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


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 45 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 8 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 0 ms]
    (10) typed CpxTrs
    (11) RewriteLemmaProof [LOWER BOUND(ID), 535 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), 43 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), 2 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 6 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 4 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), 5 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), 13 ms]
        (58) CdtProblem
        (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (60) CdtProblem
        (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (62) CdtProblem
        (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (64) CdtProblem
        (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (66) CdtProblem
        (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19 ms]
        (68) CdtProblem
        (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (70) CdtProblem
        (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (72) CdtProblem
        (73) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (74) CdtProblem
        (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (76) CdtProblem
        (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (78) CdtProblem
        (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (80) CdtProblem
        (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (82) CdtProblem
        (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms]
        (84) CdtProblem
        (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (86) CdtProblem
        (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (88) CdtProblem
        (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 5 ms]
        (90) CdtProblem
        (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (92) CdtProblem
        (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (94) CdtProblem
        (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (96) CdtProblem
        (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (98) CdtProblem
        (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (100) CdtProblem
        (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (102) CdtProblem
        (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (104) CdtProblem
        (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms]
        (106) CdtProblem
        (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (108) CdtProblem
        (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms]
        (110) CdtProblem
        (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (112) CdtProblem
        (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (114) CdtProblem
        (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (116) CdtProblem
        (117) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (118) CdtProblem
        (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (120) CdtProblem
        (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 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) CdtRhsSimplificationProcessorProof [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) CdtNarrowingProof [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), 9 ms]
        (144) CdtProblem
        (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (146) CdtProblem
        (147) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (148) CdtProblem
        (149) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms]
        (150) CdtProblem
        (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms]
        (152) CdtProblem
        (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (154) 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(b(x1)) -> C(x1)
   b(c(x1)) -> A(x1)
   c(a(x1)) -> B(x1)
   A(C(x1)) -> b(x1)
   C(B(x1)) -> a(x1)
   B(A(x1)) -> c(x1)
   a(a(a(a(a(x1))))) -> A(A(A(x1)))
   A(A(A(A(x1)))) -> a(a(a(a(x1))))
   b(b(b(b(b(x1))))) -> B(B(B(x1)))
   B(B(B(B(x1)))) -> b(b(b(b(x1))))
   c(c(c(c(c(x1))))) -> C(C(C(x1)))
   C(C(C(C(x1)))) -> c(c(c(c(x1))))
   B(a(a(a(a(x1))))) -> c(A(A(A(x1))))
   A(A(A(b(x1)))) -> a(a(a(a(C(x1)))))
   C(b(b(b(b(x1))))) -> a(B(B(B(x1))))
   B(B(B(c(x1)))) -> b(b(b(b(A(x1)))))
   A(c(c(c(c(x1))))) -> b(C(C(C(x1))))
   C(C(C(a(x1)))) -> c(c(c(c(B(x1)))))
   a(A(x1)) -> x1
   A(a(x1)) -> x1
   b(B(x1)) -> x1
   B(b(x1)) -> x1
   c(C(x1)) -> x1
   C(c(x1)) -> 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))
   encArg(cons_A(x_1)) -> A(encArg(x_1))
   encArg(cons_C(x_1)) -> C(encArg(x_1))
   encArg(cons_B(x_1)) -> B(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))
   encode_c(x_1) -> c(encArg(x_1))
   encode_A(x_1) -> A(encArg(x_1))
   encode_B(x_1) -> B(encArg(x_1))


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

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


The TRS R consists of the following rules:

   a(b(x1)) -> C(x1)
   b(c(x1)) -> A(x1)
   c(a(x1)) -> B(x1)
   A(C(x1)) -> b(x1)
   C(B(x1)) -> a(x1)
   B(A(x1)) -> c(x1)
   a(a(a(a(a(x1))))) -> A(A(A(x1)))
   A(A(A(A(x1)))) -> a(a(a(a(x1))))
   b(b(b(b(b(x1))))) -> B(B(B(x1)))
   B(B(B(B(x1)))) -> b(b(b(b(x1))))
   c(c(c(c(c(x1))))) -> C(C(C(x1)))
   C(C(C(C(x1)))) -> c(c(c(c(x1))))
   B(a(a(a(a(x1))))) -> c(A(A(A(x1))))
   A(A(A(b(x1)))) -> a(a(a(a(C(x1)))))
   C(b(b(b(b(x1))))) -> a(B(B(B(x1))))
   B(B(B(c(x1)))) -> b(b(b(b(A(x1)))))
   A(c(c(c(c(x1))))) -> b(C(C(C(x1))))
   C(C(C(a(x1)))) -> c(c(c(c(B(x1)))))
   a(A(x1)) -> x1
   A(a(x1)) -> x1
   b(B(x1)) -> x1
   B(b(x1)) -> x1
   c(C(x1)) -> x1
   C(c(x1)) -> 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))
   encArg(cons_A(x_1)) -> A(encArg(x_1))
   encArg(cons_C(x_1)) -> C(encArg(x_1))
   encArg(cons_B(x_1)) -> B(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))
   encode_c(x_1) -> c(encArg(x_1))
   encode_A(x_1) -> A(encArg(x_1))
   encode_B(x_1) -> B(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   a(b(x1)) -> C(x1)
   b(c(x1)) -> A(x1)
   c(a(x1)) -> B(x1)
   A(C(x1)) -> b(x1)
   C(B(x1)) -> a(x1)
   B(A(x1)) -> c(x1)
   a(a(a(a(a(x1))))) -> A(A(A(x1)))
   A(A(A(A(x1)))) -> a(a(a(a(x1))))
   b(b(b(b(b(x1))))) -> B(B(B(x1)))
   B(B(B(B(x1)))) -> b(b(b(b(x1))))
   c(c(c(c(c(x1))))) -> C(C(C(x1)))
   C(C(C(C(x1)))) -> c(c(c(c(x1))))
   B(a(a(a(a(x1))))) -> c(A(A(A(x1))))
   A(A(A(b(x1)))) -> a(a(a(a(C(x1)))))
   C(b(b(b(b(x1))))) -> a(B(B(B(x1))))
   B(B(B(c(x1)))) -> b(b(b(b(A(x1)))))
   A(c(c(c(c(x1))))) -> b(C(C(C(x1))))
   C(C(C(a(x1)))) -> c(c(c(c(B(x1)))))
   a(A(x1)) -> x1
   A(a(x1)) -> x1
   b(B(x1)) -> x1
   B(b(x1)) -> x1
   c(C(x1)) -> x1
   C(c(x1)) -> 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))
   encArg(cons_A(x_1)) -> A(encArg(x_1))
   encArg(cons_C(x_1)) -> C(encArg(x_1))
   encArg(cons_B(x_1)) -> B(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))
   encode_c(x_1) -> c(encArg(x_1))
   encode_A(x_1) -> A(encArg(x_1))
   encode_B(x_1) -> B(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(b(x1)) -> C(x1)
   b(c(x1)) -> A(x1)
   c(a(x1)) -> B(x1)
   A(C(x1)) -> b(x1)
   C(B(x1)) -> a(x1)
   B(A(x1)) -> c(x1)
   a(a(a(a(a(x1))))) -> A(A(A(x1)))
   A(A(A(A(x1)))) -> a(a(a(a(x1))))
   b(b(b(b(b(x1))))) -> B(B(B(x1)))
   B(B(B(B(x1)))) -> b(b(b(b(x1))))
   c(c(c(c(c(x1))))) -> C(C(C(x1)))
   C(C(C(C(x1)))) -> c(c(c(c(x1))))
   B(a(a(a(a(x1))))) -> c(A(A(A(x1))))
   A(A(A(b(x1)))) -> a(a(a(a(C(x1)))))
   C(b(b(b(b(x1))))) -> a(B(B(B(x1))))
   B(B(B(c(x1)))) -> b(b(b(b(A(x1)))))
   A(c(c(c(c(x1))))) -> b(C(C(C(x1))))
   C(C(C(a(x1)))) -> c(c(c(c(B(x1)))))
   a(A(x1)) -> x1
   A(a(x1)) -> x1
   b(B(x1)) -> x1
   B(b(x1)) -> x1
   c(C(x1)) -> x1
   C(c(x1)) -> 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))
   encArg(cons_A(x_1)) -> A(encArg(x_1))
   encArg(cons_C(x_1)) -> C(encArg(x_1))
   encArg(cons_B(x_1)) -> B(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))
   encode_c(x_1) -> c(encArg(x_1))
   encode_A(x_1) -> A(encArg(x_1))
   encode_B(x_1) -> B(encArg(x_1))

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

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

(8)
Obligation:
TRS:
Rules:
a(b(x1)) -> C(x1)
b(c(x1)) -> A(x1)
c(a(x1)) -> B(x1)
A(C(x1)) -> b(x1)
C(B(x1)) -> a(x1)
B(A(x1)) -> c(x1)
a(a(a(a(a(x1))))) -> A(A(A(x1)))
A(A(A(A(x1)))) -> a(a(a(a(x1))))
b(b(b(b(b(x1))))) -> B(B(B(x1)))
B(B(B(B(x1)))) -> b(b(b(b(x1))))
c(c(c(c(c(x1))))) -> C(C(C(x1)))
C(C(C(C(x1)))) -> c(c(c(c(x1))))
B(a(a(a(a(x1))))) -> c(A(A(A(x1))))
A(A(A(b(x1)))) -> a(a(a(a(C(x1)))))
C(b(b(b(b(x1))))) -> a(B(B(B(x1))))
B(B(B(c(x1)))) -> b(b(b(b(A(x1)))))
A(c(c(c(c(x1))))) -> b(C(C(C(x1))))
C(C(C(a(x1)))) -> c(c(c(c(B(x1)))))
a(A(x1)) -> x1
A(a(x1)) -> x1
b(B(x1)) -> x1
B(b(x1)) -> x1
c(C(x1)) -> x1
C(c(x1)) -> 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))
encArg(cons_A(x_1)) -> A(encArg(x_1))
encArg(cons_C(x_1)) -> C(encArg(x_1))
encArg(cons_B(x_1)) -> B(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))
encode_c(x_1) -> c(encArg(x_1))
encode_A(x_1) -> A(encArg(x_1))
encode_B(x_1) -> B(encArg(x_1))

Types:
a :: b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
b :: b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
C :: b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
c :: b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
A :: b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
B :: b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
encArg :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
cons_a :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_b :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_c :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_A :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_C :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_B :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
encode_a :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
encode_b :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
encode_C :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
encode_c :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
encode_A :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
encode_B :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
hole_b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B1_0 :: b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
hole_cons_a:cons_b:cons_c:cons_A:cons_C:cons_B2_0 :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
gen_cons_a:cons_b:cons_c:cons_A:cons_C:cons_B3_0 :: Nat -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B

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

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

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

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

(10)
Obligation:
TRS:
Rules:
a(b(x1)) -> C(x1)
b(c(x1)) -> A(x1)
c(a(x1)) -> B(x1)
A(C(x1)) -> b(x1)
C(B(x1)) -> a(x1)
B(A(x1)) -> c(x1)
a(a(a(a(a(x1))))) -> A(A(A(x1)))
A(A(A(A(x1)))) -> a(a(a(a(x1))))
b(b(b(b(b(x1))))) -> B(B(B(x1)))
B(B(B(B(x1)))) -> b(b(b(b(x1))))
c(c(c(c(c(x1))))) -> C(C(C(x1)))
C(C(C(C(x1)))) -> c(c(c(c(x1))))
B(a(a(a(a(x1))))) -> c(A(A(A(x1))))
A(A(A(b(x1)))) -> a(a(a(a(C(x1)))))
C(b(b(b(b(x1))))) -> a(B(B(B(x1))))
B(B(B(c(x1)))) -> b(b(b(b(A(x1)))))
A(c(c(c(c(x1))))) -> b(C(C(C(x1))))
C(C(C(a(x1)))) -> c(c(c(c(B(x1)))))
a(A(x1)) -> x1
A(a(x1)) -> x1
b(B(x1)) -> x1
B(b(x1)) -> x1
c(C(x1)) -> x1
C(c(x1)) -> 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))
encArg(cons_A(x_1)) -> A(encArg(x_1))
encArg(cons_C(x_1)) -> C(encArg(x_1))
encArg(cons_B(x_1)) -> B(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))
encode_c(x_1) -> c(encArg(x_1))
encode_A(x_1) -> A(encArg(x_1))
encode_B(x_1) -> B(encArg(x_1))

Types:
a :: b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
b :: b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
C :: b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
c :: b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
A :: b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
B :: b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
encArg :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
cons_a :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_b :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_c :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_A :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_C :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_B :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
encode_a :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
encode_b :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
encode_C :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
encode_c :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
encode_A :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
encode_B :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
hole_b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B1_0 :: b:a:C:c:A:B:encArg:encode_a:encode_b:encode_C:encode_c:encode_A:encode_B
hole_cons_a:cons_b:cons_c:cons_A:cons_C:cons_B2_0 :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
gen_cons_a:cons_b:cons_c:cons_A:cons_C:cons_B3_0 :: Nat -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B


Generator Equations:
gen_cons_a:cons_b:cons_c:cons_A:cons_C:cons_B3_0(0) <=> hole_cons_a:cons_b:cons_c:cons_A:cons_C:cons_B2_0
gen_cons_a:cons_b:cons_c:cons_A:cons_C:cons_B3_0(+(x, 1)) <=> cons_a(gen_cons_a:cons_b:cons_c:cons_A:cons_C:cons_B3_0(x))


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

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

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

(11) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_cons_a:cons_b:cons_c:cons_A:cons_C:cons_B3_0(+(1, n203_0))) -> *4_0, rt in Omega(0)

Induction Base:
encArg(gen_cons_a:cons_b:cons_c:cons_A:cons_C:cons_B3_0(+(1, 0)))

Induction Step:
encArg(gen_cons_a:cons_b:cons_c:cons_A:cons_C:cons_B3_0(+(1, +(n203_0, 1)))) ->_R^Omega(0)
a(encArg(gen_cons_a:cons_b:cons_c:cons_A:cons_C:cons_B3_0(+(1, n203_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(b(x1)) -> C(x1)
   b(c(x1)) -> A(x1)
   c(a(x1)) -> B(x1)
   A(C(x1)) -> b(x1)
   C(B(x1)) -> a(x1)
   B(A(x1)) -> c(x1)
   a(a(a(a(a(x1))))) -> A(A(A(x1)))
   A(A(A(A(x1)))) -> a(a(a(a(x1))))
   b(b(b(b(b(x1))))) -> B(B(B(x1)))
   B(B(B(B(x1)))) -> b(b(b(b(x1))))
   c(c(c(c(c(x1))))) -> C(C(C(x1)))
   C(C(C(C(x1)))) -> c(c(c(c(x1))))
   B(a(a(a(a(x1))))) -> c(A(A(A(x1))))
   A(A(A(b(x1)))) -> a(a(a(a(C(x1)))))
   C(b(b(b(b(x1))))) -> a(B(B(B(x1))))
   B(B(B(c(x1)))) -> b(b(b(b(A(x1)))))
   A(c(c(c(c(x1))))) -> b(C(C(C(x1))))
   C(C(C(a(x1)))) -> c(c(c(c(B(x1)))))
   a(A(x1)) -> x1
   A(a(x1)) -> x1
   b(B(x1)) -> x1
   B(b(x1)) -> x1
   c(C(x1)) -> x1
   C(c(x1)) -> 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))
   encArg(cons_A(x_1)) -> A(encArg(x_1))
   encArg(cons_C(x_1)) -> C(encArg(x_1))
   encArg(cons_B(x_1)) -> B(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))
   encode_c(x_1) -> c(encArg(x_1))
   encode_A(x_1) -> A(encArg(x_1))
   encode_B(x_1) -> B(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(b(x1)) -> C(x1)
   b(c(x1)) -> A(x1)
   c(a(x1)) -> B(x1)
   A(C(x1)) -> b(x1)
   C(B(x1)) -> a(x1)
   B(A(x1)) -> c(x1)
   a(a(a(a(a(x1))))) -> A(A(A(x1)))
   A(A(A(A(x1)))) -> a(a(a(a(x1))))
   b(b(b(b(b(x1))))) -> B(B(B(x1)))
   B(B(B(B(x1)))) -> b(b(b(b(x1))))
   c(c(c(c(c(x1))))) -> C(C(C(x1)))
   C(C(C(C(x1)))) -> c(c(c(c(x1))))
   B(a(a(a(a(x1))))) -> c(A(A(A(x1))))
   A(A(A(b(x1)))) -> a(a(a(a(C(x1)))))
   C(b(b(b(b(x1))))) -> a(B(B(B(x1))))
   B(B(B(c(x1)))) -> b(b(b(b(A(x1)))))
   A(c(c(c(c(x1))))) -> b(C(C(C(x1))))
   C(C(C(a(x1)))) -> c(c(c(c(B(x1)))))
   a(A(x1)) -> x1
   A(a(x1)) -> x1
   b(B(x1)) -> x1
   B(b(x1)) -> x1
   c(C(x1)) -> x1
   C(c(x1)) -> 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))
   encArg(cons_A(x_1)) -> A(encArg(x_1))
   encArg(cons_C(x_1)) -> C(encArg(x_1))
   encArg(cons_B(x_1)) -> B(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))
   encode_c(x_1) -> c(encArg(x_1))
   encode_A(x_1) -> A(encArg(x_1))
   encode_B(x_1) -> B(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   c(c_a(x1)) -> B(x1)
   a(c_a(c_a(c_a(c_a(x1))))) -> A(A(A(x1)))
   c(c_c(c_c(c_c(c_c(x1))))) -> C(C(C(x1)))
   B(c_B(c_B(c_B(x1)))) -> b(b(b(b(x1))))
   b(c_b(c_b(c_b(c_b(x1))))) -> B(B(B(x1)))
   B(c_a(c_a(c_a(c_a(x1))))) -> c(A(A(A(x1))))
   B(c_A(x1)) -> c(x1)
   C(c_C(c_C(c_C(x1)))) -> c(c(c(c(x1))))
   C(c_c(x1)) -> x1
   c(c_C(x1)) -> x1
   A(c_A(c_A(c_A(x1)))) -> a(a(a(a(x1))))
   A(c_c(c_c(c_c(c_c(x1))))) -> b(C(C(C(x1))))
   b(c_c(x1)) -> A(x1)
   C(c_B(x1)) -> a(x1)
   C(c_b(c_b(c_b(c_b(x1))))) -> a(B(B(B(x1))))
   B(c_B(c_B(c_c(x1)))) -> b(b(b(b(A(x1)))))
   b(c_B(x1)) -> x1
   A(c_C(x1)) -> b(x1)
   A(c_A(c_A(c_b(x1)))) -> a(a(a(a(C(x1)))))
   B(c_b(x1)) -> x1
   A(c_a(x1)) -> x1
   a(c_A(x1)) -> x1
   a(c_b(x1)) -> C(x1)
   C(c_C(c_C(c_a(x1)))) -> c(c(c(c(B(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))
   encArg(cons_A(x_1)) -> A(encArg(x_1))
   encArg(cons_C(x_1)) -> C(encArg(x_1))
   encArg(cons_B(x_1)) -> B(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))
   encode_c(x_1) -> c(encArg(x_1))
   encode_A(x_1) -> A(encArg(x_1))
   encode_B(x_1) -> B(encArg(x_1))
   a(x0) -> c_a(x0)
   b(x0) -> c_b(x0)
   c(x0) -> c_c(x0)
   C(x0) -> c_C(x0)
   B(x0) -> c_B(x0)
   A(x0) -> c_A(x0)

