/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 59 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 10 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 0 ms]
    (12) typed CpxTrs
    (13) RewriteLemmaProof [LOWER BOUND(ID), 495 ms]
    (14) BOUNDS(1, INF)
(15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(16) CpxTRS
(17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
    (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxTypedWeightedTrs
    (23) CompletionProof [UPPER BOUND(ID), 0 ms]
    (24) CpxTypedWeightedCompleteTrs
        (25) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (28) CpxRNTS
        (29) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (30) CpxRNTS
    (31) CompletionProof [UPPER BOUND(ID), 0 ms]
    (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (34) CpxRNTS
(35) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(36) CdtProblem
    (37) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (38) CdtProblem
    (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (42) CdtProblem
    (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (44) CdtProblem
    (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (46) CdtProblem
    (47) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 176 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) CdtProblem
    (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (64) CdtProblem
    (65) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (66) CdtProblem
    (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (70) CdtProblem
    (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
    (73) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (76) CdtProblem
    (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 1 ms]
    (78) CdtProblem
    (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) CdtProblem
    (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (82) CdtProblem
    (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (84) CdtProblem
    (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms]
    (88) CdtProblem
    (89) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (90) CdtProblem
    (91) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) CdtProblem
    (93) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (94) CdtProblem
    (95) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (96) CdtProblem
    (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem
    (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (102) CdtProblem
    (103) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (104) CdtProblem
    (105) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (106) CdtProblem
    (107) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (112) CdtProblem
    (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (114) CdtProblem
    (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (116) CdtProblem
    (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (118) CdtProblem
    (119) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (120) CdtProblem
    (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (122) CdtProblem
    (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (124) CdtProblem
    (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 3 ms]
    (126) CdtProblem
    (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (128) CdtProblem
    (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (130) CdtProblem
    (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (132) CdtProblem
    (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (134) CdtProblem
    (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 45 ms]
    (136) CdtProblem
    (137) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (138) CdtProblem
    (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms]
    (140) CdtProblem
    (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (142) CdtProblem
    (143) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 5 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), 0 ms]
    (150) CdtProblem
    (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 42 ms]
    (152) CdtProblem
    (153) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms]
    (154) CdtProblem
    (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (156) CdtProblem
    (157) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (158) CdtProblem


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

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


The TRS R consists of the following rules:

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

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

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

   encArg(c(x_1)) -> c(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encArg(cons_d(x_1)) -> d(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   encode_d(x_1) -> d(encArg(x_1))
   encode_c(x_1) -> c(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))


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

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


The TRS R consists of the following rules:

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

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

   encArg(c(x_1)) -> c(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encArg(cons_d(x_1)) -> d(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   encode_d(x_1) -> d(encArg(x_1))
   encode_c(x_1) -> c(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

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

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

   encArg(c(x_1)) -> c(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encArg(cons_d(x_1)) -> d(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   encode_d(x_1) -> d(encArg(x_1))
   encode_c(x_1) -> c(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))

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

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

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

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


The TRS R consists of the following rules:

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

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

   encArg(c(x_1)) -> c(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encArg(cons_d(x_1)) -> d(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   encode_d(x_1) -> d(encArg(x_1))
   encode_c(x_1) -> c(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

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

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

   encArg(c(x_1)) -> c(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encArg(cons_d(x_1)) -> d(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   encode_d(x_1) -> d(encArg(x_1))
   encode_c(x_1) -> c(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))

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

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

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

Types:
b :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
d :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
c :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
a :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
encArg :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
cons_b :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
cons_a :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
cons_d :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
encode_b :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
encode_d :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
encode_c :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
encode_a :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
hole_c:cons_b:cons_a:cons_d1_0 :: c:cons_b:cons_a:cons_d
gen_c:cons_b:cons_a:cons_d2_0 :: Nat -> c:cons_b:cons_a:cons_d

