)))), B(c_b(c_b(z0))))
   B(c_b(c_a(c_a(c_b(c_b(c_c(c_c(z0)))))))) -> c12(A(a(c(c(a(a(z0)))))), A(b(b(c_b(c_b(c_c(c_c(z0))))))), B(b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_a(c_a(z0)))))) -> c12(A(a(a(a(b(b(z0)))))), A(b(b(c_a(c_a(z0))))), B(b(c_a(c_a(z0)))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
   B(c_b(c_a(c_a(c_b(c_b(z0)))))) -> c12(A(a(a(a(a(a(a(a(z0)))))))), A(b(b(c_b(c_b(z0))))), B(b(c_b(c_b(z0)))), B(c_b(c_b(z0))))
   B(c_b(c_a(c_a(c_b(c_b(c_c(c_c(z0)))))))) -> c12(A(a(c(c(a(a(z0)))))), A(b(b(c_b(c_b(c_c(c_c(z0))))))), B(b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_a(c_a(z0)))))) -> c12(A(a(a(a(b(b(z0)))))), A(b(b(c_a(c_a(z0))))), B(b(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2, c11_6, c11_3, c11_4, c12_3, c12_1


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

(143) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0))))))) by 
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(c_a(b(c(c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(c_b(c(c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c_c(c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c_c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c(c_a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(c_a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c12(A(a(b(c(c(a(b(b(z0)))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))), B(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
   B(c_b(c_a(c_a(c_b(c_b(z0)))))) -> c12(A(a(a(a(a(a(a(a(z0)))))))), A(b(b(c_b(c_b(z0))))), B(b(c_b(c_b(z0)))), B(c_b(c_b(z0))))
   B(c_b(c_a(c_a(c_b(c_b(c_c(c_c(z0)))))))) -> c12(A(a(c(c(a(a(z0)))))), A(b(b(c_b(c_b(c_c(c_c(z0))))))), B(b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_a(c_a(z0)))))) -> c12(A(a(a(a(b(b(z0)))))), A(b(b(c_a(c_a(z0))))), B(b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c_c(c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c_c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c(c_a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(c_a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c12(A(a(b(c(c(a(b(b(z0)))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))), B(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
   B(c_b(c_a(c_a(c_b(c_b(z0)))))) -> c12(A(a(a(a(a(a(a(a(z0)))))))), A(b(b(c_b(c_b(z0))))), B(b(c_b(c_b(z0)))), B(c_b(c_b(z0))))
   B(c_b(c_a(c_a(c_b(c_b(c_c(c_c(z0)))))))) -> c12(A(a(c(c(a(a(z0)))))), A(b(b(c_b(c_b(c_c(c_c(z0))))))), B(b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_a(c_a(z0)))))) -> c12(A(a(a(a(b(b(z0)))))), A(b(b(c_a(c_a(z0))))), B(b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c_c(c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c_c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c(c_a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(c_a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c12(A(a(b(c(c(a(b(b(z0)))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))), B(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2, c11_6, c11_3, c11_4, c12_3, c12_1


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

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

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
   B(c_b(c_a(c_a(c_b(c_b(z0)))))) -> c12(A(a(a(a(a(a(a(a(z0)))))))), A(b(b(c_b(c_b(z0))))), B(b(c_b(c_b(z0)))), B(c_b(c_b(z0))))
   B(c_b(c_a(c_a(c_b(c_b(c_c(c_c(z0)))))))) -> c12(A(a(c(c(a(a(z0)))))), A(b(b(c_b(c_b(c_c(c_c(z0))))))), B(b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_a(c_a(z0)))))) -> c12(A(a(a(a(b(b(z0)))))), A(b(b(c_a(c_a(z0))))), B(b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c_c(c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c_c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c(c_a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(c_a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c12(A(a(b(c(c(a(b(b(z0)))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))), B(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(c_a(a(a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(c_a(a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(c_a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(a(c_a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(a(a(c_a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(c_a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c12(A(a(b(a(a(a(a(a(b(b(z0)))))))))), A(b(b(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))), B(b(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
   B(c_b(c_a(c_a(c_b(c_b(z0)))))) -> c12(A(a(a(a(a(a(a(a(z0)))))))), A(b(b(c_b(c_b(z0))))), B(b(c_b(c_b(z0)))), B(c_b(c_b(z0))))
   B(c_b(c_a(c_a(c_b(c_b(c_c(c_c(z0)))))))) -> c12(A(a(c(c(a(a(z0)))))), A(b(b(c_b(c_b(c_c(c_c(z0))))))), B(b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_a(c_a(z0)))))) -> c12(A(a(a(a(b(b(z0)))))), A(b(b(c_a(c_a(z0))))), B(b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c_c(c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c_c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c(c_a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(c_a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c12(A(a(b(c(c(a(b(b(z0)))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))), B(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(c_a(a(a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(c_a(a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(c_a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(a(c_a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(a(a(c_a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(c_a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c12(A(a(b(a(a(a(a(a(b(b(z0)))))))))), A(b(b(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))), B(b(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, B_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1