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

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

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

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


The TRS R consists of the following rules:

   c(c_a(x1)) -> B(x1)
   a(c_a(c_a(c_a(c_a(x1))))) -> A(A(A(x1)))
   c(c_c(c_c(c_c(c_c(x1))))) -> C(C(C(x1)))
   B(c_B(c_B(c_B(x1)))) -> b(b(b(b(x1))))
   b(c_b(c_b(c_b(c_b(x1))))) -> B(B(B(x1)))
   B(c_a(c_a(c_a(c_a(x1))))) -> c(A(A(A(x1))))
   B(c_A(x1)) -> c(x1)
   C(c_C(c_C(c_C(x1)))) -> c(c(c(c(x1))))
   C(c_c(x1)) -> x1
   c(c_C(x1)) -> x1
   A(c_A(c_A(c_A(x1)))) -> a(a(a(a(x1))))
   A(c_c(c_c(c_c(c_c(x1))))) -> b(C(C(C(x1))))
   b(c_c(x1)) -> A(x1)
   C(c_B(x1)) -> a(x1)
   C(c_b(c_b(c_b(c_b(x1))))) -> a(B(B(B(x1))))
   B(c_B(c_B(c_c(x1)))) -> b(b(b(b(A(x1)))))
   b(c_B(x1)) -> x1
   A(c_C(x1)) -> b(x1)
   A(c_A(c_A(c_b(x1)))) -> a(a(a(a(C(x1)))))
   B(c_b(x1)) -> x1
   A(c_a(x1)) -> x1
   a(c_A(x1)) -> x1
   a(c_b(x1)) -> C(x1)
   C(c_C(c_C(c_a(x1)))) -> c(c(c(c(B(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))
   encArg(cons_A(x_1)) -> A(encArg(x_1))
   encArg(cons_C(x_1)) -> C(encArg(x_1))
   encArg(cons_B(x_1)) -> B(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))
   encode_c(x_1) -> c(encArg(x_1))
   encode_A(x_1) -> A(encArg(x_1))
   encode_B(x_1) -> B(encArg(x_1))
   a(x0) -> c_a(x0)
   b(x0) -> c_b(x0)
   c(x0) -> c_c(x0)
   C(x0) -> c_C(x0)
   B(x0) -> c_B(x0)
   A(x0) -> c_A(x0)

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

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

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


The TRS R consists of the following rules:

   c(c_a(x1)) -> B(x1) [1]
   a(c_a(c_a(c_a(c_a(x1))))) -> A(A(A(x1))) [1]
   c(c_c(c_c(c_c(c_c(x1))))) -> C(C(C(x1))) [1]
   B(c_B(c_B(c_B(x1)))) -> b(b(b(b(x1)))) [1]
   b(c_b(c_b(c_b(c_b(x1))))) -> B(B(B(x1))) [1]
   B(c_a(c_a(c_a(c_a(x1))))) -> c(A(A(A(x1)))) [1]
   B(c_A(x1)) -> c(x1) [1]
   C(c_C(c_C(c_C(x1)))) -> c(c(c(c(x1)))) [1]
   C(c_c(x1)) -> x1 [1]
   c(c_C(x1)) -> x1 [1]
   A(c_A(c_A(c_A(x1)))) -> a(a(a(a(x1)))) [1]
   A(c_c(c_c(c_c(c_c(x1))))) -> b(C(C(C(x1)))) [1]
   b(c_c(x1)) -> A(x1) [1]
   C(c_B(x1)) -> a(x1) [1]
   C(c_b(c_b(c_b(c_b(x1))))) -> a(B(B(B(x1)))) [1]
   B(c_B(c_B(c_c(x1)))) -> b(b(b(b(A(x1))))) [1]
   b(c_B(x1)) -> x1 [1]
   A(c_C(x1)) -> b(x1) [1]
   A(c_A(c_A(c_b(x1)))) -> a(a(a(a(C(x1))))) [1]
   B(c_b(x1)) -> x1 [1]
   A(c_a(x1)) -> x1 [1]
   a(c_A(x1)) -> x1 [1]
   a(c_b(x1)) -> C(x1) [1]
   C(c_C(c_C(c_a(x1)))) -> c(c(c(c(B(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]
   encArg(cons_A(x_1)) -> A(encArg(x_1)) [0]
   encArg(cons_C(x_1)) -> C(encArg(x_1)) [0]
   encArg(cons_B(x_1)) -> B(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]
   encode_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]
   a(x0) -> c_a(x0) [0]
   b(x0) -> c_b(x0) [0]
   c(x0) -> c_c(x0) [0]
   C(x0) -> c_C(x0) [0]
   B(x0) -> c_B(x0) [0]
   A(x0) -> c_A(x0) [0]

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

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

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

   c(c_a(x1)) -> B(x1) [1]
   a(c_a(c_a(c_a(c_a(x1))))) -> A(A(A(x1))) [1]
   c(c_c(c_c(c_c(c_c(x1))))) -> C(C(C(x1))) [1]
   B(c_B(c_B(c_B(x1)))) -> b(b(b(b(x1)))) [1]
   b(c_b(c_b(c_b(c_b(x1))))) -> B(B(B(x1))) [1]
   B(c_a(c_a(c_a(c_a(x1))))) -> c(A(A(A(x1)))) [1]
   B(c_A(x1)) -> c(x1) [1]
   C(c_C(c_C(c_C(x1)))) -> c(c(c(c(x1)))) [1]
   C(c_c(x1)) -> x1 [1]
   c(c_C(x1)) -> x1 [1]
   A(c_A(c_A(c_A(x1)))) -> a(a(a(a(x1)))) [1]
   A(c_c(c_c(c_c(c_c(x1))))) -> b(C(C(C(x1)))) [1]
   b(c_c(x1)) -> A(x1) [1]
   C(c_B(x1)) -> a(x1) [1]
   C(c_b(c_b(c_b(c_b(x1))))) -> a(B(B(B(x1)))) [1]
   B(c_B(c_B(c_c(x1)))) -> b(b(b(b(A(x1))))) [1]
   b(c_B(x1)) -> x1 [1]
   A(c_C(x1)) -> b(x1) [1]
   A(c_A(c_A(c_b(x1)))) -> a(a(a(a(C(x1))))) [1]
   B(c_b(x1)) -> x1 [1]
   A(c_a(x1)) -> x1 [1]
   a(c_A(x1)) -> x1 [1]
   a(c_b(x1)) -> C(x1) [1]
   C(c_C(c_C(c_a(x1)))) -> c(c(c(c(B(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]
   encArg(cons_A(x_1)) -> A(encArg(x_1)) [0]
   encArg(cons_C(x_1)) -> C(encArg(x_1)) [0]
   encArg(cons_B(x_1)) -> B(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]
   encode_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]
   a(x0) -> c_a(x0) [0]
   b(x0) -> c_b(x0) [0]
   c(x0) -> c_c(x0) [0]
   C(x0) -> c_C(x0) [0]
   B(x0) -> c_B(x0) [0]
   A(x0) -> c_A(x0) [0]

The TRS has the following type information:
c :: c_a:c_c:c_B:c_b:c_A:c_C -> c_a:c_c:c_B:c_b:c_A:c_C
c_a :: c_a:c_c:c_B:c_b:c_A:c_C -> c_a:c_c:c_B:c_b:c_A:c_C
B :: c_a:c_c:c_B:c_b:c_A:c_C -> c_a:c_c:c_B:c_b:c_A:c_C
a :: c_a:c_c:c_B:c_b:c_A:c_C -> c_a:c_c:c_B:c_b:c_A:c_C
A :: c_a:c_c:c_B:c_b:c_A:c_C -> c_a:c_c:c_B:c_b:c_A:c_C
c_c :: c_a:c_c:c_B:c_b:c_A:c_C -> c_a:c_c:c_B:c_b:c_A:c_C
C :: c_a:c_c:c_B:c_b:c_A:c_C -> c_a:c_c:c_B:c_b:c_A:c_C
c_B :: c_a:c_c:c_B:c_b:c_A:c_C -> c_a:c_c:c_B:c_b:c_A:c_C
b :: c_a:c_c:c_B:c_b:c_A:c_C -> c_a:c_c:c_B:c_b:c_A:c_C
c_b :: c_a:c_c:c_B:c_b:c_A:c_C -> c_a:c_c:c_B:c_b:c_A:c_C
c_A :: c_a:c_c:c_B:c_b:c_A:c_C -> c_a:c_c:c_B:c_b:c_A:c_C
c_C :: c_a:c_c:c_B:c_b:c_A:c_C -> c_a:c_c:c_B:c_b:c_A:c_C
encArg :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C
cons_a :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_b :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_c :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_A :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_C :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_B :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
encode_a :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C
encode_b :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C
encode_C :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C
encode_c :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C
encode_A :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C
encode_B :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C

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
   encode_c_1
   encode_A_1
   encode_B_1
   a_1
   b_1
   c_1
   C_1
   B_1
   A_1

Due to the following rules being added:

   encArg(v0) -> const [0]
   encode_a(v0) -> const [0]
   encode_b(v0) -> const [0]
   encode_C(v0) -> const [0]
   encode_c(v0) -> const [0]
   encode_A(v0) -> const [0]
   encode_B(v0) -> const [0]
   a(v0) -> const [0]
   b(v0) -> const [0]
   c(v0) -> const [0]
   C(v0) -> const [0]
   B(v0) -> const [0]
   A(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:

   c(c_a(x1)) -> B(x1) [1]
   a(c_a(c_a(c_a(c_a(x1))))) -> A(A(A(x1))) [1]
   c(c_c(c_c(c_c(c_c(x1))))) -> C(C(C(x1))) [1]
   B(c_B(c_B(c_B(x1)))) -> b(b(b(b(x1)))) [1]
   b(c_b(c_b(c_b(c_b(x1))))) -> B(B(B(x1))) [1]
   B(c_a(c_a(c_a(c_a(x1))))) -> c(A(A(A(x1)))) [1]
   B(c_A(x1)) -> c(x1) [1]
   C(c_C(c_C(c_C(x1)))) -> c(c(c(c(x1)))) [1]
   C(c_c(x1)) -> x1 [1]
   c(c_C(x1)) -> x1 [1]
   A(c_A(c_A(c_A(x1)))) -> a(a(a(a(x1)))) [1]
   A(c_c(c_c(c_c(c_c(x1))))) -> b(C(C(C(x1)))) [1]
   b(c_c(x1)) -> A(x1) [1]
   C(c_B(x1)) -> a(x1) [1]
   C(c_b(c_b(c_b(c_b(x1))))) -> a(B(B(B(x1)))) [1]
   B(c_B(c_B(c_c(x1)))) -> b(b(b(b(A(x1))))) [1]
   b(c_B(x1)) -> x1 [1]
   A(c_C(x1)) -> b(x1) [1]
   A(c_A(c_A(c_b(x1)))) -> a(a(a(a(C(x1))))) [1]
   B(c_b(x1)) -> x1 [1]
   A(c_a(x1)) -> x1 [1]
   a(c_A(x1)) -> x1 [1]
   a(c_b(x1)) -> C(x1) [1]
   C(c_C(c_C(c_a(x1)))) -> c(c(c(c(B(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]
   encArg(cons_A(x_1)) -> A(encArg(x_1)) [0]
   encArg(cons_C(x_1)) -> C(encArg(x_1)) [0]
   encArg(cons_B(x_1)) -> B(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]
   encode_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]
   a(x0) -> c_a(x0) [0]
   b(x0) -> c_b(x0) [0]
   c(x0) -> c_c(x0) [0]
   C(x0) -> c_C(x0) [0]
   B(x0) -> c_B(x0) [0]
   A(x0) -> c_A(x0) [0]
   encArg(v0) -> const [0]
   encode_a(v0) -> const [0]
   encode_b(v0) -> const [0]
   encode_C(v0) -> const [0]
   encode_c(v0) -> const [0]
   encode_A(v0) -> const [0]
   encode_B(v0) -> const [0]
   a(v0) -> const [0]
   b(v0) -> const [0]
   c(v0) -> const [0]
   C(v0) -> const [0]
   B(v0) -> const [0]
   A(v0) -> const [0]

The TRS has the following type information:
c :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
c_a :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
B :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
a :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
A :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
c_c :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
C :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
c_B :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
b :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
c_b :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
c_A :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
c_C :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
encArg :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:const
cons_a :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_b :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_c :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_A :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_C :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_B :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
encode_a :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:const
encode_b :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:const
encode_C :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:const
encode_c :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:const
encode_A :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:const
encode_B :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:const
const :: c_a:c_c:c_B:c_b:c_A:c_C:const
const1 :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B