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

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

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

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

(12)
Obligation:
Innermost TRS:
Rules:
b(b(d(d(b(b(x1)))))) -> c(c(d(d(b(b(x1))))))
b(b(a(a(c(c(x1)))))) -> b(b(c(c(x1))))
a(a(d(d(x1)))) -> d(d(c(c(x1))))
b(b(b(b(b(b(x1)))))) -> a(a(b(b(c(c(x1))))))
d(d(c(c(x1)))) -> b(b(d(d(x1))))
d(d(c(c(x1)))) -> d(d(b(b(d(d(x1))))))
d(d(a(a(c(c(x1)))))) -> b(b(b(b(x1))))
encArg(c(x_1)) -> c(encArg(x_1))
encArg(cons_b(x_1)) -> b(encArg(x_1))
encArg(cons_a(x_1)) -> a(encArg(x_1))
encArg(cons_d(x_1)) -> d(encArg(x_1))
encode_b(x_1) -> b(encArg(x_1))
encode_d(x_1) -> d(encArg(x_1))
encode_c(x_1) -> c(encArg(x_1))
encode_a(x_1) -> a(encArg(x_1))

Types:
b :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
d :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
c :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
a :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
encArg :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
cons_b :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
cons_a :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
cons_d :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
encode_b :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
encode_d :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
encode_c :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
encode_a :: c:cons_b:cons_a:cons_d -> c:cons_b:cons_a:cons_d
hole_c:cons_b:cons_a:cons_d1_0 :: c:cons_b:cons_a:cons_d
gen_c:cons_b:cons_a:cons_d2_0 :: Nat -> c:cons_b:cons_a:cons_d


Generator Equations:
gen_c:cons_b:cons_a:cons_d2_0(0) <=> hole_c:cons_b:cons_a:cons_d1_0
gen_c:cons_b:cons_a:cons_d2_0(+(x, 1)) <=> c(gen_c:cons_b:cons_a:cons_d2_0(x))


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

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

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

(13) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_c:cons_b:cons_a:cons_d2_0(+(1, n32_0))) -> *3_0, rt in Omega(0)

Induction Base:
encArg(gen_c:cons_b:cons_a:cons_d2_0(+(1, 0)))

Induction Step:
encArg(gen_c:cons_b:cons_a:cons_d2_0(+(1, +(n32_0, 1)))) ->_R^Omega(0)
c(encArg(gen_c:cons_b:cons_a:cons_d2_0(+(1, n32_0)))) ->_IH
c(*3_0)

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

(14)
BOUNDS(1, INF)

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

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

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


The TRS R consists of the following rules:

   b(b(d(d(b(b(x1)))))) -> c(c(d(d(b(b(x1))))))
   b(b(a(a(c(c(x1)))))) -> b(b(c(c(x1))))
   a(a(d(d(x1)))) -> d(d(c(c(x1))))
   b(b(b(b(b(b(x1)))))) -> a(a(b(b(c(c(x1))))))
   d(d(c(c(x1)))) -> b(b(d(d(x1))))
   d(d(c(c(x1)))) -> d(d(b(b(d(d(x1))))))
   d(d(a(a(c(c(x1)))))) -> b(b(b(b(x1))))
   encArg(c(x_1)) -> c(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encArg(cons_d(x_1)) -> d(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   encode_d(x_1) -> d(encArg(x_1))
   encode_c(x_1) -> c(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   a(c_a(c_d(c_d(x1)))) -> d(d(c(c(x1))))
   b(c_b(c_b(c_b(c_b(c_b(x1)))))) -> a(a(b(b(c(c(x1))))))
   d(c_d(c_a(c_a(c(c(x1)))))) -> b(b(b(b(x1))))
   d(c_d(c(c(x1)))) -> d(d(b(b(d(d(x1))))))
   b(c_b(c_d(c_d(c_b(c_b(x1)))))) -> c(c(d(d(b(b(x1))))))
   b(c_b(c_a(c_a(c(c(x1)))))) -> b(b(c(c(x1))))
   d(c_d(c(c(x1)))) -> b(b(d(d(x1))))