Compound Symbols:   c8_2, c12_4, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2, c11_6, c11_3, c11_4, c12_3, c12_1, c12_2


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

(147) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0))))) by 
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(c_a(b(a(a(b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(c_b(a(a(b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(c_a(a(b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(a(c_a(b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(a(a(c_b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(c_b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c12(A(a(b(a(a(b(c(c(a(a(z0)))))))))), A(b(b(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), B(b(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c12(A(a(b(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(b(b(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))), B(b(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c12(A(a(b(a(a(b(a(a(b(b(z0)))))))))), A(b(b(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))), B(b(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))))

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
   B(c_b(c_a(c_a(c_b(c_b(z0)))))) -> c12(A(a(a(a(a(a(a(a(z0)))))))), A(b(b(c_b(c_b(z0))))), B(b(c_b(c_b(z0)))), B(c_b(c_b(z0))))
   B(c_b(c_a(c_a(c_b(c_b(c_c(c_c(z0)))))))) -> c12(A(a(c(c(a(a(z0)))))), A(b(b(c_b(c_b(c_c(c_c(z0))))))), B(b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_a(c_a(z0)))))) -> c12(A(a(a(a(b(b(z0)))))), A(b(b(c_a(c_a(z0))))), B(b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c_c(c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c_c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c(c_a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(c_a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c12(A(a(b(c(c(a(b(b(z0)))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))), B(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(c_a(a(a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(c_a(a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(c_a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(a(c_a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(a(a(c_a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(c_a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c12(A(a(b(a(a(a(a(a(b(b(z0)))))))))), A(b(b(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))), B(b(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(c_a(a(b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(a(c_a(b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(a(a(c_b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(c_b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c12(A(a(b(a(a(b(c(c(a(a(z0)))))))))), A(b(b(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), B(b(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c12(A(a(b(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(b(b(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))), B(b(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c12(A(a(b(a(a(b(a(a(b(b(z0)))))))))), A(b(b(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))), B(b(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
   B(c_b(c_a(c_a(c_b(c_b(z0)))))) -> c12(A(a(a(a(a(a(a(a(z0)))))))), A(b(b(c_b(c_b(z0))))), B(b(c_b(c_b(z0)))), B(c_b(c_b(z0))))
   B(c_b(c_a(c_a(c_b(c_b(c_c(c_c(z0)))))))) -> c12(A(a(c(c(a(a(z0)))))), A(b(b(c_b(c_b(c_c(c_c(z0))))))), B(b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_a(c_a(z0)))))) -> c12(A(a(a(a(b(b(z0)))))), A(b(b(c_a(c_a(z0))))), B(b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c_c(c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c_c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c(c_a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(c_a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c12(A(a(b(c(c(a(b(b(z0)))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))), B(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(c_a(a(a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(c_a(a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(c_a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(a(c_a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(a(a(c_a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(c_a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c12(A(a(b(a(a(a(a(a(b(b(z0)))))))))), A(b(b(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))), B(b(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(c_a(a(b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(a(c_a(b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(a(a(c_b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(c_b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c12(A(a(b(a(a(b(c(c(a(a(z0)))))))))), A(b(b(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), B(b(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c12(A(a(b(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(b(b(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))), B(b(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c12(A(a(b(a(a(b(a(a(b(b(z0)))))))))), A(b(b(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))), B(b(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1, B_1