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:

   c(c_a(x1)) -> B(x1) [1]
   a(c_a(c_a(c_a(c_a(c_A(c_A(c_A(x1')))))))) -> A(A(a(a(a(a(x1')))))) [2]
   a(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(x1''))))))))) -> A(A(b(C(C(C(x1'')))))) [2]
   a(c_a(c_a(c_a(c_a(c_C(x11)))))) -> A(A(b(x11))) [2]
   a(c_a(c_a(c_a(c_a(c_A(c_A(c_b(x12)))))))) -> A(A(a(a(a(a(C(x12))))))) [2]
   a(c_a(c_a(c_a(c_a(c_a(x13)))))) -> A(A(x13)) [2]
   a(c_a(c_a(c_a(c_a(x1))))) -> A(A(c_A(x1))) [1]
   a(c_a(c_a(c_a(c_a(x1))))) -> A(A(const)) [1]
   c(c_c(c_c(c_c(c_c(c_C(c_C(c_C(x14)))))))) -> C(C(c(c(c(c(x14)))))) [2]
   c(c_c(c_c(c_c(c_c(c_c(x15)))))) -> C(C(x15)) [2]
   c(c_c(c_c(c_c(c_c(c_B(x16)))))) -> C(C(a(x16))) [2]
   c(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(x17))))))))) -> C(C(a(B(B(B(x17)))))) [2]
   c(c_c(c_c(c_c(c_c(c_C(c_C(c_a(x18)))))))) -> C(C(c(c(c(c(B(x18))))))) [2]
   c(c_c(c_c(c_c(c_c(x1))))) -> C(C(c_C(x1))) [1]
   c(c_c(c_c(c_c(c_c(x1))))) -> C(C(const)) [1]
   B(c_B(c_B(c_B(c_b(c_b(c_b(c_b(x19)))))))) -> b(b(b(B(B(B(x19)))))) [2]
   B(c_B(c_B(c_B(c_c(x110))))) -> b(b(b(A(x110)))) [2]
   B(c_B(c_B(c_B(c_B(x111))))) -> b(b(b(x111))) [2]
   B(c_B(c_B(c_B(x1)))) -> b(b(b(c_b(x1)))) [1]
   B(c_B(c_B(c_B(x1)))) -> b(b(b(const))) [1]
   b(c_b(c_b(c_b(c_b(c_B(c_B(c_B(x112)))))))) -> B(B(b(b(b(b(x112)))))) [2]
   b(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(x113))))))))) -> B(B(c(A(A(A(x113)))))) [2]
   b(c_b(c_b(c_b(c_b(c_A(x114)))))) -> B(B(c(x114))) [2]
   b(c_b(c_b(c_b(c_b(c_B(c_B(c_c(x115)))))))) -> B(B(b(b(b(b(A(x115))))))) [2]
   b(c_b(c_b(c_b(c_b(c_b(x116)))))) -> B(B(x116)) [2]
   b(c_b(c_b(c_b(c_b(x1))))) -> B(B(c_B(x1))) [1]
   b(c_b(c_b(c_b(c_b(x1))))) -> B(B(const)) [1]
   B(c_a(c_a(c_a(c_a(c_A(c_A(c_A(x117)))))))) -> c(A(A(a(a(a(a(x117))))))) [2]
   B(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(x118))))))))) -> c(A(A(b(C(C(C(x118))))))) [2]
   B(c_a(c_a(c_a(c_a(c_C(x119)))))) -> c(A(A(b(x119)))) [2]
   B(c_a(c_a(c_a(c_a(c_A(c_A(c_b(x120)))))))) -> c(A(A(a(a(a(a(C(x120)))))))) [2]
   B(c_a(c_a(c_a(c_a(c_a(x121)))))) -> c(A(A(x121))) [2]
   B(c_a(c_a(c_a(c_a(x1))))) -> c(A(A(c_A(x1)))) [1]
   B(c_a(c_a(c_a(c_a(x1))))) -> c(A(A(const))) [1]
   B(c_A(x1)) -> c(x1) [1]
   C(c_C(c_C(c_C(c_a(x122))))) -> c(c(c(B(x122)))) [2]
   C(c_C(c_C(c_C(c_c(c_c(c_c(c_c(x123)))))))) -> c(c(c(C(C(C(x123)))))) [2]
   C(c_C(c_C(c_C(c_C(x124))))) -> c(c(c(x124))) [2]
   C(c_C(c_C(c_C(x1)))) -> c(c(c(c_c(x1)))) [1]
   C(c_C(c_C(c_C(x1)))) -> c(c(c(const))) [1]
   C(c_c(x1)) -> x1 [1]
   c(c_C(x1)) -> x1 [1]
   A(c_A(c_A(c_A(c_a(c_a(c_a(c_a(x125)))))))) -> a(a(a(A(A(A(x125)))))) [2]
   A(c_A(c_A(c_A(c_A(x126))))) -> a(a(a(x126))) [2]
   A(c_A(c_A(c_A(c_b(x127))))) -> a(a(a(C(x127)))) [2]
   A(c_A(c_A(c_A(x1)))) -> a(a(a(c_a(x1)))) [1]
   A(c_A(c_A(c_A(x1)))) -> a(a(a(const))) [1]
   A(c_c(c_c(c_c(c_c(c_C(c_C(c_C(x128)))))))) -> b(C(C(c(c(c(c(x128))))))) [2]
   A(c_c(c_c(c_c(c_c(c_c(x129)))))) -> b(C(C(x129))) [2]
   A(c_c(c_c(c_c(c_c(c_B(x130)))))) -> b(C(C(a(x130)))) [2]
   A(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(x131))))))))) -> b(C(C(a(B(B(B(x131))))))) [2]
   A(c_c(c_c(c_c(c_c(c_C(c_C(c_a(x132)))))))) -> b(C(C(c(c(c(c(B(x132)))))))) [2]
   A(c_c(c_c(c_c(c_c(x1))))) -> b(C(C(c_C(x1)))) [1]
   A(c_c(c_c(c_c(c_c(x1))))) -> b(C(C(const))) [1]
   b(c_c(x1)) -> A(x1) [1]
   C(c_B(x1)) -> a(x1) [1]
   C(c_b(c_b(c_b(c_b(c_B(c_B(c_B(x133)))))))) -> a(B(B(b(b(b(b(x133))))))) [2]
   C(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(x134))))))))) -> a(B(B(c(A(A(A(x134))))))) [2]
   C(c_b(c_b(c_b(c_b(c_A(x135)))))) -> a(B(B(c(x135)))) [2]
   C(c_b(c_b(c_b(c_b(c_B(c_B(c_c(x136)))))))) -> a(B(B(b(b(b(b(A(x136)))))))) [2]
   C(c_b(c_b(c_b(c_b(c_b(x137)))))) -> a(B(B(x137))) [2]
   C(c_b(c_b(c_b(c_b(x1))))) -> a(B(B(c_B(x1)))) [1]
   C(c_b(c_b(c_b(c_b(x1))))) -> a(B(B(const))) [1]
   B(c_B(c_B(c_c(c_A(c_A(c_A(x138))))))) -> b(b(b(b(a(a(a(a(x138)))))))) [2]
   B(c_B(c_B(c_c(c_c(c_c(c_c(c_c(x139)))))))) -> b(b(b(b(b(C(C(C(x139)))))))) [2]
   B(c_B(c_B(c_c(c_C(x140))))) -> b(b(b(b(b(x140))))) [2]
   B(c_B(c_B(c_c(c_A(c_A(c_b(x141))))))) -> b(b(b(b(a(a(a(a(C(x141))))))))) [2]
   B(c_B(c_B(c_c(c_a(x142))))) -> b(b(b(b(x142)))) [2]
   B(c_B(c_B(c_c(x1)))) -> b(b(b(b(c_A(x1))))) [1]
   B(c_B(c_B(c_c(x1)))) -> b(b(b(b(const)))) [1]
   b(c_B(x1)) -> x1 [1]
   A(c_C(x1)) -> b(x1) [1]
   A(c_A(c_A(c_b(c_C(c_C(c_C(x143))))))) -> a(a(a(a(c(c(c(c(x143)))))))) [2]
   A(c_A(c_A(c_b(c_c(x144))))) -> a(a(a(a(x144)))) [2]
   A(c_A(c_A(c_b(c_B(x145))))) -> a(a(a(a(a(x145))))) [2]
   A(c_A(c_A(c_b(c_b(c_b(c_b(c_b(x146)))))))) -> a(a(a(a(a(B(B(B(x146)))))))) [2]
   A(c_A(c_A(c_b(c_C(c_C(c_a(x147))))))) -> a(a(a(a(c(c(c(c(B(x147))))))))) [2]
   A(c_A(c_A(c_b(x1)))) -> a(a(a(a(c_C(x1))))) [1]
   A(c_A(c_A(c_b(x1)))) -> a(a(a(a(const)))) [1]
   B(c_b(x1)) -> x1 [1]
   A(c_a(x1)) -> x1 [1]
   a(c_A(x1)) -> x1 [1]
   a(c_b(x1)) -> C(x1) [1]
   C(c_C(c_C(c_a(c_B(c_B(c_B(x148))))))) -> c(c(c(c(b(b(b(b(x148)))))))) [2]
   C(c_C(c_C(c_a(c_a(c_a(c_a(c_a(x149)))))))) -> c(c(c(c(c(A(A(A(x149)))))))) [2]
   C(c_C(c_C(c_a(c_A(x150))))) -> c(c(c(c(c(x150))))) [2]
   C(c_C(c_C(c_a(c_B(c_B(c_c(x151))))))) -> c(c(c(c(b(b(b(b(A(x151))))))))) [2]
   C(c_C(c_C(c_a(c_b(x152))))) -> c(c(c(c(x152)))) [2]
   C(c_C(c_C(c_a(x1)))) -> c(c(c(c(c_B(x1))))) [1]
   C(c_C(c_C(c_a(x1)))) -> c(c(c(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(cons_A(x_12))) -> a(A(encArg(x_12))) [0]
   encArg(cons_a(cons_C(x_13))) -> a(C(encArg(x_13))) [0]
   encArg(cons_a(cons_B(x_14))) -> a(B(encArg(x_14))) [0]
   encArg(cons_a(x_1)) -> a(const) [0]
   encArg(cons_b(cons_a(x_15))) -> b(a(encArg(x_15))) [0]
   encArg(cons_b(cons_b(x_16))) -> b(b(encArg(x_16))) [0]
   encArg(cons_b(cons_c(x_17))) -> b(c(encArg(x_17))) [0]
   encArg(cons_b(cons_A(x_18))) -> b(A(encArg(x_18))) [0]
   encArg(cons_b(cons_C(x_19))) -> b(C(encArg(x_19))) [0]
   encArg(cons_b(cons_B(x_110))) -> b(B(encArg(x_110))) [0]
   encArg(cons_b(x_1)) -> b(const) [0]
   encArg(cons_c(cons_a(x_111))) -> c(a(encArg(x_111))) [0]
   encArg(cons_c(cons_b(x_112))) -> c(b(encArg(x_112))) [0]
   encArg(cons_c(cons_c(x_113))) -> c(c(encArg(x_113))) [0]
   encArg(cons_c(cons_A(x_114))) -> c(A(encArg(x_114))) [0]
   encArg(cons_c(cons_C(x_115))) -> c(C(encArg(x_115))) [0]
   encArg(cons_c(cons_B(x_116))) -> c(B(encArg(x_116))) [0]
   encArg(cons_c(x_1)) -> c(const) [0]
   encArg(cons_A(cons_a(x_117))) -> A(a(encArg(x_117))) [0]
   encArg(cons_A(cons_b(x_118))) -> A(b(encArg(x_118))) [0]
   encArg(cons_A(cons_c(x_119))) -> A(c(encArg(x_119))) [0]
   encArg(cons_A(cons_A(x_120))) -> A(A(encArg(x_120))) [0]
   encArg(cons_A(cons_C(x_121))) -> A(C(encArg(x_121))) [0]
   encArg(cons_A(cons_B(x_122))) -> A(B(encArg(x_122))) [0]
   encArg(cons_A(x_1)) -> A(const) [0]
   encArg(cons_C(cons_a(x_123))) -> C(a(encArg(x_123))) [0]
   encArg(cons_C(cons_b(x_124))) -> C(b(encArg(x_124))) [0]
   encArg(cons_C(cons_c(x_125))) -> C(c(encArg(x_125))) [0]
   encArg(cons_C(cons_A(x_126))) -> C(A(encArg(x_126))) [0]
   encArg(cons_C(cons_C(x_127))) -> C(C(encArg(x_127))) [0]
   encArg(cons_C(cons_B(x_128))) -> C(B(encArg(x_128))) [0]
   encArg(cons_C(x_1)) -> C(const) [0]
   encArg(cons_B(cons_a(x_129))) -> B(a(encArg(x_129))) [0]
   encArg(cons_B(cons_b(x_130))) -> B(b(encArg(x_130))) [0]
   encArg(cons_B(cons_c(x_131))) -> B(c(encArg(x_131))) [0]
   encArg(cons_B(cons_A(x_132))) -> B(A(encArg(x_132))) [0]
   encArg(cons_B(cons_C(x_133))) -> B(C(encArg(x_133))) [0]
   encArg(cons_B(cons_B(x_134))) -> B(B(encArg(x_134))) [0]
   encArg(cons_B(x_1)) -> B(const) [0]
   encode_a(cons_a(x_135)) -> a(a(encArg(x_135))) [0]
   encode_a(cons_b(x_136)) -> a(b(encArg(x_136))) [0]
   encode_a(cons_c(x_137)) -> a(c(encArg(x_137))) [0]
   encode_a(cons_A(x_138)) -> a(A(encArg(x_138))) [0]
   encode_a(cons_C(x_139)) -> a(C(encArg(x_139))) [0]
   encode_a(cons_B(x_140)) -> a(B(encArg(x_140))) [0]
   encode_a(x_1) -> a(const) [0]
   encode_b(cons_a(x_141)) -> b(a(encArg(x_141))) [0]
   encode_b(cons_b(x_142)) -> b(b(encArg(x_142))) [0]
   encode_b(cons_c(x_143)) -> b(c(encArg(x_143))) [0]
   encode_b(cons_A(x_144)) -> b(A(encArg(x_144))) [0]
   encode_b(cons_C(x_145)) -> b(C(encArg(x_145))) [0]
   encode_b(cons_B(x_146)) -> b(B(encArg(x_146))) [0]
   encode_b(x_1) -> b(const) [0]
   encode_C(cons_a(x_147)) -> C(a(encArg(x_147))) [0]
   encode_C(cons_b(x_148)) -> C(b(encArg(x_148))) [0]
   encode_C(cons_c(x_149)) -> C(c(encArg(x_149))) [0]
   encode_C(cons_A(x_150)) -> C(A(encArg(x_150))) [0]
   encode_C(cons_C(x_151)) -> C(C(encArg(x_151))) [0]
   encode_C(cons_B(x_152)) -> C(B(encArg(x_152))) [0]
   encode_C(x_1) -> C(const) [0]
   encode_c(cons_a(x_153)) -> c(a(encArg(x_153))) [0]
   encode_c(cons_b(x_154)) -> c(b(encArg(x_154))) [0]
   encode_c(cons_c(x_155)) -> c(c(encArg(x_155))) [0]
   encode_c(cons_A(x_156)) -> c(A(encArg(x_156))) [0]
   encode_c(cons_C(x_157)) -> c(C(encArg(x_157))) [0]
   encode_c(cons_B(x_158)) -> c(B(encArg(x_158))) [0]
   encode_c(x_1) -> c(const) [0]
   encode_A(cons_a(x_159)) -> A(a(encArg(x_159))) [0]
   encode_A(cons_b(x_160)) -> A(b(encArg(x_160))) [0]
   encode_A(cons_c(x_161)) -> A(c(encArg(x_161))) [0]
   encode_A(cons_A(x_162)) -> A(A(encArg(x_162))) [0]
   encode_A(cons_C(x_163)) -> A(C(encArg(x_163))) [0]
   encode_A(cons_B(x_164)) -> A(B(encArg(x_164))) [0]
   encode_A(x_1) -> A(const) [0]
   encode_B(cons_a(x_165)) -> B(a(encArg(x_165))) [0]
   encode_B(cons_b(x_166)) -> B(b(encArg(x_166))) [0]
   encode_B(cons_c(x_167)) -> B(c(encArg(x_167))) [0]
   encode_B(cons_A(x_168)) -> B(A(encArg(x_168))) [0]
   encode_B(cons_C(x_169)) -> B(C(encArg(x_169))) [0]
   encode_B(cons_B(x_170)) -> B(B(encArg(x_170))) [0]
   encode_B(x_1) -> B(const) [0]
   a(x0) -> c_a(x0) [0]
   b(x0) -> c_b(x0) [0]
   c(x0) -> c_c(x0) [0]
   C(x0) -> c_C(x0) [0]
   B(x0) -> c_B(x0) [0]
   A(x0) -> c_A(x0) [0]
   encArg(v0) -> const [0]
   encode_a(v0) -> const [0]
   encode_b(v0) -> const [0]
   encode_C(v0) -> const [0]
   encode_c(v0) -> const [0]
   encode_A(v0) -> const [0]
   encode_B(v0) -> const [0]
   a(v0) -> const [0]
   b(v0) -> const [0]
   c(v0) -> const [0]
   C(v0) -> const [0]
   B(v0) -> const [0]
   A(v0) -> const [0]

The TRS has the following type information:
c :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
c_a :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
B :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
a :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
A :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
c_c :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
C :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
c_B :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
b :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
c_b :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
c_A :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
c_C :: c_a:c_c:c_B:c_b:c_A:c_C:const -> c_a:c_c:c_B:c_b:c_A:c_C:const
encArg :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:const
cons_a :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_b :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_c :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_A :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_C :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_B :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
encode_a :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:const
encode_b :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:const
encode_C :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:const
encode_c :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:const
encode_A :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:const
encode_B :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:const
const :: c_a:c_c:c_B:c_b:c_A:c_C:const
const1 :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B