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

   encArg(c(x_1)) -> c(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encArg(cons_a(x_1)) -> a(encArg(x_1))
   encArg(cons_d(x_1)) -> d(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   encode_d(x_1) -> d(encArg(x_1))
   encode_c(x_1) -> c(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   a(x0) -> c_a(x0)
   b(x0) -> c_b(x0)
   d(x0) -> c_d(x0)

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

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

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


The TRS R consists of the following rules:

   a(c_a(c_d(c_d(x1)))) -> d(d(c(c(x1)))) [1]
   b(c_b(c_b(c_b(c_b(c_b(x1)))))) -> a(a(b(b(c(c(x1)))))) [1]
   d(c_d(c_a(c_a(c(c(x1)))))) -> b(b(b(b(x1)))) [1]
   d(c_d(c(c(x1)))) -> d(d(b(b(d(d(x1)))))) [1]
   b(c_b(c_d(c_d(c_b(c_b(x1)))))) -> c(c(d(d(b(b(x1)))))) [1]
   b(c_b(c_a(c_a(c(c(x1)))))) -> b(b(c(c(x1)))) [1]
   d(c_d(c(c(x1)))) -> b(b(d(d(x1)))) [1]
   encArg(c(x_1)) -> c(encArg(x_1)) [0]
   encArg(cons_b(x_1)) -> b(encArg(x_1)) [0]
   encArg(cons_a(x_1)) -> a(encArg(x_1)) [0]
   encArg(cons_d(x_1)) -> d(encArg(x_1)) [0]
   encode_b(x_1) -> b(encArg(x_1)) [0]
   encode_d(x_1) -> d(encArg(x_1)) [0]
   encode_c(x_1) -> c(encArg(x_1)) [0]
   encode_a(x_1) -> a(encArg(x_1)) [0]
   a(x0) -> c_a(x0) [0]
   b(x0) -> c_b(x0) [0]
   d(x0) -> c_d(x0) [0]

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

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

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

   a(c_a(c_d(c_d(x1)))) -> d(d(c(c(x1)))) [1]
   b(c_b(c_b(c_b(c_b(c_b(x1)))))) -> a(a(b(b(c(c(x1)))))) [1]
   d(c_d(c_a(c_a(c(c(x1)))))) -> b(b(b(b(x1)))) [1]
   d(c_d(c(c(x1)))) -> d(d(b(b(d(d(x1)))))) [1]
   b(c_b(c_d(c_d(c_b(c_b(x1)))))) -> c(c(d(d(b(b(x1)))))) [1]
   b(c_b(c_a(c_a(c(c(x1)))))) -> b(b(c(c(x1)))) [1]
   d(c_d(c(c(x1)))) -> b(b(d(d(x1)))) [1]
   encArg(c(x_1)) -> c(encArg(x_1)) [0]
   encArg(cons_b(x_1)) -> b(encArg(x_1)) [0]
   encArg(cons_a(x_1)) -> a(encArg(x_1)) [0]
   encArg(cons_d(x_1)) -> d(encArg(x_1)) [0]
   encode_b(x_1) -> b(encArg(x_1)) [0]
   encode_d(x_1) -> d(encArg(x_1)) [0]
   encode_c(x_1) -> c(encArg(x_1)) [0]
   encode_a(x_1) -> a(encArg(x_1)) [0]
   a(x0) -> c_a(x0) [0]
   b(x0) -> c_b(x0) [0]
   d(x0) -> c_d(x0) [0]

The TRS has the following type information:
a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d
c_a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d
c_d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d
d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d
c :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d
b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d
c_b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d
encArg :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d
cons_b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d
cons_a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d
cons_d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d
encode_b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d
encode_d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d
encode_c :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d
encode_a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d

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

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

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

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

(c) The following functions are completely defined:

   encArg_1
   encode_b_1
   encode_d_1
   encode_c_1
   encode_a_1
   a_1
   b_1
   d_1