Compound Symbols:   c8_2, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2, c11_6, c11_3, c11_4, c12_4, c12_3, c12_1, c12_2


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

(149) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0)) by 
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(c_b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(c_b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
   B(c_b(c_a(c_a(c_b(c_b(z0)))))) -> c12(A(a(a(a(a(a(a(a(z0)))))))), A(b(b(c_b(c_b(z0))))), B(b(c_b(c_b(z0)))), B(c_b(c_b(z0))))
   B(c_b(c_a(c_a(c_b(c_b(c_c(c_c(z0)))))))) -> c12(A(a(c(c(a(a(z0)))))), A(b(b(c_b(c_b(c_c(c_c(z0))))))), B(b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_a(c_a(z0)))))) -> c12(A(a(a(a(b(b(z0)))))), A(b(b(c_a(c_a(z0))))), B(b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c_c(c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c_c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c(c_a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(c_a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c12(A(a(b(c(c(a(b(b(z0)))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))), B(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(c_a(a(a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(c_a(a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(c_a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(a(c_a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(a(a(c_a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(c_a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c12(A(a(b(a(a(a(a(a(b(b(z0)))))))))), A(b(b(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))), B(b(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(c_a(a(b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(a(c_a(b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(a(a(c_b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(c_b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c12(A(a(b(a(a(b(c(c(a(a(z0)))))))))), A(b(b(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), B(b(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c12(A(a(b(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(b(b(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))), B(b(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c12(A(a(b(a(a(b(a(a(b(b(z0)))))))))), A(b(b(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))), B(b(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(c_b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(c_b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
   B(c_b(c_a(c_a(c_b(c_b(z0)))))) -> c12(A(a(a(a(a(a(a(a(z0)))))))), A(b(b(c_b(c_b(z0))))), B(b(c_b(c_b(z0)))), B(c_b(c_b(z0))))
   B(c_b(c_a(c_a(c_b(c_b(c_c(c_c(z0)))))))) -> c12(A(a(c(c(a(a(z0)))))), A(b(b(c_b(c_b(c_c(c_c(z0))))))), B(b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_a(c_a(z0)))))) -> c12(A(a(a(a(b(b(z0)))))), A(b(b(c_a(c_a(z0))))), B(b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c_c(c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c_c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c(c_a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(c_a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c12(A(a(b(c(c(a(b(b(z0)))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))), B(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(c_a(a(a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(c_a(a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(c_a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(a(c_a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(a(a(c_a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(c_a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c12(A(a(b(a(a(a(a(a(b(b(z0)))))))))), A(b(b(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))), B(b(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(c_a(a(b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(a(c_a(b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(a(a(c_b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(c_b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c12(A(a(b(a(a(b(c(c(a(a(z0)))))))))), A(b(b(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), B(b(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c12(A(a(b(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(b(b(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))), B(b(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c12(A(a(b(a(a(b(a(a(b(b(z0)))))))))), A(b(b(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))), B(b(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(c_b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(c_b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1, B_1

Compound Symbols:   c8_2, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2, c11_6, c11_3, c11_4, c12_4, c12_3, c12_1, c12_2


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

(151) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0)) by 
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(c_a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(c_a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(a(a(c(c(x0))))))