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) -{ 1 }-> x1 :|: x1 >= 0, z = 1 + x1
   A(z) -{ 1 }-> b(x1) :|: x1 >= 0, z = 1 + x1
   A(z) -{ 2 }-> b(C(C(x129))) :|: z = 1 + (1 + (1 + (1 + (1 + x129)))), x129 >= 0
   A(z) -{ 2 }-> b(C(C(c(c(c(c(x128))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x128)))))), x128 >= 0
   A(z) -{ 2 }-> b(C(C(c(c(c(c(B(x132)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x132)))))), x132 >= 0
   A(z) -{ 2 }-> b(C(C(a(x130)))) :|: z = 1 + (1 + (1 + (1 + (1 + x130)))), x130 >= 0
   A(z) -{ 2 }-> b(C(C(a(B(B(B(x131))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x131))))))), x131 >= 0
   A(z) -{ 1 }-> b(C(C(0))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   A(z) -{ 1 }-> b(C(C(1 + x1))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   A(z) -{ 2 }-> a(a(a(x126))) :|: z = 1 + (1 + (1 + (1 + x126))), x126 >= 0
   A(z) -{ 2 }-> a(a(a(a(x144)))) :|: z = 1 + (1 + (1 + (1 + x144))), x144 >= 0
   A(z) -{ 2 }-> a(a(a(a(c(c(c(c(x143)))))))) :|: x143 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x143)))))
   A(z) -{ 2 }-> a(a(a(a(c(c(c(c(B(x147))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x147))))), x147 >= 0
   A(z) -{ 2 }-> a(a(a(a(a(x145))))) :|: x145 >= 0, z = 1 + (1 + (1 + (1 + x145)))
   A(z) -{ 2 }-> a(a(a(a(a(B(B(B(x146)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x146)))))), x146 >= 0
   A(z) -{ 1 }-> a(a(a(a(0)))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   A(z) -{ 1 }-> a(a(a(a(1 + x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   A(z) -{ 2 }-> a(a(a(C(x127)))) :|: z = 1 + (1 + (1 + (1 + x127))), x127 >= 0
   A(z) -{ 2 }-> a(a(a(A(A(A(x125)))))) :|: x125 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x125))))))
   A(z) -{ 1 }-> a(a(a(0))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   A(z) -{ 1 }-> a(a(a(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) -{ 1 }-> x1 :|: x1 >= 0, z = 1 + x1
   B(z) -{ 1 }-> c(x1) :|: x1 >= 0, z = 1 + x1
   B(z) -{ 2 }-> c(A(A(x121))) :|: z = 1 + (1 + (1 + (1 + (1 + x121)))), x121 >= 0
   B(z) -{ 2 }-> c(A(A(b(x119)))) :|: z = 1 + (1 + (1 + (1 + (1 + x119)))), x119 >= 0
   B(z) -{ 2 }-> c(A(A(b(C(C(C(x118))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x118))))))), x118 >= 0
   B(z) -{ 2 }-> c(A(A(a(a(a(a(x117))))))) :|: x117 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x117))))))
   B(z) -{ 2 }-> c(A(A(a(a(a(a(C(x120)))))))) :|: x120 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x120))))))
   B(z) -{ 1 }-> c(A(A(0))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   B(z) -{ 1 }-> c(A(A(1 + x1))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   B(z) -{ 2 }-> b(b(b(x111))) :|: z = 1 + (1 + (1 + (1 + x111))), x111 >= 0
   B(z) -{ 2 }-> b(b(b(b(x142)))) :|: z = 1 + (1 + (1 + (1 + x142))), x142 >= 0
   B(z) -{ 2 }-> b(b(b(b(b(x140))))) :|: z = 1 + (1 + (1 + (1 + x140))), x140 >= 0
   B(z) -{ 2 }-> b(b(b(b(b(C(C(C(x139)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x139)))))), x139 >= 0
   B(z) -{ 2 }-> b(b(b(b(a(a(a(a(x138)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x138))))), x138 >= 0
   B(z) -{ 2 }-> b(b(b(b(a(a(a(a(C(x141))))))))) :|: x141 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x141)))))
   B(z) -{ 1 }-> b(b(b(b(0)))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   B(z) -{ 1 }-> b(b(b(b(1 + x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   B(z) -{ 2 }-> b(b(b(B(B(B(x19)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x19)))))), x19 >= 0
   B(z) -{ 2 }-> b(b(b(A(x110)))) :|: z = 1 + (1 + (1 + (1 + x110))), x110 >= 0
   B(z) -{ 1 }-> b(b(b(0))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   B(z) -{ 1 }-> b(b(b(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) -{ 1 }-> x1 :|: x1 >= 0, z = 1 + x1
   C(z) -{ 2 }-> c(c(c(x124))) :|: x124 >= 0, z = 1 + (1 + (1 + (1 + x124)))
   C(z) -{ 2 }-> c(c(c(c(x152)))) :|: x152 >= 0, z = 1 + (1 + (1 + (1 + x152)))
   C(z) -{ 2 }-> c(c(c(c(c(x150))))) :|: x150 >= 0, z = 1 + (1 + (1 + (1 + x150)))
   C(z) -{ 2 }-> c(c(c(c(c(A(A(A(x149)))))))) :|: x149 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x149))))))
   C(z) -{ 2 }-> c(c(c(c(b(b(b(b(x148)))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x148))))), x148 >= 0
   C(z) -{ 2 }-> c(c(c(c(b(b(b(b(A(x151))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x151))))), x151 >= 0
   C(z) -{ 1 }-> c(c(c(c(0)))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   C(z) -{ 1 }-> c(c(c(c(1 + x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   C(z) -{ 2 }-> c(c(c(C(C(C(x123)))))) :|: x123 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x123))))))
   C(z) -{ 2 }-> c(c(c(B(x122)))) :|: x122 >= 0, z = 1 + (1 + (1 + (1 + x122)))
   C(z) -{ 1 }-> c(c(c(0))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   C(z) -{ 1 }-> c(c(c(1 + x1))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   C(z) -{ 1 }-> a(x1) :|: x1 >= 0, z = 1 + x1
   C(z) -{ 2 }-> a(B(B(x137))) :|: z = 1 + (1 + (1 + (1 + (1 + x137)))), x137 >= 0
   C(z) -{ 2 }-> a(B(B(c(x135)))) :|: z = 1 + (1 + (1 + (1 + (1 + x135)))), x135 >= 0
   C(z) -{ 2 }-> a(B(B(c(A(A(A(x134))))))) :|: x134 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x134)))))))
   C(z) -{ 2 }-> a(B(B(b(b(b(b(x133))))))) :|: x133 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x133))))))
   C(z) -{ 2 }-> a(B(B(b(b(b(b(A(x136)))))))) :|: x136 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x136))))))
   C(z) -{ 1 }-> a(B(B(0))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   C(z) -{ 1 }-> a(B(B(1 + x1))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   C(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   C(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   a(z) -{ 1 }-> x1 :|: x1 >= 0, z = 1 + x1
   a(z) -{ 1 }-> C(x1) :|: x1 >= 0, z = 1 + x1
   a(z) -{ 2 }-> A(A(x13)) :|: x13 >= 0, z = 1 + (1 + (1 + (1 + (1 + x13))))
   a(z) -{ 2 }-> A(A(b(x11))) :|: x11 >= 0, z = 1 + (1 + (1 + (1 + (1 + x11))))
   a(z) -{ 2 }-> A(A(b(C(C(C(x1'')))))) :|: x1'' >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1'')))))))
   a(z) -{ 2 }-> A(A(a(a(a(a(x1')))))) :|: x1' >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1'))))))
   a(z) -{ 2 }-> A(A(a(a(a(a(C(x12))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x12)))))), x12 >= 0
   a(z) -{ 1 }-> A(A(0)) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 1 }-> A(A(1 + x1)) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   b(z) -{ 1 }-> x1 :|: x1 >= 0, z = 1 + x1
   b(z) -{ 2 }-> B(B(x116)) :|: z = 1 + (1 + (1 + (1 + (1 + x116)))), x116 >= 0
   b(z) -{ 2 }-> B(B(c(x114))) :|: z = 1 + (1 + (1 + (1 + (1 + x114)))), x114 >= 0
   b(z) -{ 2 }-> B(B(c(A(A(A(x113)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x113))))))), x113 >= 0
   b(z) -{ 2 }-> B(B(b(b(b(b(x112)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x112)))))), x112 >= 0
   b(z) -{ 2 }-> B(B(b(b(b(b(A(x115))))))) :|: x115 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x115))))))
   b(z) -{ 1 }-> B(B(0)) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   b(z) -{ 1 }-> B(B(1 + x1)) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   b(z) -{ 1 }-> A(x1) :|: x1 >= 0, z = 1 + x1
   b(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   b(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   c(z) -{ 1 }-> x1 :|: x1 >= 0, z = 1 + x1
   c(z) -{ 2 }-> C(C(x15)) :|: z = 1 + (1 + (1 + (1 + (1 + x15)))), x15 >= 0
   c(z) -{ 2 }-> C(C(c(c(c(c(x14)))))) :|: x14 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x14))))))
   c(z) -{ 2 }-> C(C(c(c(c(c(B(x18))))))) :|: x18 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x18))))))
   c(z) -{ 2 }-> C(C(a(x16))) :|: z = 1 + (1 + (1 + (1 + (1 + x16)))), x16 >= 0
   c(z) -{ 2 }-> C(C(a(B(B(B(x17)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x17))))))), x17 >= 0
   c(z) -{ 1 }-> C(C(0)) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   c(z) -{ 1 }-> C(C(1 + x1)) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   c(z) -{ 1 }-> B(x1) :|: x1 >= 0, z = 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_113))) :|: x_113 >= 0, z = 1 + (1 + x_113)
   encArg(z) -{ 0 }-> c(b(encArg(x_112))) :|: x_112 >= 0, z = 1 + (1 + x_112)
   encArg(z) -{ 0 }-> c(a(encArg(x_111))) :|: z = 1 + (1 + x_111), x_111 >= 0
   encArg(z) -{ 0 }-> c(C(encArg(x_115))) :|: z = 1 + (1 + x_115), x_115 >= 0
   encArg(z) -{ 0 }-> c(B(encArg(x_116))) :|: z = 1 + (1 + x_116), x_116 >= 0
   encArg(z) -{ 0 }-> c(A(encArg(x_114))) :|: z = 1 + (1 + x_114), x_114 >= 0
   encArg(z) -{ 0 }-> c(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> b(c(encArg(x_17))) :|: x_17 >= 0, z = 1 + (1 + x_17)
   encArg(z) -{ 0 }-> b(b(encArg(x_16))) :|: x_16 >= 0, z = 1 + (1 + x_16)
   encArg(z) -{ 0 }-> b(a(encArg(x_15))) :|: x_15 >= 0, z = 1 + (1 + x_15)
   encArg(z) -{ 0 }-> b(C(encArg(x_19))) :|: z = 1 + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> b(B(encArg(x_110))) :|: z = 1 + (1 + x_110), x_110 >= 0
   encArg(z) -{ 0 }-> b(A(encArg(x_18))) :|: z = 1 + (1 + x_18), x_18 >= 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(C(encArg(x_13))) :|: z = 1 + (1 + x_13), x_13 >= 0
   encArg(z) -{ 0 }-> a(B(encArg(x_14))) :|: x_14 >= 0, z = 1 + (1 + x_14)
   encArg(z) -{ 0 }-> a(A(encArg(x_12))) :|: z = 1 + (1 + x_12), x_12 >= 0
   encArg(z) -{ 0 }-> a(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> C(c(encArg(x_125))) :|: z = 1 + (1 + x_125), x_125 >= 0
   encArg(z) -{ 0 }-> C(b(encArg(x_124))) :|: x_124 >= 0, z = 1 + (1 + x_124)
   encArg(z) -{ 0 }-> C(a(encArg(x_123))) :|: x_123 >= 0, z = 1 + (1 + x_123)
   encArg(z) -{ 0 }-> C(C(encArg(x_127))) :|: z = 1 + (1 + x_127), x_127 >= 0
   encArg(z) -{ 0 }-> C(B(encArg(x_128))) :|: x_128 >= 0, z = 1 + (1 + x_128)
   encArg(z) -{ 0 }-> C(A(encArg(x_126))) :|: z = 1 + (1 + x_126), x_126 >= 0
   encArg(z) -{ 0 }-> C(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> B(c(encArg(x_131))) :|: z = 1 + (1 + x_131), x_131 >= 0
   encArg(z) -{ 0 }-> B(b(encArg(x_130))) :|: x_130 >= 0, z = 1 + (1 + x_130)
   encArg(z) -{ 0 }-> B(a(encArg(x_129))) :|: z = 1 + (1 + x_129), x_129 >= 0
   encArg(z) -{ 0 }-> B(C(encArg(x_133))) :|: z = 1 + (1 + x_133), x_133 >= 0
   encArg(z) -{ 0 }-> B(B(encArg(x_134))) :|: z = 1 + (1 + x_134), x_134 >= 0
   encArg(z) -{ 0 }-> B(A(encArg(x_132))) :|: x_132 >= 0, z = 1 + (1 + x_132)
   encArg(z) -{ 0 }-> B(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> A(c(encArg(x_119))) :|: z = 1 + (1 + x_119), x_119 >= 0
   encArg(z) -{ 0 }-> A(b(encArg(x_118))) :|: z = 1 + (1 + x_118), x_118 >= 0
   encArg(z) -{ 0 }-> A(a(encArg(x_117))) :|: z = 1 + (1 + x_117), x_117 >= 0
   encArg(z) -{ 0 }-> A(C(encArg(x_121))) :|: z = 1 + (1 + x_121), x_121 >= 0
   encArg(z) -{ 0 }-> A(B(encArg(x_122))) :|: x_122 >= 0, z = 1 + (1 + x_122)
   encArg(z) -{ 0 }-> A(A(encArg(x_120))) :|: x_120 >= 0, z = 1 + (1 + x_120)
   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_161))) :|: z = 1 + x_161, x_161 >= 0
   encode_A(z) -{ 0 }-> A(b(encArg(x_160))) :|: x_160 >= 0, z = 1 + x_160
   encode_A(z) -{ 0 }-> A(a(encArg(x_159))) :|: x_159 >= 0, z = 1 + x_159
   encode_A(z) -{ 0 }-> A(C(encArg(x_163))) :|: z = 1 + x_163, x_163 >= 0
   encode_A(z) -{ 0 }-> A(B(encArg(x_164))) :|: z = 1 + x_164, x_164 >= 0
   encode_A(z) -{ 0 }-> A(A(encArg(x_162))) :|: x_162 >= 0, z = 1 + x_162
   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_167))) :|: z = 1 + x_167, x_167 >= 0
   encode_B(z) -{ 0 }-> B(b(encArg(x_166))) :|: z = 1 + x_166, x_166 >= 0
   encode_B(z) -{ 0 }-> B(a(encArg(x_165))) :|: z = 1 + x_165, x_165 >= 0
   encode_B(z) -{ 0 }-> B(C(encArg(x_169))) :|: z = 1 + x_169, x_169 >= 0
   encode_B(z) -{ 0 }-> B(B(encArg(x_170))) :|: z = 1 + x_170, x_170 >= 0
   encode_B(z) -{ 0 }-> B(A(encArg(x_168))) :|: z = 1 + x_168, x_168 >= 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_149))) :|: z = 1 + x_149, x_149 >= 0
   encode_C(z) -{ 0 }-> C(b(encArg(x_148))) :|: z = 1 + x_148, x_148 >= 0
   encode_C(z) -{ 0 }-> C(a(encArg(x_147))) :|: z = 1 + x_147, x_147 >= 0
   encode_C(z) -{ 0 }-> C(C(encArg(x_151))) :|: z = 1 + x_151, x_151 >= 0
   encode_C(z) -{ 0 }-> C(B(encArg(x_152))) :|: z = 1 + x_152, x_152 >= 0
   encode_C(z) -{ 0 }-> C(A(encArg(x_150))) :|: z = 1 + x_150, x_150 >= 0
   encode_C(z) -{ 0 }-> C(0) :|: x_1 >= 0, z = x_1
   encode_C(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_a(z) -{ 0 }-> a(c(encArg(x_137))) :|: z = 1 + x_137, x_137 >= 0
   encode_a(z) -{ 0 }-> a(b(encArg(x_136))) :|: x_136 >= 0, z = 1 + x_136
   encode_a(z) -{ 0 }-> a(a(encArg(x_135))) :|: z = 1 + x_135, x_135 >= 0
   encode_a(z) -{ 0 }-> a(C(encArg(x_139))) :|: z = 1 + x_139, x_139 >= 0
   encode_a(z) -{ 0 }-> a(B(encArg(x_140))) :|: z = 1 + x_140, x_140 >= 0
   encode_a(z) -{ 0 }-> a(A(encArg(x_138))) :|: x_138 >= 0, z = 1 + x_138
   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_143))) :|: x_143 >= 0, z = 1 + x_143
   encode_b(z) -{ 0 }-> b(b(encArg(x_142))) :|: z = 1 + x_142, x_142 >= 0
   encode_b(z) -{ 0 }-> b(a(encArg(x_141))) :|: z = 1 + x_141, x_141 >= 0
   encode_b(z) -{ 0 }-> b(C(encArg(x_145))) :|: x_145 >= 0, z = 1 + x_145
   encode_b(z) -{ 0 }-> b(B(encArg(x_146))) :|: x_146 >= 0, z = 1 + x_146
   encode_b(z) -{ 0 }-> b(A(encArg(x_144))) :|: x_144 >= 0, z = 1 + x_144
   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_155))) :|: x_155 >= 0, z = 1 + x_155
   encode_c(z) -{ 0 }-> c(b(encArg(x_154))) :|: x_154 >= 0, z = 1 + x_154
   encode_c(z) -{ 0 }-> c(a(encArg(x_153))) :|: x_153 >= 0, z = 1 + x_153
   encode_c(z) -{ 0 }-> c(C(encArg(x_157))) :|: z = 1 + x_157, x_157 >= 0
   encode_c(z) -{ 0 }-> c(B(encArg(x_158))) :|: z = 1 + x_158, x_158 >= 0
   encode_c(z) -{ 0 }-> c(A(encArg(x_156))) :|: x_156 >= 0, z = 1 + x_156
   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(c(c(c(c(B(z - 7)))))))) :|: z - 7 >= 0
   A(z) -{ 2 }-> b(C(C(c(c(c(c(z - 7))))))) :|: z - 7 >= 0
   A(z) -{ 2 }-> b(C(C(a(B(B(B(z - 8))))))) :|: z - 8 >= 0
   A(z) -{ 2 }-> b(C(C(a(z - 5)))) :|: z - 5 >= 0
   A(z) -{ 1 }-> b(C(C(0))) :|: z - 4 >= 0
   A(z) -{ 2 }-> b(C(C(z - 5))) :|: z - 5 >= 0
   A(z) -{ 1 }-> b(C(C(1 + (z - 4)))) :|: z - 4 >= 0
   A(z) -{ 1 }-> b(z - 1) :|: z - 1 >= 0
   A(z) -{ 2 }-> a(a(a(a(c(c(c(c(B(z - 6))))))))) :|: z - 6 >= 0
   A(z) -{ 2 }-> a(a(a(a(c(c(c(c(z - 6)))))))) :|: z - 6 >= 0
   A(z) -{ 2 }-> a(a(a(a(a(B(B(B(z - 7)))))))) :|: z - 7 >= 0
   A(z) -{ 2 }-> a(a(a(a(a(z - 4))))) :|: z - 4 >= 0
   A(z) -{ 1 }-> a(a(a(a(0)))) :|: z - 3 >= 0
   A(z) -{ 2 }-> a(a(a(a(z - 4)))) :|: z - 4 >= 0
   A(z) -{ 1 }-> a(a(a(a(1 + (z - 3))))) :|: z - 3 >= 0
   A(z) -{ 2 }-> a(a(a(C(z - 4)))) :|: z - 4 >= 0
   A(z) -{ 2 }-> a(a(a(A(A(A(z - 7)))))) :|: z - 7 >= 0
   A(z) -{ 1 }-> a(a(a(0))) :|: z - 3 >= 0
   A(z) -{ 2 }-> a(a(a(z - 4))) :|: z - 4 >= 0
   A(z) -{ 1 }-> a(a(a(1 + (z - 3)))) :|: z - 3 >= 0
   A(z) -{ 0 }-> 0 :|: z >= 0
   A(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   A(z) -{ 0 }-> 1 + z :|: z >= 0
   B(z) -{ 2 }-> c(A(A(b(C(C(C(z - 8))))))) :|: z - 8 >= 0
   B(z) -{ 2 }-> c(A(A(b(z - 5)))) :|: z - 5 >= 0
   B(z) -{ 2 }-> c(A(A(a(a(a(a(C(z - 7)))))))) :|: z - 7 >= 0
   B(z) -{ 2 }-> c(A(A(a(a(a(a(z - 7))))))) :|: z - 7 >= 0
   B(z) -{ 1 }-> c(A(A(0))) :|: z - 4 >= 0
   B(z) -{ 2 }-> c(A(A(z - 5))) :|: z - 5 >= 0
   B(z) -{ 1 }-> c(A(A(1 + (z - 4)))) :|: z - 4 >= 0
   B(z) -{ 1 }-> c(z - 1) :|: z - 1 >= 0
   B(z) -{ 2 }-> b(b(b(b(b(C(C(C(z - 7)))))))) :|: z - 7 >= 0
   B(z) -{ 2 }-> b(b(b(b(b(z - 4))))) :|: z - 4 >= 0
   B(z) -{ 2 }-> b(b(b(b(a(a(a(a(C(z - 6))))))))) :|: z - 6 >= 0
   B(z) -{ 2 }-> b(b(b(b(a(a(a(a(z - 6)))))))) :|: z - 6 >= 0
   B(z) -{ 1 }-> b(b(b(b(0)))) :|: z - 3 >= 0
   B(z) -{ 2 }-> b(b(b(b(z - 4)))) :|: z - 4 >= 0
   B(z) -{ 1 }-> b(b(b(b(1 + (z - 3))))) :|: z - 3 >= 0
   B(z) -{ 2 }-> b(b(b(B(B(B(z - 7)))))) :|: z - 7 >= 0
   B(z) -{ 2 }-> b(b(b(A(z - 4)))) :|: z - 4 >= 0
   B(z) -{ 1 }-> b(b(b(0))) :|: z - 3 >= 0
   B(z) -{ 2 }-> b(b(b(z - 4))) :|: z - 4 >= 0
   B(z) -{ 1 }-> b(b(b(1 + (z - 3)))) :|: z - 3 >= 0
   B(z) -{ 0 }-> 0 :|: z >= 0
   B(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   B(z) -{ 0 }-> 1 + z :|: z >= 0
   C(z) -{ 2 }-> c(c(c(c(c(A(A(A(z - 7)))))))) :|: z - 7 >= 0
   C(z) -{ 2 }-> c(c(c(c(c(z - 4))))) :|: z - 4 >= 0
   C(z) -{ 2 }-> c(c(c(c(b(b(b(b(A(z - 6))))))))) :|: z - 6 >= 0
   C(z) -{ 2 }-> c(c(c(c(b(b(b(b(z - 6)))))))) :|: z - 6 >= 0
   C(z) -{ 1 }-> c(c(c(c(0)))) :|: z - 3 >= 0
   C(z) -{ 2 }-> c(c(c(c(z - 4)))) :|: z - 4 >= 0
   C(z) -{ 1 }-> c(c(c(c(1 + (z - 3))))) :|: z - 3 >= 0
   C(z) -{ 2 }-> c(c(c(C(C(C(z - 7)))))) :|: z - 7 >= 0
   C(z) -{ 2 }-> c(c(c(B(z - 4)))) :|: z - 4 >= 0
   C(z) -{ 1 }-> c(c(c(0))) :|: z - 3 >= 0
   C(z) -{ 2 }-> c(c(c(z - 4))) :|: z - 4 >= 0
   C(z) -{ 1 }-> c(c(c(1 + (z - 3)))) :|: z - 3 >= 0
   C(z) -{ 2 }-> a(B(B(c(A(A(A(z - 8))))))) :|: z - 8 >= 0
   C(z) -{ 2 }-> a(B(B(c(z - 5)))) :|: z - 5 >= 0
   C(z) -{ 2 }-> a(B(B(b(b(b(b(A(z - 7)))))))) :|: z - 7 >= 0
   C(z) -{ 2 }-> a(B(B(b(b(b(b(z - 7))))))) :|: z - 7 >= 0
   C(z) -{ 1 }-> a(B(B(0))) :|: z - 4 >= 0
   C(z) -{ 2 }-> a(B(B(z - 5))) :|: z - 5 >= 0
   C(z) -{ 1 }-> a(B(B(1 + (z - 4)))) :|: z - 4 >= 0
   C(z) -{ 1 }-> a(z - 1) :|: z - 1 >= 0
   C(z) -{ 0 }-> 0 :|: z >= 0
   C(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   C(z) -{ 0 }-> 1 + z :|: z >= 0
   a(z) -{ 1 }-> C(z - 1) :|: z - 1 >= 0
   a(z) -{ 2 }-> A(A(b(C(C(C(z - 8)))))) :|: z - 8 >= 0
   a(z) -{ 2 }-> A(A(b(z - 5))) :|: z - 5 >= 0
   a(z) -{ 2 }-> A(A(a(a(a(a(C(z - 7))))))) :|: z - 7 >= 0
   a(z) -{ 2 }-> A(A(a(a(a(a(z - 7)))))) :|: z - 7 >= 0
   a(z) -{ 1 }-> A(A(0)) :|: z - 4 >= 0
   a(z) -{ 2 }-> A(A(z - 5)) :|: z - 5 >= 0
   a(z) -{ 1 }-> A(A(1 + (z - 4))) :|: z - 4 >= 0
   a(z) -{ 0 }-> 0 :|: z >= 0
   a(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   a(z) -{ 0 }-> 1 + z :|: z >= 0
   b(z) -{ 2 }-> B(B(c(A(A(A(z - 8)))))) :|: z - 8 >= 0
   b(z) -{ 2 }-> B(B(c(z - 5))) :|: z - 5 >= 0
   b(z) -{ 2 }-> B(B(b(b(b(b(A(z - 7))))))) :|: z - 7 >= 0
   b(z) -{ 2 }-> B(B(b(b(b(b(z - 7)))))) :|: z - 7 >= 0
   b(z) -{ 1 }-> B(B(0)) :|: z - 4 >= 0
   b(z) -{ 2 }-> B(B(z - 5)) :|: z - 5 >= 0
   b(z) -{ 1 }-> B(B(1 + (z - 4))) :|: z - 4 >= 0
   b(z) -{ 1 }-> A(z - 1) :|: z - 1 >= 0
   b(z) -{ 0 }-> 0 :|: z >= 0
   b(z) -{ 1 }-> z - 1 :|: z - 1 >= 0
   b(z) -{ 0 }-> 1 + z :|: z >= 0
   c(z) -{ 2 }-> C(C(c(c(c(c(B(z - 7))))))) :|: z - 7 >= 0
   c(z) -{ 2 }-> C(C(c(c(c(c(z - 7)))))) :|: z - 7 >= 0
   c(z) -{ 2 }-> C(C(a(B(B(B(z - 8)))))) :|: z - 8 >= 0
   c(z) -{ 2 }-> C(C(a(z - 5))) :|: z - 5 >= 0
   c(z) -{ 1 }-> C(C(0)) :|: z - 4 >= 0
   c(z) -{ 2 }-> C(C(z - 5)) :|: z - 5 >= 0
   c(z) -{ 1 }-> C(C(1 + (z - 4))) :|: z - 4 >= 0
   c(z) -{ 1 }-> B(z - 1) :|: z - 1 >= 0
   c(z) -{ 0 }-> 0 :|: z >= 0
   c(z) -{ 1 }-> z - 1 :|: z - 1 >= 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(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(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(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 }-> 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(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(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(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(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(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(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
   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(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(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(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]
   encode_c(v0) -> null_encode_c [0]
   encode_A(v0) -> null_encode_A [0]
   encode_B(v0) -> null_encode_B [0]
   a(v0) -> null_a [0]
   b(v0) -> null_b [0]
   c(v0) -> null_c [0]
   C(v0) -> null_C [0]
   B(v0) -> null_B [0]
   A(v0) -> null_A [0]