Due to the following rules being added:

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

And the following fresh constants:    const

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

(24)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

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

The TRS has the following type information:
a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
c_a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
c_d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
c :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
c_b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
encArg :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
cons_b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
cons_a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
cons_d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
encode_b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
encode_d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
encode_c :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
encode_a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
const :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const

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

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

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

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

   a(c_a(c_d(c_d(x1)))) -> d(c_d(c(c(x1)))) [1]
   a(c_a(c_d(c_d(x1)))) -> d(const) [1]
   b(c_b(c_b(c_b(c_b(c_b(x1)))))) -> a(a(b(c_b(c(c(x1)))))) [1]
   b(c_b(c_b(c_b(c_b(c_b(x1)))))) -> a(a(b(const))) [1]
   d(c_d(c_a(c_a(c(c(c_b(c_b(c_b(c_b(c_b(x1'))))))))))) -> b(b(b(a(a(b(b(c(c(x1'))))))))) [2]
   d(c_d(c_a(c_a(c(c(c_b(c_d(c_d(c_b(c_b(x1''))))))))))) -> b(b(b(c(c(d(d(b(b(x1''))))))))) [2]
   d(c_d(c_a(c_a(c(c(c_b(c_a(c_a(c(c(x11))))))))))) -> b(b(b(b(b(c(c(x11))))))) [2]
   d(c_d(c_a(c_a(c(c(x1)))))) -> b(b(b(c_b(x1)))) [1]
   d(c_d(c_a(c_a(c(c(x1)))))) -> b(b(b(const))) [1]
   d(c_d(c(c(c_d(c_a(c_a(c(c(x12))))))))) -> d(d(b(b(d(b(b(b(b(x12))))))))) [2]
   d(c_d(c(c(c_d(c(c(x13))))))) -> d(d(b(b(d(d(d(b(b(d(d(x13))))))))))) [2]
   d(c_d(c(c(c_d(c(c(x14))))))) -> d(d(b(b(d(b(b(d(d(x14))))))))) [2]
   d(c_d(c(c(x1)))) -> d(d(b(b(d(c_d(x1)))))) [1]
   d(c_d(c(c(x1)))) -> d(d(b(b(d(const))))) [1]
   b(c_b(c_d(c_d(c_b(c_b(c_b(c_b(c_b(c_b(c_b(x15))))))))))) -> c(c(d(d(b(a(a(b(b(c(c(x15))))))))))) [2]
   b(c_b(c_d(c_d(c_b(c_b(c_b(c_d(c_d(c_b(c_b(x16))))))))))) -> c(c(d(d(b(c(c(d(d(b(b(x16))))))))))) [2]