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_c(z0)) -> c(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(z0)))) -> b(b(z0))
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c(c(a(a(z0))))
   b(c_b(c_b(c_b(z0)))) -> a(a(a(a(a(a(z0))))))
   b(c_b(c_a(c_a(z0)))) -> a(a(b(b(z0))))
   c(z0) -> c_c(z0)
   c(c_c(c_a(c_a(z0)))) -> b(b(a(a(c(c(z0))))))
Tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c7(C(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c7(C(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c7(C(c(encArg(z0))))
   ENCARG(cons_a(cons_a(x0))) -> c1(A(c_a(encArg(x0))), ENCARG(cons_a(x0)))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c1(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c1(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_c(z0)))) -> c1(A(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c1(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c1(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_c(z0)))) -> c1(A(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_a(cons_b(x0))) -> c1(ENCARG(cons_b(x0)))
   ENCARG(cons_a(cons_c(cons_a(z0)))) -> c1(A(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_a(cons_c(cons_b(z0)))) -> c1(A(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_a(cons_c(cons_c(z0)))) -> c1(A(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   ENCARG(cons_b(cons_a(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_b(z0)))) -> c2(B(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_b(cons_a(cons_c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
   ENCARG(cons_b(cons_b(x0))) -> c2(B(c_b(encArg(x0))), ENCARG(cons_b(x0)))
   ENCARG(cons_b(cons_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c2(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_b(cons_b(cons_c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_b(cons_c(cons_a(z0)))) -> c2(B(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_b(cons_c(cons_b(z0)))) -> c2(B(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_b(cons_c(cons_c(z0)))) -> c2(B(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   ENCARG(cons_b(cons_c(x0))) -> c2(ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_a(cons_a(z0)))) -> c3(C(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_c(cons_a(cons_b(z0)))) -> c3(C(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_c(cons_a(cons_c(z0)))) -> c3(C(a(c(encArg(z0)))), ENCARG(cons_a(cons_c(z0))))
   ENCARG(cons_c(cons_a(x0))) -> c3(ENCARG(cons_a(x0)))
   ENCARG(cons_c(cons_b(cons_a(z0)))) -> c3(C(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_c(cons_b(cons_b(z0)))) -> c3(C(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_c(cons_b(cons_c(z0)))) -> c3(C(b(c(encArg(z0)))), ENCARG(cons_b(cons_c(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
   ENCARG(cons_c(cons_c(x0))) -> c3(C(c_c(encArg(x0))), ENCARG(cons_c(x0)))
   ENCARG(cons_c(cons_c(cons_a(z0)))) -> c3(C(c(a(encArg(z0)))), ENCARG(cons_c(cons_a(z0))))
   ENCARG(cons_c(cons_c(cons_b(z0)))) -> c3(C(c(b(encArg(z0)))), ENCARG(cons_c(cons_b(z0))))
   ENCARG(cons_c(cons_c(cons_c(z0)))) -> c3(C(c(c(encArg(z0)))), ENCARG(cons_c(cons_c(z0))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
   B(c_b(c_a(c_a(c_b(c_b(z0)))))) -> c12(A(a(a(a(a(a(a(a(z0)))))))), A(b(b(c_b(c_b(z0))))), B(b(c_b(c_b(z0)))), B(c_b(c_b(z0))))
   B(c_b(c_a(c_a(c_b(c_b(c_c(c_c(z0)))))))) -> c12(A(a(c(c(a(a(z0)))))), A(b(b(c_b(c_b(c_c(c_c(z0))))))), B(b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_a(c_a(z0)))))) -> c12(A(a(a(a(b(b(z0)))))), A(b(b(c_a(c_a(z0))))), B(b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c_c(c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c_c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c(c_a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(c_a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c12(A(a(b(c(c(a(b(b(z0)))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))), B(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(c_a(a(a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(c_a(a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(c_a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(a(c_a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(a(a(c_a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(c_a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c12(A(a(b(a(a(a(a(a(b(b(z0)))))))))), A(b(b(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))), B(b(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(c_a(a(b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(a(c_a(b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(a(a(c_b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(c_b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c12(A(a(b(a(a(b(c(c(a(a(z0)))))))))), A(b(b(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), B(b(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c12(A(a(b(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(b(b(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))), B(b(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c12(A(a(b(a(a(b(a(a(b(b(z0)))))))))), A(b(b(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))), B(b(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(c_b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(c_b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(c_a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(c_a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(a(a(c(c(x0))))))