And the following fresh constants:    null_encArg, null_encode_a, null_encode_b, null_encode_C, null_encode_c, null_encode_A, null_encode_B, null_a, null_b, null_c, null_C, null_B, null_A, 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:

   c(c_a(x1)) -> B(x1) [1]
   a(c_a(c_a(c_a(c_a(x1))))) -> A(A(A(x1))) [1]
   c(c_c(c_c(c_c(c_c(x1))))) -> C(C(C(x1))) [1]
   B(c_B(c_B(c_B(x1)))) -> b(b(b(b(x1)))) [1]
   b(c_b(c_b(c_b(c_b(x1))))) -> B(B(B(x1))) [1]
   B(c_a(c_a(c_a(c_a(x1))))) -> c(A(A(A(x1)))) [1]
   B(c_A(x1)) -> c(x1) [1]
   C(c_C(c_C(c_C(x1)))) -> c(c(c(c(x1)))) [1]
   C(c_c(x1)) -> x1 [1]
   c(c_C(x1)) -> x1 [1]
   A(c_A(c_A(c_A(x1)))) -> a(a(a(a(x1)))) [1]
   A(c_c(c_c(c_c(c_c(x1))))) -> b(C(C(C(x1)))) [1]
   b(c_c(x1)) -> A(x1) [1]
   C(c_B(x1)) -> a(x1) [1]
   C(c_b(c_b(c_b(c_b(x1))))) -> a(B(B(B(x1)))) [1]
   B(c_B(c_B(c_c(x1)))) -> b(b(b(b(A(x1))))) [1]
   b(c_B(x1)) -> x1 [1]
   A(c_C(x1)) -> b(x1) [1]
   A(c_A(c_A(c_b(x1)))) -> a(a(a(a(C(x1))))) [1]
   B(c_b(x1)) -> x1 [1]
   A(c_a(x1)) -> x1 [1]
   a(c_A(x1)) -> x1 [1]
   a(c_b(x1)) -> C(x1) [1]
   C(c_C(c_C(c_a(x1)))) -> c(c(c(c(B(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]
   encArg(cons_A(x_1)) -> A(encArg(x_1)) [0]
   encArg(cons_C(x_1)) -> C(encArg(x_1)) [0]
   encArg(cons_B(x_1)) -> B(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]
   encode_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]
   a(x0) -> c_a(x0) [0]
   b(x0) -> c_b(x0) [0]
   c(x0) -> c_c(x0) [0]
   C(x0) -> c_C(x0) [0]
   B(x0) -> c_B(x0) [0]
   A(x0) -> c_A(x0) [0]
   encArg(v0) -> null_encArg [0]
   encode_a(v0) -> null_encode_a [0]
   encode_b(v0) -> null_encode_b [0]
   encode_C(v0) -> null_encode_C [0]
   encode_c(v0) -> null_encode_c [0]
   encode_A(v0) -> null_encode_A [0]
   encode_B(v0) -> null_encode_B [0]
   a(v0) -> null_a [0]
   b(v0) -> null_b [0]
   c(v0) -> null_c [0]
   C(v0) -> null_C [0]
   B(v0) -> null_B [0]
   A(v0) -> null_A [0]

The TRS has the following type information:
c :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
c_a :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
B :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
a :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
A :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
c_c :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
C :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
c_B :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
b :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
c_b :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
c_A :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
c_C :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
encArg :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
cons_a :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_b :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_c :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_A :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_C :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
cons_B :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> cons_a:cons_b:cons_c:cons_A:cons_C:cons_B
encode_a :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
encode_b :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
encode_C :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
encode_c :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
encode_A :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
encode_B :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B -> c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
null_encArg :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
null_encode_a :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
null_encode_b :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
null_encode_C :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
null_encode_c :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
null_encode_A :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
null_encode_B :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
null_a :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
null_b :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
null_c :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
null_C :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
null_B :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
null_A :: c_a:c_c:c_B:c_b:c_A:c_C:null_encArg:null_encode_a:null_encode_b:null_encode_C:null_encode_c:null_encode_A:null_encode_B:null_a:null_b:null_c:null_C:null_B:null_A
const :: cons_a:cons_b:cons_c:cons_A:cons_C:cons_B

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_encode_c => 0
   null_encode_A => 0
   null_encode_B => 0
   null_a => 0
   null_b => 0
   null_c => 0
   null_C => 0
   null_B => 0
   null_A => 0
   const => 0

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

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

   A(z) -{ 1 }-> x1 :|: x1 >= 0, z = 1 + x1
   A(z) -{ 1 }-> b(x1) :|: x1 >= 0, z = 1 + x1
   A(z) -{ 1 }-> b(C(C(C(x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   A(z) -{ 1 }-> a(a(a(a(x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   A(z) -{ 1 }-> a(a(a(a(C(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 }-> x1 :|: x1 >= 0, z = 1 + x1
   B(z) -{ 1 }-> c(x1) :|: x1 >= 0, z = 1 + x1
   B(z) -{ 1 }-> c(A(A(A(x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   B(z) -{ 1 }-> b(b(b(b(x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   B(z) -{ 1 }-> b(b(b(b(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 }-> x1 :|: x1 >= 0, z = 1 + x1
   C(z) -{ 1 }-> c(c(c(c(x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   C(z) -{ 1 }-> c(c(c(c(B(x1))))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   C(z) -{ 1 }-> a(x1) :|: x1 >= 0, z = 1 + x1
   C(z) -{ 1 }-> a(B(B(B(x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   C(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   C(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   a(z) -{ 1 }-> x1 :|: x1 >= 0, z = 1 + x1
   a(z) -{ 1 }-> C(x1) :|: x1 >= 0, z = 1 + x1
   a(z) -{ 1 }-> A(A(A(x1))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   a(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   b(z) -{ 1 }-> x1 :|: x1 >= 0, z = 1 + x1
   b(z) -{ 1 }-> B(B(B(x1))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   b(z) -{ 1 }-> A(x1) :|: x1 >= 0, z = 1 + x1
   b(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   b(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   c(z) -{ 1 }-> x1 :|: x1 >= 0, z = 1 + x1
   c(z) -{ 1 }-> C(C(C(x1))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   c(z) -{ 1 }-> B(x1) :|: x1 >= 0, z = 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 }-> 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
   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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_C(z0) -> C(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   encode_A(z0) -> A(encArg(z0))
   encode_B(z0) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> 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))
   ENCARG(cons_A(z0)) -> c4(A''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_C(z0)) -> c5(C''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_B(z0)) -> c6(B''(encArg(z0)), ENCARG(z0))
   ENCODE_A(z0) -> c7(A'(encArg(z0)), ENCARG(z0))
   ENCODE_B(z0) -> c8(B'(encArg(z0)), ENCARG(z0))
   ENCODE_C(z0) -> c9(C''(encArg(z0)), ENCARG(z0))
   ENCODE_C'(z0) -> c10(C'(encArg(z0)), ENCARG(z0))
   ENCODE_A'(z0) -> c11(A''(encArg(z0)), ENCARG(z0))
   ENCODE_B'(z0) -> c12(B''(encArg(z0)), ENCARG(z0))
   A'(z0) -> c13
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(z0) -> c17
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(z0) -> c21
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(z0) -> c25
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(z0) -> c31
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(z0) -> c37
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
S tuples:
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
K tuples:none
Defined Rule Symbols:   c_1, a_1, B_1, b_1, C_1, A_1, encArg_1, encode_a_1, encode_b_1, encode_C_1, encode_c_1, encode_A_1, encode_B_1