   b(c_b(c_d(c_d(c_b(c_b(c_b(c_a(c_a(c(c(x17))))))))))) -> c(c(d(d(b(b(b(c(c(x17))))))))) [2]
   b(c_b(c_d(c_d(c_b(c_b(x1)))))) -> c(c(d(d(b(c_b(x1)))))) [1]
   b(c_b(c_d(c_d(c_b(c_b(x1)))))) -> c(c(d(d(b(const))))) [1]
   b(c_b(c_a(c_a(c(c(x1)))))) -> b(c_b(c(c(x1)))) [1]
   b(c_b(c_a(c_a(c(c(x1)))))) -> b(const) [1]
   d(c_d(c(c(c_d(c_a(c_a(c(c(x18))))))))) -> b(b(d(b(b(b(b(x18))))))) [2]
   d(c_d(c(c(c_d(c(c(x19))))))) -> b(b(d(d(d(b(b(d(d(x19))))))))) [2]
   d(c_d(c(c(c_d(c(c(x110))))))) -> b(b(d(b(b(d(d(x110))))))) [2]
   d(c_d(c(c(x1)))) -> b(b(d(c_d(x1)))) [1]
   d(c_d(c(c(x1)))) -> b(b(d(const))) [1]
   encArg(c(x_1)) -> c(encArg(x_1)) [0]
   encArg(cons_b(c(x_1'))) -> b(c(encArg(x_1'))) [0]
   encArg(cons_b(cons_b(x_1''))) -> b(b(encArg(x_1''))) [0]
   encArg(cons_b(cons_a(x_11))) -> b(a(encArg(x_11))) [0]
   encArg(cons_b(cons_d(x_12))) -> b(d(encArg(x_12))) [0]
   encArg(cons_b(x_1)) -> b(const) [0]
   encArg(cons_a(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(cons_a(x_15))) -> a(a(encArg(x_15))) [0]
   encArg(cons_a(cons_d(x_16))) -> a(d(encArg(x_16))) [0]
   encArg(cons_a(x_1)) -> a(const) [0]
   encArg(cons_d(c(x_17))) -> d(c(encArg(x_17))) [0]
   encArg(cons_d(cons_b(x_18))) -> d(b(encArg(x_18))) [0]
   encArg(cons_d(cons_a(x_19))) -> d(a(encArg(x_19))) [0]
   encArg(cons_d(cons_d(x_110))) -> d(d(encArg(x_110))) [0]
   encArg(cons_d(x_1)) -> d(const) [0]
   encode_b(c(x_111)) -> b(c(encArg(x_111))) [0]
   encode_b(cons_b(x_112)) -> b(b(encArg(x_112))) [0]
   encode_b(cons_a(x_113)) -> b(a(encArg(x_113))) [0]
   encode_b(cons_d(x_114)) -> b(d(encArg(x_114))) [0]
   encode_b(x_1) -> b(const) [0]
   encode_d(c(x_115)) -> d(c(encArg(x_115))) [0]
   encode_d(cons_b(x_116)) -> d(b(encArg(x_116))) [0]
   encode_d(cons_a(x_117)) -> d(a(encArg(x_117))) [0]
   encode_d(cons_d(x_118)) -> d(d(encArg(x_118))) [0]
   encode_d(x_1) -> d(const) [0]
   encode_c(x_1) -> c(encArg(x_1)) [0]
   encode_a(c(x_119)) -> a(c(encArg(x_119))) [0]
   encode_a(cons_b(x_120)) -> a(b(encArg(x_120))) [0]
   encode_a(cons_a(x_121)) -> a(a(encArg(x_121))) [0]
   encode_a(cons_d(x_122)) -> a(d(encArg(x_122))) [0]
   encode_a(x_1) -> a(const) [0]
   a(x0) -> c_a(x0) [0]
   b(x0) -> c_b(x0) [0]
   d(x0) -> c_d(x0) [0]
   encArg(v0) -> const [0]
   encode_b(v0) -> const [0]
   encode_d(v0) -> const [0]
   encode_c(v0) -> const [0]
   encode_a(v0) -> const [0]
   a(v0) -> const [0]
   b(v0) -> const [0]
   d(v0) -> const [0]