S tuples:
   A(c_a(c_a(c_a(z0)))) -> c8(B(c_b(z0)), B(z0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c_c(a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c(c(c_a(a(x0))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c8(B(c(c(a(c_a(z0))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c8(B(c(c(a(b(b(z0)))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c8(B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(c_a(a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(c_a(a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(c_a(a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(a(a(a(a(c_a(a(x0))))))), B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c8(B(a(a(a(a(a(c_a(z0))))))), B(c_b(c_b(c_b(z0)))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c8(B(a(a(a(a(a(b(b(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c8(B(c_b(c_b(c_b(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(c_a(b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(a(a(c_b(b(x0))))), B(c_b(c_a(c_a(x0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c8(B(a(a(b(c_b(z0))))), B(c_b(c_a(c_a(z0)))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c8(B(a(a(b(c(c(a(a(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c8(B(a(a(b(a(a(a(a(a(a(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c8(B(a(a(b(a(a(b(b(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   A(c_a(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c8(B(c_b(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(c_c(c_a(a(x0)))), C(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c_c(a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c_c(a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(z0)))))) -> c10(C(c(c_a(c_a(z0)))), C(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(c_a(b(b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(z0)))))))) -> c10(C(c(b(b(z0)))), C(a(a(c_a(c_a(z0))))), A(a(c_a(c_a(z0)))), A(c_a(c_a(z0))))
   B(c_b(c_b(c_b(c_c(c_c(x0)))))) -> c10(C(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(c(a(c_b(b(x0))))), C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))) -> c10(C(c(a(b(c_b(z0))))), C(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)))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))))) -> c10(C(c(a(b(c(c(a(a(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))))) -> c10(C(c(a(b(a(a(a(a(a(a(z0)))))))))), C(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))))) -> c10(C(c(a(b(a(a(b(b(z0)))))))), C(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(x0))))))))) -> c10(C(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(c_a(a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(c_a(a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(c_a(a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(c_a(a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(c_a(a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(c_a(a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(c_a(a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(c_a(a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(c_a(c_a(a(x0)))))), A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)), A(x0))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(c_a(a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(c_a(a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(z0)))) -> c11(A(a(a(a(c_a(c_a(z0)))))), A(a(a(a(a(z0))))), A(a(a(a(z0)))), A(a(a(z0))), A(a(z0)), A(z0))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(c_a(b(b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))))
   B(c_b(c_b(c_b(c_a(c_a(z0)))))) -> c11(A(a(a(a(b(b(z0)))))), A(a(a(a(a(c_a(c_a(z0))))))), A(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))))
   B(c_b(c_b(c_b(x0)))) -> c11(A(a(a(a(a(x0))))), A(a(a(a(x0)))), A(a(a(x0))), A(a(x0)))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_b(b(x0))))))), A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))), A(c_a(c_a(c_a(x0)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))) -> c11(A(a(a(a(a(b(c_b(z0))))))), A(a(a(a(a(c_a(c_a(c_a(z0)))))))), A(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)))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c11(A(a(a(a(a(b(c(c(a(a(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_b(c_b(z0)))))))), A(c_a(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c11(A(a(a(a(a(b(a(a(b(b(z0)))))))))), A(a(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))))), A(a(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))))), A(a(a(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))), A(a(c_a(c_a(c_a(c_b(c_a(c_a(z0)))))))), A(c_a(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_b(c_b(c_a(c_a(c_a(x0))))))) -> c11(A(a(a(a(a(c_a(c_a(c_a(x0)))))))), A(a(a(a(c_a(c_a(c_a(x0))))))), A(a(a(c_a(c_a(c_a(x0)))))), A(a(c_a(c_a(c_a(x0))))))