Defined Pair Symbols:   ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, A'_1, B'_1, C'_1, C''_1, B''_1, A''_1

Compound Symbols:   c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c7_2, c8_2, c9_2, c10_2, c11_2, c12_2, c13, c14_3, c15, c16_1, c17, c18_3, c19_1, c20, c21, c22_1, c23_3, c24, c25, c26_4, c27, c28_1, c29_4, c30_5, c31, c32_4, c33_4, c34_1, c35_5, c36, c37, c38_4, c39_4, c40_1, c41_5, c42


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

(39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 6 trailing nodes:
   A''(z0) -> c37
   B''(z0) -> c31
   B'(z0) -> c17
   C'(z0) -> c21
   C''(z0) -> c25
   A'(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_C(z0) -> C(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   encode_A(z0) -> A(encArg(z0))
   encode_B(z0) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> 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))
   ENCARG(cons_A(z0)) -> c4(A''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_C(z0)) -> c5(C''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_B(z0)) -> c6(B''(encArg(z0)), ENCARG(z0))
   ENCODE_A(z0) -> c7(A'(encArg(z0)), ENCARG(z0))
   ENCODE_B(z0) -> c8(B'(encArg(z0)), ENCARG(z0))
   ENCODE_C(z0) -> c9(C''(encArg(z0)), ENCARG(z0))
   ENCODE_C'(z0) -> c10(C'(encArg(z0)), ENCARG(z0))
   ENCODE_A'(z0) -> c11(A''(encArg(z0)), ENCARG(z0))
   ENCODE_B'(z0) -> c12(B''(encArg(z0)), ENCARG(z0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
S tuples:
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
K tuples:none
Defined Rule Symbols:   c_1, a_1, B_1, b_1, C_1, A_1, encArg_1, encode_a_1, encode_b_1, encode_C_1, encode_c_1, encode_A_1, encode_B_1

Defined Pair Symbols:   ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, A'_1, B'_1, C'_1, C''_1, B''_1, A''_1

Compound Symbols:   c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c7_2, c8_2, c9_2, c10_2, c11_2, c12_2, c14_3, c15, c16_1, c18_3, c19_1, c20, c22_1, c23_3, c24, c26_4, c27, c28_1, c29_4, c30_5, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42


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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_C(z0) -> C(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   encode_A(z0) -> A(encArg(z0))
   encode_B(z0) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> 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))
   ENCARG(cons_A(z0)) -> c4(A''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_C(z0)) -> c5(C''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_B(z0)) -> c6(B''(encArg(z0)), ENCARG(z0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_A(z0) -> c13(ENCARG(z0))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_B(z0) -> c13(ENCARG(z0))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C(z0) -> c13(ENCARG(z0))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_C'(z0) -> c13(ENCARG(z0))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_A'(z0) -> c13(ENCARG(z0))
   ENCODE_B'(z0) -> c13(B''(encArg(z0)))
   ENCODE_B'(z0) -> c13(ENCARG(z0))
S tuples:
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
K tuples:none
Defined Rule Symbols:   c_1, a_1, B_1, b_1, C_1, A_1, encArg_1, encode_a_1, encode_b_1, encode_C_1, encode_c_1, encode_A_1, encode_B_1

Defined Pair Symbols:   ENCARG_1, A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c15, c16_1, c18_3, c19_1, c20, c22_1, c23_3, c24, c26_4, c27, c28_1, c29_4, c30_5, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_1


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

(43) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 6 leading nodes:
   ENCODE_A(z0) -> c13(ENCARG(z0))
   ENCODE_B(z0) -> c13(ENCARG(z0))
   ENCODE_C(z0) -> c13(ENCARG(z0))
   ENCODE_C'(z0) -> c13(ENCARG(z0))
   ENCODE_A'(z0) -> c13(ENCARG(z0))
   ENCODE_B'(z0) -> c13(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_C(z0) -> C(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   encode_A(z0) -> A(encArg(z0))
   encode_B(z0) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> 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))
   ENCARG(cons_A(z0)) -> c4(A''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_C(z0)) -> c5(C''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_B(z0)) -> c6(B''(encArg(z0)), ENCARG(z0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(encArg(z0)))
S tuples:
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
K tuples:none
Defined Rule Symbols:   c_1, a_1, B_1, b_1, C_1, A_1, encArg_1, encode_a_1, encode_b_1, encode_C_1, encode_c_1, encode_A_1, encode_B_1

Defined Pair Symbols:   ENCARG_1, A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c15, c16_1, c18_3, c19_1, c20, c22_1, c23_3, c24, c26_4, c27, c28_1, c29_4, c30_5, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_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))
   encode_c(z0) -> c(encArg(z0))
   encode_A(z0) -> A(encArg(z0))
   encode_B(z0) -> B(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> 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))
   ENCARG(cons_A(z0)) -> c4(A''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_C(z0)) -> c5(C''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_B(z0)) -> c6(B''(encArg(z0)), ENCARG(z0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(encArg(z0)))
S tuples:
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   ENCARG_1, A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c15, c16_1, c18_3, c19_1, c20, c22_1, c23_3, c24, c26_4, c27, c28_1, c29_4, c30_5, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_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)))
   ENCARG(cons_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   ENCARG(cons_b(z0)) -> c2(B'(encArg(z0)), ENCARG(z0))
   ENCARG(cons_c(z0)) -> c3(C'(encArg(z0)), ENCARG(z0))
   ENCARG(cons_A(z0)) -> c4(A''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_C(z0)) -> c5(C''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_B(z0)) -> c6(B''(encArg(z0)), ENCARG(z0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(z0)))
S tuples:
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   ENCARG_1, A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c15, c16_1, c18_3, c19_1, c20, c22_1, c23_3, c24, c26_4, c27, c28_1, c29_4, c30_5, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_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)))
   ENCARG(cons_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   ENCARG(cons_c(z0)) -> c3(C'(encArg(z0)), ENCARG(z0))
   ENCARG(cons_A(z0)) -> c4(A''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_C(z0)) -> c5(C''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_B(z0)) -> c6(B''(encArg(z0)), ENCARG(z0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(z0)))
S tuples:
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   ENCARG_1, A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c3_2, c4_2, c5_2, c6_2, c14_3, c15, c16_1, c18_3, c19_1, c20, c22_1, c23_3, c24, c26_4, c27, c28_1, c29_4, c30_5, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   ENCARG(cons_A(z0)) -> c4(A''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_C(z0)) -> c5(C''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_B(z0)) -> c6(B''(encArg(z0)), ENCARG(z0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
S tuples:
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   ENCARG_1, A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c4_2, c5_2, c6_2, c14_3, c15, c16_1, c18_3, c19_1, c20, c22_1, c23_3, c24, c26_4, c27, c28_1, c29_4, c30_5, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2


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

(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_A(z0)) -> c4(A''(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   ENCARG(cons_C(z0)) -> c5(C''(encArg(z0)), ENCARG(z0))
   ENCARG(cons_B(z0)) -> c6(B''(encArg(z0)), ENCARG(z0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
S tuples:
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   ENCARG_1, A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c5_2, c6_2, c14_3, c15, c16_1, c18_3, c19_1, c20, c22_1, c23_3, c24, c26_4, c27, c28_1, c29_4, c30_5, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_C(z0)) -> c5(C''(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   ENCARG(cons_B(z0)) -> c6(B''(encArg(z0)), ENCARG(z0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
S tuples:
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   ENCARG_1, A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c6_2, c14_3, c15, c16_1, c18_3, c19_1, c20, c22_1, c23_3, c24, c26_4, c27, c28_1, c29_4, c30_5, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2


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

(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_B(z0)) -> c6(B''(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
S tuples:
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0))
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1

Compound Symbols:   c14_3, c15, c16_1, c18_3, c19_1, c20, c22_1, c23_3, c24, c26_4, c27, c28_1, c29_4, c30_5, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(A(z0))), A''(A(z0)), A''(z0)) by 
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), 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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1

Compound Symbols:   c15, c16_1, c18_3, c19_1, c20, c22_1, c23_3, c24, c26_4, c27, c28_1, c29_4, c30_5, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3


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

(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(B(z0))), B''(B(z0)), B''(z0)) by 
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c23_3, c24, c26_4, c27, c28_1, c29_4, c30_5, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(C(z0))), C''(C(z0)), C''(z0)) by 
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c26_4, c27, c28_1, c29_4, c30_5, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3


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(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0)) by 
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c29_4, c30_5, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4


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

(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0)) by 
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(c_B(B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(c_B(B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(c_B(B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c30_5, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4


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

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c30_5, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0)) by 
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c32_4, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5


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

(73) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0)) by 
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c33_4, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0)) by 
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(c_A(A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(c_A(A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(c_A(A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4


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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c35_5, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0)) by 
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c38_4, c39_4, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5


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

(81) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0)) by 
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c39_4, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4


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

(83) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0)) by 
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(c_C(C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(c_C(C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(c_C(C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4


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

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c41_5, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3


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

(87) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0)) by 
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A(z0) -> c13(A'(encArg(z0)))
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5


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

(89) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_A(z0) -> c13(A'(encArg(z0))) by 
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCODE_B(z0) -> c13(B'(encArg(z0)))
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1, ENCODE_A_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5


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

(91) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_B(z0) -> c13(B'(encArg(z0))) by 
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCODE_C(z0) -> c13(C''(encArg(z0)))
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5


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

(93) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_C(z0) -> c13(C''(encArg(z0))) by 
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCODE_C'(z0) -> c13(C'(encArg(z0)))
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5


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

(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_C'(z0) -> c13(C'(encArg(z0))) by 
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCODE_A'(z0) -> c13(A''(encArg(z0)))
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_A'_1, ENCODE_B'_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5


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

(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_A'(z0) -> c13(A''(encArg(z0))) by 
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCODE_B'(z0) -> c13(B''(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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCODE_B'_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c13_1, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5


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

(99) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_B'(z0) -> c13(B''(encArg(z0))) by 
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(encArg(z0))))

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(encArg(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1


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

(101) 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))))
   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_C(z0)))) -> c1(A'(a(C(encArg(z0)))), ENCARG(cons_a(cons_C(z0))))
   ENCARG(cons_a(cons_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(z0))))

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   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_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1


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(103) 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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(z0))))
   ENCARG(cons_a(cons_b(cons_B(z0)))) -> c1(A'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_a(cons_c(z0))) -> c1(A'(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(z0))))
   ENCARG(cons_a(cons_b(cons_B(z0)))) -> c1(A'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1


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

(105) 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))))
   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_C(z0)))) -> c1(A'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(z0))))
   ENCARG(cons_a(cons_c(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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))))
   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_C(z0)))) -> c1(A'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(z0))))
   ENCARG(cons_a(cons_c(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1


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

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_a(cons_A(z0))) -> c1(A'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_1


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

(109) 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))))
   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_C(z0)))) -> c1(A'(A(C(encArg(z0)))), ENCARG(cons_A(cons_C(z0))))
   ENCARG(cons_a(cons_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_a(cons_C(z0))) -> c1(A'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_1


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

(111) 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))))
   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_C(z0)))) -> c1(A'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(z0))))
   ENCARG(cons_a(cons_C(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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))))
   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_C(z0)))) -> c1(A'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(z0))))
   ENCARG(cons_a(cons_C(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_1


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

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_a(cons_B(z0))) -> c1(A'(B(encArg(z0))), ENCARG(cons_B(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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(x0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c1_2, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_1


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

(115) 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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(z0))))
   ENCARG(cons_a(cons_B(cons_B(z0)))) -> c1(A'(B(B(encArg(z0)))), ENCARG(cons_B(cons_B(z0))))

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(x0)))
   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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(z0))))
   ENCARG(cons_a(cons_B(cons_B(z0)))) -> c1(A'(B(B(encArg(z0)))), ENCARG(cons_B(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1


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

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(x0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1


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

(119) 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))))
   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_C(z0)))) -> c2(B'(a(C(encArg(z0)))), ENCARG(cons_a(cons_C(z0))))
   ENCARG(cons_b(cons_a(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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))))
   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_C(z0)))) -> c2(B'(a(C(encArg(z0)))), ENCARG(cons_a(cons_C(z0))))
   ENCARG(cons_b(cons_a(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1


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

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   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_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(z0))))
   ENCARG(cons_b(cons_a(x0))) -> c2(ENCARG(cons_a(x0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_1


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

(123) 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))))
   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_C(z0)))) -> c2(B'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(z0))))
   ENCARG(cons_b(cons_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_b(cons_c(z0))) -> c2(B'(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_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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_b(cons_A(z0)))) -> c2(B'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_1


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

(125) 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))))
   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_C(z0)))) -> c2(B'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(z0))))
   ENCARG(cons_b(cons_c(cons_B(z0)))) -> c2(B'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_b(cons_A(z0))) -> c2(B'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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_b(cons_A(z0)))) -> c2(B'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c2(B'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(z0))))
   ENCARG(cons_b(cons_c(cons_B(z0)))) -> c2(B'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_1


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(127) 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))))
   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_C(z0)))) -> c2(B'(A(C(encArg(z0)))), ENCARG(cons_A(cons_C(z0))))
   ENCARG(cons_b(cons_A(cons_B(z0)))) -> c2(B'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))

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(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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_b(cons_A(z0)))) -> c2(B'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c2(B'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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))))
   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_C(z0)))) -> c2(B'(A(C(encArg(z0)))), ENCARG(cons_A(cons_C(z0))))
   ENCARG(cons_b(cons_A(cons_B(z0)))) -> c2(B'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_1


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

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_b(cons_C(z0))) -> c2(B'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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_b(cons_A(z0)))) -> c2(B'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c2(B'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c2(B'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c2(B'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_b(cons_A(x0))) -> c2(ENCARG(cons_A(x0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_1


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

(131) 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))))
   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_C(z0)))) -> c2(B'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(z0))))
   ENCARG(cons_b(cons_C(cons_B(z0)))) -> c2(B'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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_b(cons_A(z0)))) -> c2(B'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c2(B'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c2(B'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c2(B'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_b(cons_A(x0))) -> c2(ENCARG(cons_A(x0)))
   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))))
   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_C(z0)))) -> c2(B'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(z0))))
   ENCARG(cons_b(cons_C(cons_B(z0)))) -> c2(B'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_1


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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_b(cons_B(z0))) -> c2(B'(B(encArg(z0))), ENCARG(cons_B(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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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_b(cons_A(z0)))) -> c2(B'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c2(B'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c2(B'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c2(B'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_b(cons_A(x0))) -> c2(ENCARG(cons_A(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))))
   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_C(z0)))) -> c2(B'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(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(x0))) -> c2(ENCARG(cons_C(x0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c2_2, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_1


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

(135) 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))))
   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_C(z0)))) -> c2(B'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(z0))))
   ENCARG(cons_b(cons_B(cons_B(z0)))) -> c2(B'(B(B(encArg(z0)))), ENCARG(cons_B(cons_B(z0))))

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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_b(cons_A(z0)))) -> c2(B'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c2(B'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c2(B'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c2(B'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_b(cons_A(x0))) -> c2(ENCARG(cons_A(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))))
   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_C(z0)))) -> c2(B'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(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(x0))) -> c2(ENCARG(cons_C(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_B(cons_A(z0)))) -> c2(B'(B(A(encArg(z0)))), ENCARG(cons_B(cons_A(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_B(cons_B(z0)))) -> c2(B'(B(B(encArg(z0)))), ENCARG(cons_B(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_2, c2_1


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

(137) 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))))
   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_C(z0)))) -> c3(C'(a(C(encArg(z0)))), ENCARG(cons_a(cons_C(z0))))
   ENCARG(cons_c(cons_a(cons_B(z0)))) -> c3(C'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(z0))))

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   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)))
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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_b(cons_A(z0)))) -> c2(B'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c2(B'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c2(B'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c2(B'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_b(cons_A(x0))) -> c2(ENCARG(cons_A(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))))
   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_C(z0)))) -> c2(B'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(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(x0))) -> c2(ENCARG(cons_C(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_B(cons_A(z0)))) -> c2(B'(B(A(encArg(z0)))), ENCARG(cons_B(cons_A(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_B(cons_B(z0)))) -> c2(B'(B(B(encArg(z0)))), ENCARG(cons_B(cons_B(z0))))
   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))))
   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_C(z0)))) -> c3(C'(a(C(encArg(z0)))), ENCARG(cons_a(cons_C(z0))))
   ENCARG(cons_c(cons_a(cons_B(z0)))) -> c3(C'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_2, c2_1


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

(139) 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))))
   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_C(z0)))) -> c3(C'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(z0))))
   ENCARG(cons_c(cons_b(cons_B(z0)))) -> c3(C'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(z0))))

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_c(cons_c(z0))) -> c3(C'(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_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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_b(cons_A(z0)))) -> c2(B'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c2(B'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c2(B'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c2(B'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_b(cons_A(x0))) -> c2(ENCARG(cons_A(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))))
   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_C(z0)))) -> c2(B'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(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(x0))) -> c2(ENCARG(cons_C(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_B(cons_A(z0)))) -> c2(B'(B(A(encArg(z0)))), ENCARG(cons_B(cons_A(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_B(cons_B(z0)))) -> c2(B'(B(B(encArg(z0)))), ENCARG(cons_B(cons_B(z0))))
   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))))
   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_C(z0)))) -> c3(C'(a(C(encArg(z0)))), ENCARG(cons_a(cons_C(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_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))))
   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_C(z0)))) -> c3(C'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(z0))))
   ENCARG(cons_c(cons_b(cons_B(z0)))) -> c3(C'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_2, c2_1


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

(141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 1 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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_c(cons_c(z0))) -> c3(C'(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_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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_b(cons_A(z0)))) -> c2(B'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c2(B'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c2(B'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c2(B'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_b(cons_A(x0))) -> c2(ENCARG(cons_A(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))))
   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_C(z0)))) -> c2(B'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(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(x0))) -> c2(ENCARG(cons_C(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_B(cons_A(z0)))) -> c2(B'(B(A(encArg(z0)))), ENCARG(cons_B(cons_A(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_B(cons_B(z0)))) -> c2(B'(B(B(encArg(z0)))), ENCARG(cons_B(cons_B(z0))))
   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))))
   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_C(z0)))) -> c3(C'(a(C(encArg(z0)))), ENCARG(cons_a(cons_C(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_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(cons_A(z0)))) -> c3(C'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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(cons_B(z0)))) -> c3(C'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(z0))))
   ENCARG(cons_c(cons_b(x0))) -> c3(ENCARG(cons_b(x0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_2, c2_1, c3_1


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(143) 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))))
   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_C(z0)))) -> c3(C'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(z0))))
   ENCARG(cons_c(cons_c(cons_B(z0)))) -> c3(C'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))

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(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_c(cons_A(z0))) -> c3(C'(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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_b(cons_A(z0)))) -> c2(B'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c2(B'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c2(B'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c2(B'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_b(cons_A(x0))) -> c2(ENCARG(cons_A(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))))
   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_C(z0)))) -> c2(B'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(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(x0))) -> c2(ENCARG(cons_C(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_B(cons_A(z0)))) -> c2(B'(B(A(encArg(z0)))), ENCARG(cons_B(cons_A(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_B(cons_B(z0)))) -> c2(B'(B(B(encArg(z0)))), ENCARG(cons_B(cons_B(z0))))
   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))))
   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_C(z0)))) -> c3(C'(a(C(encArg(z0)))), ENCARG(cons_a(cons_C(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_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(cons_A(z0)))) -> c3(C'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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(cons_B(z0)))) -> c3(C'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c3(C'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(z0))))
   ENCARG(cons_c(cons_c(cons_B(z0)))) -> c3(C'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_2, c2_1, c3_1


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

(145) 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))))
   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_C(z0)))) -> c3(C'(A(C(encArg(z0)))), ENCARG(cons_A(cons_C(z0))))
   ENCARG(cons_c(cons_A(cons_B(z0)))) -> c3(C'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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_b(cons_A(z0)))) -> c2(B'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c2(B'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c2(B'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c2(B'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_b(cons_A(x0))) -> c2(ENCARG(cons_A(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))))
   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_C(z0)))) -> c2(B'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(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(x0))) -> c2(ENCARG(cons_C(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_B(cons_A(z0)))) -> c2(B'(B(A(encArg(z0)))), ENCARG(cons_B(cons_A(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_B(cons_B(z0)))) -> c2(B'(B(B(encArg(z0)))), ENCARG(cons_B(cons_B(z0))))
   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))))
   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_C(z0)))) -> c3(C'(a(C(encArg(z0)))), ENCARG(cons_a(cons_C(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_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(cons_A(z0)))) -> c3(C'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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(cons_B(z0)))) -> c3(C'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c3(C'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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))))
   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_C(z0)))) -> c3(C'(A(C(encArg(z0)))), ENCARG(cons_A(cons_C(z0))))
   ENCARG(cons_c(cons_A(cons_B(z0)))) -> c3(C'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_2, c2_1, c3_1


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

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_c(cons_C(z0))) -> c3(C'(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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_b(cons_A(z0)))) -> c2(B'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c2(B'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c2(B'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c2(B'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_b(cons_A(x0))) -> c2(ENCARG(cons_A(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))))
   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_C(z0)))) -> c2(B'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(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(x0))) -> c2(ENCARG(cons_C(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_B(cons_A(z0)))) -> c2(B'(B(A(encArg(z0)))), ENCARG(cons_B(cons_A(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_B(cons_B(z0)))) -> c2(B'(B(B(encArg(z0)))), ENCARG(cons_B(cons_B(z0))))
   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))))
   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_C(z0)))) -> c3(C'(a(C(encArg(z0)))), ENCARG(cons_a(cons_C(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_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(cons_A(z0)))) -> c3(C'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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(cons_B(z0)))) -> c3(C'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c3(C'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c3(C'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c3(C'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_c(cons_A(x0))) -> c3(ENCARG(cons_A(x0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_2, c2_1, c3_1


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

(149) 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))))
   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_C(z0)))) -> c3(C'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(z0))))
   ENCARG(cons_c(cons_C(cons_B(z0)))) -> c3(C'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_c(cons_B(z0))) -> c3(C'(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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_b(cons_A(z0)))) -> c2(B'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c2(B'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c2(B'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c2(B'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_b(cons_A(x0))) -> c2(ENCARG(cons_A(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))))
   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_C(z0)))) -> c2(B'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(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(x0))) -> c2(ENCARG(cons_C(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_B(cons_A(z0)))) -> c2(B'(B(A(encArg(z0)))), ENCARG(cons_B(cons_A(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_B(cons_B(z0)))) -> c2(B'(B(B(encArg(z0)))), ENCARG(cons_B(cons_B(z0))))
   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))))
   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_C(z0)))) -> c3(C'(a(C(encArg(z0)))), ENCARG(cons_a(cons_C(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_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(cons_A(z0)))) -> c3(C'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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(cons_B(z0)))) -> c3(C'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c3(C'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c3(C'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c3(C'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_c(cons_A(x0))) -> c3(ENCARG(cons_A(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))))
   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_C(z0)))) -> c3(C'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(z0))))
   ENCARG(cons_c(cons_C(cons_B(z0)))) -> c3(C'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c3_2, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_2, c2_1, c3_1


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

(151) 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))))
   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_C(z0)))) -> c3(C'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(z0))))
   ENCARG(cons_c(cons_B(cons_B(z0)))) -> c3(C'(B(B(encArg(z0)))), ENCARG(cons_B(cons_B(z0))))

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

(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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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_b(cons_A(z0)))) -> c2(B'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c2(B'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c2(B'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c2(B'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_b(cons_A(x0))) -> c2(ENCARG(cons_A(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))))
   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_C(z0)))) -> c2(B'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(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(x0))) -> c2(ENCARG(cons_C(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_B(cons_A(z0)))) -> c2(B'(B(A(encArg(z0)))), ENCARG(cons_B(cons_A(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_B(cons_B(z0)))) -> c2(B'(B(B(encArg(z0)))), ENCARG(cons_B(cons_B(z0))))
   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))))
   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_C(z0)))) -> c3(C'(a(C(encArg(z0)))), ENCARG(cons_a(cons_C(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_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(cons_A(z0)))) -> c3(C'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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(cons_B(z0)))) -> c3(C'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c3(C'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c3(C'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c3(C'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_c(cons_A(x0))) -> c3(ENCARG(cons_A(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))))
   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_C(z0)))) -> c3(C'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(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_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))))
   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_C(z0)))) -> c3(C'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(z0))))
   ENCARG(cons_c(cons_B(cons_B(z0)))) -> c3(C'(B(B(encArg(z0)))), ENCARG(cons_B(cons_B(z0))))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1