   B(c_b(c_a(c_a(z0)))) -> c12(A(c_a(b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(c_a(b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(c_a(b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(c_a(b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))), B(b(x0)), B(x0))
   B(c_b(c_a(c_a(z0)))) -> c12(A(a(c_b(c_b(z0)))), A(b(b(z0))), B(b(z0)), B(z0))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(c_b(c(c(a(a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(c_b(a(a(a(a(a(a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(c_b(a(a(b(b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(x0)))) -> c12(A(b(b(x0))))
   B(c_b(c_a(c_a(c_b(c_b(z0)))))) -> c12(A(a(a(a(a(a(a(a(z0)))))))), A(b(b(c_b(c_b(z0))))), B(b(c_b(c_b(z0)))), B(c_b(c_b(z0))))
   B(c_b(c_a(c_a(c_b(c_b(c_c(c_c(z0)))))))) -> c12(A(a(c(c(a(a(z0)))))), A(b(b(c_b(c_b(c_c(c_c(z0))))))), B(b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_a(c_a(z0)))))) -> c12(A(a(a(a(b(b(z0)))))), A(b(b(c_a(c_a(z0))))), B(b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c_c(c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c_c(a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(a(b(c(c(c_a(a(x0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))) -> c12(A(a(b(c(c(a(c_a(z0))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(z0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(z0))))))), B(c_b(c_b(c_b(c_c(c_c(z0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))))) -> c12(A(a(b(c(c(a(b(b(z0)))))))), A(b(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))), B(b(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0)))))))))), B(c_b(c_b(c_b(c_c(c_c(c_a(c_a(c_a(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(x0))))))))) -> c12(A(b(b(c_b(c_b(c_b(c_c(c_c(x0)))))))), B(b(c_b(c_b(c_b(c_c(c_c(x0))))))), B(c_b(c_b(c_b(c_c(c_c(x0)))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(c_a(a(a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(c_a(a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(c_a(a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(a(c_a(a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(a(b(a(a(a(a(c_a(a(x0))))))))), A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))), B(c_b(c_b(c_b(x0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))) -> c12(A(a(b(a(a(a(a(a(c_a(z0))))))))), A(b(b(c_b(c_b(c_b(z0)))))), B(b(c_b(c_b(c_b(z0))))), B(c_b(c_b(c_b(z0)))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))))) -> c12(A(a(b(a(a(a(a(a(b(b(z0)))))))))), A(b(b(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))), B(b(c_b(c_b(c_b(c_a(c_a(c_a(z0)))))))), B(c_b(c_b(c_b(c_a(c_a(c_a(z0))))))))
   B(c_b(c_a(c_a(c_b(c_b(c_b(x0))))))) -> c12(A(b(b(c_b(c_b(c_b(x0)))))), B(b(c_b(c_b(c_b(x0))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(c_a(a(b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(a(c_a(b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(a(b(a(a(c_b(b(x0))))))), A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))), B(c_b(c_a(c_a(x0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))) -> c12(A(a(b(a(a(b(c_b(z0))))))), A(b(b(c_b(c_a(c_a(z0)))))), B(b(c_b(c_a(c_a(z0))))), B(c_b(c_a(c_a(z0)))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))))) -> c12(A(a(b(a(a(b(c(c(a(a(z0)))))))))), A(b(b(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))), B(b(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0)))))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(c_c(c_c(z0))))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))))) -> c12(A(a(b(a(a(b(a(a(a(a(a(a(z0)))))))))))), A(b(b(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))), B(b(c_b(c_a(c_a(c_b(c_b(c_b(z0)))))))), B(c_b(c_a(c_a(c_b(c_b(c_b(z0))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))))) -> c12(A(a(b(a(a(b(a(a(b(b(z0)))))))))), A(b(b(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))), B(b(c_b(c_a(c_a(c_b(c_a(c_a(z0)))))))), B(c_b(c_a(c_a(c_b(c_a(c_a(z0))))))))
   B(c_b(c_a(c_a(c_b(c_a(c_a(x0))))))) -> c12(A(b(b(c_b(c_a(c_a(x0)))))), B(b(c_b(c_a(c_a(x0))))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(c_a(a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(c_b(a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(c_b(a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(c_b(a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(c_a(c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(x0)))) -> c14(B(b(c_a(a(c_c(c(x0)))))), B(a(a(c(c(x0))))), A(a(c(c(x0)))), A(c(c(x0))), C(c(x0)), C(x0))
   C(c_c(c_a(c_a(z0)))) -> c14(B(b(c_a(a(c(c_c(z0)))))), B(a(a(c(c(z0))))), A(a(c(c(z0)))), A(c(c(z0))), C(c(z0)), C(z0))
   C(c_c(c_a(c_a(c_c(c_a(c_a(z0))))))) -> c14(B(b(c_a(a(c(b(b(a(a(c(c(z0))))))))))), B(a(a(c(c(c_c(c_a(c_a(z0)))))))), A(a(c(c(c_c(c_a(c_a(z0))))))), A(c(c(c_c(c_a(c_a(z0)))))), C(c(c_c(c_a(c_a(z0))))), C(c_c(c_a(c_a(z0)))))
   C(c_c(c_a(c_a(x0)))) -> c14(B(a(a(c(c(x0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1

Defined Pair Symbols:   A_1, C_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCARG_1, B_1

Compound Symbols:   c8_2, c14_6, c7_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1, c8_1, c10_4, c10_1, c10_2, c11_6, c11_3, c11_4, c12_4, c12_3, c12_1, c12_2, c14_1