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

(154)
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))
   encArg(cons_A(z0)) -> A(encArg(z0))
   encArg(cons_C(z0)) -> C(encArg(z0))
   encArg(cons_B(z0)) -> B(encArg(z0))
   a(z0) -> c_a(z0)
   a(c_a(c_a(c_a(c_a(z0))))) -> A(A(A(z0)))
   a(c_A(z0)) -> z0
   a(c_b(z0)) -> C(z0)
   b(z0) -> c_b(z0)
   b(c_b(c_b(c_b(c_b(z0))))) -> B(B(B(z0)))
   b(c_c(z0)) -> A(z0)
   b(c_B(z0)) -> z0
   c(z0) -> c_c(z0)
   c(c_a(z0)) -> B(z0)
   c(c_c(c_c(c_c(c_c(z0))))) -> C(C(C(z0)))
   c(c_C(z0)) -> z0
   A(z0) -> c_A(z0)
   A(c_A(c_A(c_A(z0)))) -> a(a(a(a(z0))))
   A(c_c(c_c(c_c(c_c(z0))))) -> b(C(C(C(z0))))
   A(c_C(z0)) -> b(z0)
   A(c_A(c_A(c_b(z0)))) -> a(a(a(a(C(z0)))))
   A(c_a(z0)) -> z0
   C(z0) -> c_C(z0)
   C(c_C(c_C(c_C(z0)))) -> c(c(c(c(z0))))
   C(c_c(z0)) -> z0
   C(c_B(z0)) -> a(z0)
   C(c_b(c_b(c_b(c_b(z0))))) -> a(B(B(B(z0))))
   C(c_C(c_C(c_a(z0)))) -> c(c(c(c(B(z0)))))
   B(z0) -> c_B(z0)
   B(c_B(c_B(c_B(z0)))) -> b(b(b(b(z0))))
   B(c_a(c_a(c_a(c_a(z0))))) -> c(A(A(A(z0))))
   B(c_A(z0)) -> c(z0)
   B(c_B(c_B(c_c(z0)))) -> b(b(b(b(A(z0)))))
   B(c_b(z0)) -> z0
Tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   ENCARG(cons_A(cons_a(z0))) -> c4(A''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_A(cons_b(z0))) -> c4(A''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_A(cons_c(z0))) -> c4(A''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_A(cons_A(z0))) -> c4(A''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_A(cons_C(z0))) -> c4(A''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_A(cons_B(z0))) -> c4(A''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_C(cons_a(z0))) -> c5(C''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_C(cons_b(z0))) -> c5(C''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_C(cons_c(z0))) -> c5(C''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_C(cons_A(z0))) -> c5(C''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_C(cons_C(z0))) -> c5(C''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_C(cons_B(z0))) -> c5(C''(B(encArg(z0))), ENCARG(cons_B(z0)))
   ENCARG(cons_B(cons_a(z0))) -> c6(B''(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_B(cons_b(z0))) -> c6(B''(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_B(cons_c(z0))) -> c6(B''(c(encArg(z0))), ENCARG(cons_c(z0)))
   ENCARG(cons_B(cons_A(z0))) -> c6(B''(A(encArg(z0))), ENCARG(cons_A(z0)))
   ENCARG(cons_B(cons_C(z0))) -> c6(B''(C(encArg(z0))), ENCARG(cons_C(z0)))
   ENCARG(cons_B(cons_B(z0))) -> c6(B''(B(encArg(z0))), ENCARG(cons_B(z0)))
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   ENCODE_A(cons_a(z0)) -> c13(A'(a(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c13(A'(b(encArg(z0))))
   ENCODE_A(cons_c(z0)) -> c13(A'(c(encArg(z0))))
   ENCODE_A(cons_A(z0)) -> c13(A'(A(encArg(z0))))
   ENCODE_A(cons_C(z0)) -> c13(A'(C(encArg(z0))))
   ENCODE_A(cons_B(z0)) -> c13(A'(B(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c13(B'(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c13(B'(b(encArg(z0))))
   ENCODE_B(cons_c(z0)) -> c13(B'(c(encArg(z0))))
   ENCODE_B(cons_A(z0)) -> c13(B'(A(encArg(z0))))
   ENCODE_B(cons_C(z0)) -> c13(B'(C(encArg(z0))))
   ENCODE_B(cons_B(z0)) -> c13(B'(B(encArg(z0))))
   ENCODE_C(cons_a(z0)) -> c13(C''(a(encArg(z0))))
   ENCODE_C(cons_b(z0)) -> c13(C''(b(encArg(z0))))
   ENCODE_C(cons_c(z0)) -> c13(C''(c(encArg(z0))))
   ENCODE_C(cons_A(z0)) -> c13(C''(A(encArg(z0))))
   ENCODE_C(cons_C(z0)) -> c13(C''(C(encArg(z0))))
   ENCODE_C(cons_B(z0)) -> c13(C''(B(encArg(z0))))
   ENCODE_C'(cons_a(z0)) -> c13(C'(a(encArg(z0))))
   ENCODE_C'(cons_b(z0)) -> c13(C'(b(encArg(z0))))
   ENCODE_C'(cons_c(z0)) -> c13(C'(c(encArg(z0))))
   ENCODE_C'(cons_A(z0)) -> c13(C'(A(encArg(z0))))
   ENCODE_C'(cons_C(z0)) -> c13(C'(C(encArg(z0))))
   ENCODE_C'(cons_B(z0)) -> c13(C'(B(encArg(z0))))
   ENCODE_A'(cons_a(z0)) -> c13(A''(a(encArg(z0))))
   ENCODE_A'(cons_b(z0)) -> c13(A''(b(encArg(z0))))
   ENCODE_A'(cons_c(z0)) -> c13(A''(c(encArg(z0))))
   ENCODE_A'(cons_A(z0)) -> c13(A''(A(encArg(z0))))
   ENCODE_A'(cons_C(z0)) -> c13(A''(C(encArg(z0))))
   ENCODE_A'(cons_B(z0)) -> c13(A''(B(encArg(z0))))
   ENCODE_B'(cons_a(z0)) -> c13(B''(a(encArg(z0))))
   ENCODE_B'(cons_b(z0)) -> c13(B''(b(encArg(z0))))
   ENCODE_B'(cons_c(z0)) -> c13(B''(c(encArg(z0))))
   ENCODE_B'(cons_A(z0)) -> c13(B''(A(encArg(z0))))
   ENCODE_B'(cons_C(z0)) -> c13(B''(C(encArg(z0))))
   ENCODE_B'(cons_B(z0)) -> c13(B''(B(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_a(cons_A(z0)))) -> c1(A'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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_a(cons_B(z0)))) -> c1(A'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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))))
   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_C(z0)))) -> c1(A'(b(C(encArg(z0)))), ENCARG(cons_b(cons_C(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_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(cons_A(z0)))) -> c1(A'(c(A(encArg(z0)))), ENCARG(cons_c(cons_A(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(cons_B(z0)))) -> c1(A'(c(B(encArg(z0)))), ENCARG(cons_c(cons_B(z0))))
   ENCARG(cons_a(cons_c(x0))) -> c1(ENCARG(cons_c(x0)))
   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_A(cons_A(z0)))) -> c1(A'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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_A(cons_B(z0)))) -> c1(A'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   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(cons_A(z0)))) -> c1(A'(C(A(encArg(z0)))), ENCARG(cons_C(cons_A(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(cons_B(z0)))) -> c1(A'(C(B(encArg(z0)))), ENCARG(cons_C(cons_B(z0))))
   ENCARG(cons_a(cons_C(x0))) -> c1(ENCARG(cons_C(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))))
   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_C(z0)))) -> c1(A'(B(C(encArg(z0)))), ENCARG(cons_B(cons_C(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(x0))) -> c1(ENCARG(cons_B(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(cons_A(z0)))) -> c2(B'(a(A(encArg(z0)))), ENCARG(cons_a(cons_A(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(cons_B(z0)))) -> c2(B'(a(B(encArg(z0)))), ENCARG(cons_a(cons_B(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_b(cons_A(z0)))) -> c2(B'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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_b(cons_B(z0)))) -> c2(B'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c2(B'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c2(B'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c2(B'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_b(cons_A(x0))) -> c2(ENCARG(cons_A(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))))
   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_C(z0)))) -> c2(B'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(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(x0))) -> c2(ENCARG(cons_C(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_B(cons_A(z0)))) -> c2(B'(B(A(encArg(z0)))), ENCARG(cons_B(cons_A(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_B(cons_B(z0)))) -> c2(B'(B(B(encArg(z0)))), ENCARG(cons_B(cons_B(z0))))
   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))))
   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_C(z0)))) -> c3(C'(a(C(encArg(z0)))), ENCARG(cons_a(cons_C(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_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(cons_A(z0)))) -> c3(C'(b(A(encArg(z0)))), ENCARG(cons_b(cons_A(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(cons_B(z0)))) -> c3(C'(b(B(encArg(z0)))), ENCARG(cons_b(cons_B(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))))
   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_C(z0)))) -> c3(C'(c(C(encArg(z0)))), ENCARG(cons_c(cons_C(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_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(cons_A(z0)))) -> c3(C'(A(A(encArg(z0)))), ENCARG(cons_A(cons_A(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(cons_B(z0)))) -> c3(C'(A(B(encArg(z0)))), ENCARG(cons_A(cons_B(z0))))
   ENCARG(cons_c(cons_A(x0))) -> c3(ENCARG(cons_A(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))))
   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_C(z0)))) -> c3(C'(C(C(encArg(z0)))), ENCARG(cons_C(cons_C(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_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(cons_A(z0)))) -> c3(C'(B(A(encArg(z0)))), ENCARG(cons_B(cons_A(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(cons_B(z0)))) -> c3(C'(B(B(encArg(z0)))), ENCARG(cons_B(cons_B(z0))))
   ENCARG(cons_c(cons_B(x0))) -> c3(ENCARG(cons_B(x0)))
S tuples:
   A'(c_A(z0)) -> c15
   A'(c_b(z0)) -> c16(C''(z0))
   B'(c_c(z0)) -> c19(A''(z0))
   B'(c_B(z0)) -> c20
   C'(c_a(z0)) -> c22(B''(z0))
   C'(c_C(z0)) -> c24
   C''(c_c(z0)) -> c27
   C''(c_B(z0)) -> c28(A'(z0))
   B''(c_A(z0)) -> c34(C'(z0))
   B''(c_b(z0)) -> c36
   A''(c_C(z0)) -> c40(B'(z0))
   A''(c_a(z0)) -> c42
   A'(c_a(c_a(c_a(c_a(x0))))) -> c14(A''(c_A(A(x0))), A''(A(x0)), A''(x0))
   A'(c_a(c_a(c_a(c_a(z0))))) -> c14(A''(A(c_A(z0))), A''(A(z0)), A''(z0))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c14(A''(A(a(a(a(a(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   A'(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c14(A''(A(b(C(C(C(z0)))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   A'(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c14(A''(A(b(z0))), A''(A(c_C(z0))), A''(c_C(z0)))
   A'(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c14(A''(A(a(a(a(a(C(z0))))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   A'(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c14(A''(A(z0)), A''(A(c_a(z0))), A''(c_a(z0)))
   B'(c_b(c_b(c_b(c_b(x0))))) -> c18(B''(c_B(B(x0))), B''(B(x0)), B''(x0))
   B'(c_b(c_b(c_b(c_b(z0))))) -> c18(B''(B(c_B(z0))), B''(B(z0)), B''(z0))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c18(B''(B(b(b(b(b(z0)))))), B''(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   B'(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c18(B''(B(c(A(A(A(z0)))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   B'(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c18(B''(B(c(z0))), B''(B(c_A(z0))), B''(c_A(z0)))
   B'(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c18(B''(B(b(b(b(b(A(z0))))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   B'(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c18(B''(B(z0)), B''(B(c_b(z0))), B''(c_b(z0)))
   C'(c_c(c_c(c_c(c_c(x0))))) -> c23(C''(c_C(C(x0))), C''(C(x0)), C''(x0))
   C'(c_c(c_c(c_c(c_c(z0))))) -> c23(C''(C(c_C(z0))), C''(C(z0)), C''(z0))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c23(C''(C(c(c(c(c(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   C'(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c23(C''(C(z0)), C''(C(c_c(z0))), C''(c_c(z0)))
   C'(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c23(C''(C(a(z0))), C''(C(c_B(z0))), C''(c_B(z0)))
   C'(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c23(C''(C(a(B(B(B(z0)))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   C'(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c23(C''(C(c(c(c(c(B(z0))))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c_c(c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(x0)))) -> c26(C'(c(c_c(c(x0)))), C'(c(c(x0))), C'(c(x0)), C'(x0))
   C''(c_C(c_C(c_C(z0)))) -> c26(C'(c(c(c_c(z0)))), C'(c(c(z0))), C'(c(z0)), C'(z0))
   C''(c_C(c_C(c_C(c_a(z0))))) -> c26(C'(c(c(B(z0)))), C'(c(c(c_a(z0)))), C'(c(c_a(z0))), C'(c_a(z0)))
   C''(c_C(c_C(c_C(c_c(c_c(c_c(c_c(z0)))))))) -> c26(C'(c(c(C(C(C(z0)))))), C'(c(c(c_c(c_c(c_c(c_c(z0))))))), C'(c(c_c(c_c(c_c(c_c(z0)))))), C'(c_c(c_c(c_c(c_c(z0))))))
   C''(c_C(c_C(c_C(c_C(z0))))) -> c26(C'(c(c(z0))), C'(c(c(c_C(z0)))), C'(c(c_C(z0))), C'(c_C(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(A'(B(c_B(B(x0)))), B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_b(c_b(c_b(c_b(z0))))) -> c29(A'(B(B(c_B(z0)))), B''(B(B(z0))), B''(B(z0)), B''(z0))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_B(z0)))))))) -> c29(A'(B(B(b(b(b(b(z0))))))), B''(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)))))
   C''(c_b(c_b(c_b(c_b(c_a(c_a(c_a(c_a(z0))))))))) -> c29(A'(B(B(c(A(A(A(z0))))))), B''(B(B(c_a(c_a(c_a(c_a(z0))))))), B''(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_b(c_b(c_b(c_b(c_A(z0)))))) -> c29(A'(B(B(c(z0)))), B''(B(B(c_A(z0)))), B''(B(c_A(z0))), B''(c_A(z0)))
   C''(c_b(c_b(c_b(c_b(c_B(c_B(c_c(z0)))))))) -> c29(A'(B(B(b(b(b(b(A(z0)))))))), B''(B(B(c_B(c_B(c_c(z0)))))), B''(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_b(c_b(c_b(c_b(c_b(z0)))))) -> c29(A'(B(B(z0))), B''(B(B(c_b(z0)))), B''(B(c_b(z0))), B''(c_b(z0)))
   C''(c_b(c_b(c_b(c_b(x0))))) -> c29(B''(B(B(x0))), B''(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c_c(c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c_c(c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(x0)))) -> c30(C'(c(c(c_c(B(x0))))), C'(c(c(B(x0)))), C'(c(B(x0))), C'(B(x0)), B''(x0))
   C''(c_C(c_C(c_a(z0)))) -> c30(C'(c(c(c(c_B(z0))))), C'(c(c(B(z0)))), C'(c(B(z0))), C'(B(z0)), B''(z0))
   C''(c_C(c_C(c_a(c_B(c_B(c_B(z0))))))) -> c30(C'(c(c(c(b(b(b(b(z0)))))))), C'(c(c(B(c_B(c_B(c_B(z0))))))), C'(c(B(c_B(c_B(c_B(z0)))))), C'(B(c_B(c_B(c_B(z0))))), B''(c_B(c_B(c_B(z0)))))
   C''(c_C(c_C(c_a(c_a(c_a(c_a(c_a(z0)))))))) -> c30(C'(c(c(c(c(A(A(A(z0)))))))), C'(c(c(B(c_a(c_a(c_a(c_a(z0)))))))), C'(c(B(c_a(c_a(c_a(c_a(z0))))))), C'(B(c_a(c_a(c_a(c_a(z0)))))), B''(c_a(c_a(c_a(c_a(z0))))))
   C''(c_C(c_C(c_a(c_A(z0))))) -> c30(C'(c(c(c(c(z0))))), C'(c(c(B(c_A(z0))))), C'(c(B(c_A(z0)))), C'(B(c_A(z0))), B''(c_A(z0)))
   C''(c_C(c_C(c_a(c_B(c_B(c_c(z0))))))) -> c30(C'(c(c(c(b(b(b(b(A(z0))))))))), C'(c(c(B(c_B(c_B(c_c(z0))))))), C'(c(B(c_B(c_B(c_c(z0)))))), C'(B(c_B(c_B(c_c(z0))))), B''(c_B(c_B(c_c(z0)))))
   C''(c_C(c_C(c_a(c_b(z0))))) -> c30(C'(c(c(c(z0)))), C'(c(c(B(c_b(z0))))), C'(c(B(c_b(z0)))), C'(B(c_b(z0))), B''(c_b(z0)))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(c_b(b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(x0)))) -> c32(B'(b(c_b(b(x0)))), B'(b(b(x0))), B'(b(x0)), B'(x0))
   B''(c_B(c_B(c_B(z0)))) -> c32(B'(b(b(c_b(z0)))), B'(b(b(z0))), B'(b(z0)), B'(z0))
   B''(c_B(c_B(c_B(c_b(c_b(c_b(c_b(z0)))))))) -> c32(B'(b(b(B(B(B(z0)))))), B'(b(b(c_b(c_b(c_b(c_b(z0))))))), B'(b(c_b(c_b(c_b(c_b(z0)))))), B'(c_b(c_b(c_b(c_b(z0))))))
   B''(c_B(c_B(c_B(c_c(z0))))) -> c32(B'(b(b(A(z0)))), B'(b(b(c_c(z0)))), B'(b(c_c(z0))), B'(c_c(z0)))
   B''(c_B(c_B(c_B(c_B(z0))))) -> c32(B'(b(b(z0))), B'(b(b(c_B(z0)))), B'(b(c_B(z0))), B'(c_B(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(C'(A(c_A(A(x0)))), A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_a(c_a(c_a(c_a(z0))))) -> c33(C'(A(A(c_A(z0)))), A''(A(A(z0))), A''(A(z0)), A''(z0))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_A(z0)))))))) -> c33(C'(A(A(a(a(a(a(z0))))))), A''(A(A(c_A(c_A(c_A(z0)))))), A''(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_a(c_a(c_a(c_a(c_c(c_c(c_c(c_c(z0))))))))) -> c33(C'(A(A(b(C(C(C(z0))))))), A''(A(A(c_c(c_c(c_c(c_c(z0))))))), A''(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_a(c_a(c_a(c_a(c_C(z0)))))) -> c33(C'(A(A(b(z0)))), A''(A(A(c_C(z0)))), A''(A(c_C(z0))), A''(c_C(z0)))
   B''(c_a(c_a(c_a(c_a(c_A(c_A(c_b(z0)))))))) -> c33(C'(A(A(a(a(a(a(C(z0)))))))), A''(A(A(c_A(c_A(c_b(z0)))))), A''(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_a(c_a(c_a(c_a(c_a(z0)))))) -> c33(C'(A(A(z0))), A''(A(A(c_a(z0)))), A''(A(c_a(z0))), A''(c_a(z0)))
   B''(c_a(c_a(c_a(c_a(x0))))) -> c33(A''(A(A(x0))), A''(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(c_b(b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(c_b(b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(x0)))) -> c35(B'(b(b(c_b(A(x0))))), B'(b(b(A(x0)))), B'(b(A(x0))), B'(A(x0)), A''(x0))
   B''(c_B(c_B(c_c(z0)))) -> c35(B'(b(b(b(c_A(z0))))), B'(b(b(A(z0)))), B'(b(A(z0))), B'(A(z0)), A''(z0))
   B''(c_B(c_B(c_c(c_A(c_A(c_A(z0))))))) -> c35(B'(b(b(b(a(a(a(a(z0)))))))), B'(b(b(A(c_A(c_A(c_A(z0))))))), B'(b(A(c_A(c_A(c_A(z0)))))), B'(A(c_A(c_A(c_A(z0))))), A''(c_A(c_A(c_A(z0)))))
   B''(c_B(c_B(c_c(c_c(c_c(c_c(c_c(z0)))))))) -> c35(B'(b(b(b(b(C(C(C(z0)))))))), B'(b(b(A(c_c(c_c(c_c(c_c(z0)))))))), B'(b(A(c_c(c_c(c_c(c_c(z0))))))), B'(A(c_c(c_c(c_c(c_c(z0)))))), A''(c_c(c_c(c_c(c_c(z0))))))
   B''(c_B(c_B(c_c(c_C(z0))))) -> c35(B'(b(b(b(b(z0))))), B'(b(b(A(c_C(z0))))), B'(b(A(c_C(z0)))), B'(A(c_C(z0))), A''(c_C(z0)))
   B''(c_B(c_B(c_c(c_A(c_A(c_b(z0))))))) -> c35(B'(b(b(b(a(a(a(a(C(z0))))))))), B'(b(b(A(c_A(c_A(c_b(z0))))))), B'(b(A(c_A(c_A(c_b(z0)))))), B'(A(c_A(c_A(c_b(z0))))), A''(c_A(c_A(c_b(z0)))))
   B''(c_B(c_B(c_c(c_a(z0))))) -> c35(B'(b(b(b(z0)))), B'(b(b(A(c_a(z0))))), B'(b(A(c_a(z0)))), B'(A(c_a(z0))), A''(c_a(z0)))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(c_a(a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(x0)))) -> c38(A'(a(c_a(a(x0)))), A'(a(a(x0))), A'(a(x0)), A'(x0))
   A''(c_A(c_A(c_A(z0)))) -> c38(A'(a(a(c_a(z0)))), A'(a(a(z0))), A'(a(z0)), A'(z0))
   A''(c_A(c_A(c_A(c_a(c_a(c_a(c_a(z0)))))))) -> c38(A'(a(a(A(A(A(z0)))))), A'(a(a(c_a(c_a(c_a(c_a(z0))))))), A'(a(c_a(c_a(c_a(c_a(z0)))))), A'(c_a(c_a(c_a(c_a(z0))))))
   A''(c_A(c_A(c_A(c_A(z0))))) -> c38(A'(a(a(z0))), A'(a(a(c_A(z0)))), A'(a(c_A(z0))), A'(c_A(z0)))
   A''(c_A(c_A(c_A(c_b(z0))))) -> c38(A'(a(a(C(z0)))), A'(a(a(c_b(z0)))), A'(a(c_b(z0))), A'(c_b(z0)))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(B'(C(c_C(C(x0)))), C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_c(c_c(c_c(c_c(z0))))) -> c39(B'(C(C(c_C(z0)))), C''(C(C(z0))), C''(C(z0)), C''(z0))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_C(z0)))))))) -> c39(B'(C(C(c(c(c(c(z0))))))), C''(C(C(c_C(c_C(c_C(z0)))))), C''(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_c(c_c(c_c(c_c(c_c(z0)))))) -> c39(B'(C(C(z0))), C''(C(C(c_c(z0)))), C''(C(c_c(z0))), C''(c_c(z0)))
   A''(c_c(c_c(c_c(c_c(c_B(z0)))))) -> c39(B'(C(C(a(z0)))), C''(C(C(c_B(z0)))), C''(C(c_B(z0))), C''(c_B(z0)))
   A''(c_c(c_c(c_c(c_c(c_b(c_b(c_b(c_b(z0))))))))) -> c39(B'(C(C(a(B(B(B(z0))))))), C''(C(C(c_b(c_b(c_b(c_b(z0))))))), C''(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_c(c_c(c_c(c_c(c_C(c_C(c_a(z0)))))))) -> c39(B'(C(C(c(c(c(c(B(z0)))))))), C''(C(C(c_C(c_C(c_a(z0)))))), C''(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
   A''(c_c(c_c(c_c(c_c(x0))))) -> c39(C''(C(C(x0))), C''(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(c_a(a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(c_a(a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(x0)))) -> c41(A'(a(a(c_a(C(x0))))), A'(a(a(C(x0)))), A'(a(C(x0))), A'(C(x0)), C''(x0))
   A''(c_A(c_A(c_b(z0)))) -> c41(A'(a(a(a(c_C(z0))))), A'(a(a(C(z0)))), A'(a(C(z0))), A'(C(z0)), C''(z0))
   A''(c_A(c_A(c_b(c_C(c_C(c_C(z0))))))) -> c41(A'(a(a(a(c(c(c(c(z0)))))))), A'(a(a(C(c_C(c_C(c_C(z0))))))), A'(a(C(c_C(c_C(c_C(z0)))))), A'(C(c_C(c_C(c_C(z0))))), C''(c_C(c_C(c_C(z0)))))
   A''(c_A(c_A(c_b(c_c(z0))))) -> c41(A'(a(a(a(z0)))), A'(a(a(C(c_c(z0))))), A'(a(C(c_c(z0)))), A'(C(c_c(z0))), C''(c_c(z0)))
   A''(c_A(c_A(c_b(c_B(z0))))) -> c41(A'(a(a(a(a(z0))))), A'(a(a(C(c_B(z0))))), A'(a(C(c_B(z0)))), A'(C(c_B(z0))), C''(c_B(z0)))
   A''(c_A(c_A(c_b(c_b(c_b(c_b(c_b(z0)))))))) -> c41(A'(a(a(a(a(B(B(B(z0)))))))), A'(a(a(C(c_b(c_b(c_b(c_b(z0)))))))), A'(a(C(c_b(c_b(c_b(c_b(z0))))))), A'(C(c_b(c_b(c_b(c_b(z0)))))), C''(c_b(c_b(c_b(c_b(z0))))))
   A''(c_A(c_A(c_b(c_C(c_C(c_a(z0))))))) -> c41(A'(a(a(a(c(c(c(c(B(z0))))))))), A'(a(a(C(c_C(c_C(c_a(z0))))))), A'(a(C(c_C(c_C(c_a(z0)))))), A'(C(c_C(c_C(c_a(z0))))), C''(c_C(c_C(c_a(z0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, a_1, b_1, c_1, A_1, C_1, B_1

Defined Pair Symbols:   A'_1, B'_1, C'_1, C''_1, B''_1, A''_1, ENCARG_1, ENCODE_A_1, ENCODE_B_1, ENCODE_C_1, ENCODE_C'_1, ENCODE_A'_1, ENCODE_B'_1

Compound Symbols:   c15, c16_1, c19_1, c20, c22_1, c24, c27, c28_1, c34_1, c36, c40_1, c42, c4_2, c5_2, c6_2, c14_3, c18_3, c23_3, c26_4, c29_4, c29_3, c30_5, c32_4, c33_4, c33_3, c35_5, c38_4, c39_4, c39_3, c41_5, c13_1, c1_2, c1_1, c2_2, c2_1, c3_2, c3_1