The TRS has the following type information:
a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
c_a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
c_d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
c :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
c_b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
encArg :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
cons_b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
cons_a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
cons_d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
encode_b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
encode_d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
encode_c :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
encode_a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const
const :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:const

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

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

   const => 0

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

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

   a(z) -{ 1 }-> d(0) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   a(z) -{ 1 }-> d(1 + (1 + (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 }-> b(0) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1))))
   b(z) -{ 1 }-> b(1 + (1 + (1 + x1))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1))))
   b(z) -{ 1 }-> a(a(b(0))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1))))
   b(z) -{ 1 }-> a(a(b(1 + (1 + (1 + x1))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1))))
   b(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   b(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   b(z) -{ 2 }-> 1 + (1 + d(d(b(b(b(1 + (1 + x17))))))) :|: x17 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x17)))))))))
   b(z) -{ 2 }-> 1 + (1 + d(d(b(a(a(b(b(1 + (1 + x15))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x15))))))))), x15 >= 0
   b(z) -{ 1 }-> 1 + (1 + d(d(b(0)))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1))))
   b(z) -{ 1 }-> 1 + (1 + d(d(b(1 + x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1))))
   b(z) -{ 2 }-> 1 + (1 + d(d(b(1 + (1 + d(d(b(b(x16))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x16))))))))), x16 >= 0
   d(z) -{ 2 }-> d(d(b(b(d(d(d(b(b(d(d(x13))))))))))) :|: x13 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x13)))))
   d(z) -{ 2 }-> d(d(b(b(d(b(b(d(d(x14))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x14))))), x14 >= 0
   d(z) -{ 2 }-> d(d(b(b(d(b(b(b(b(x12))))))))) :|: x12 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x12)))))))
   d(z) -{ 1 }-> d(d(b(b(d(0))))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   d(z) -{ 1 }-> d(d(b(b(d(1 + x1))))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   d(z) -{ 2 }-> b(b(d(d(d(b(b(d(d(x19))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x19))))), x19 >= 0
   d(z) -{ 2 }-> b(b(d(b(b(d(d(x110))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x110))))), x110 >= 0
   d(z) -{ 2 }-> b(b(d(b(b(b(b(x18))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x18))))))), x18 >= 0
   d(z) -{ 1 }-> b(b(d(0))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   d(z) -{ 1 }-> b(b(d(1 + x1))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   d(z) -{ 2 }-> b(b(b(b(b(1 + (1 + x11)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x11))))))))), x11 >= 0
   d(z) -{ 2 }-> b(b(b(a(a(b(b(1 + (1 + x1')))))))) :|: x1' >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1')))))))))
   d(z) -{ 1 }-> b(b(b(0))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1))))
   d(z) -{ 1 }-> b(b(b(1 + x1))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + x1))))
   d(z) -{ 2 }-> b(b(b(1 + (1 + d(d(b(b(x1'')))))))) :|: x1'' >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1'')))))))))
   d(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   d(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   encArg(z) -{ 0 }-> d(d(encArg(x_110))) :|: z = 1 + (1 + x_110), x_110 >= 0
   encArg(z) -{ 0 }-> d(b(encArg(x_18))) :|: z = 1 + (1 + x_18), x_18 >= 0
   encArg(z) -{ 0 }-> d(a(encArg(x_19))) :|: z = 1 + (1 + x_19), x_19 >= 0
   encArg(z) -{ 0 }-> d(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> d(1 + encArg(x_17)) :|: x_17 >= 0, z = 1 + (1 + x_17)
   encArg(z) -{ 0 }-> b(d(encArg(x_12))) :|: z = 1 + (1 + x_12), x_12 >= 0
   encArg(z) -{ 0 }-> b(b(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0
   encArg(z) -{ 0 }-> b(a(encArg(x_11))) :|: x_11 >= 0, z = 1 + (1 + x_11)
   encArg(z) -{ 0 }-> b(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> b(1 + encArg(x_1')) :|: z = 1 + (1 + x_1'), x_1' >= 0
   encArg(z) -{ 0 }-> a(d(encArg(x_16))) :|: x_16 >= 0, z = 1 + (1 + x_16)
   encArg(z) -{ 0 }-> a(b(encArg(x_14))) :|: x_14 >= 0, z = 1 + (1 + x_14)
   encArg(z) -{ 0 }-> a(a(encArg(x_15))) :|: x_15 >= 0, z = 1 + (1 + x_15)
   encArg(z) -{ 0 }-> a(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> a(1 + encArg(x_13)) :|: z = 1 + (1 + x_13), x_13 >= 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_a(z) -{ 0 }-> a(d(encArg(x_122))) :|: x_122 >= 0, z = 1 + x_122
   encode_a(z) -{ 0 }-> a(b(encArg(x_120))) :|: x_120 >= 0, z = 1 + x_120
   encode_a(z) -{ 0 }-> a(a(encArg(x_121))) :|: z = 1 + x_121, x_121 >= 0
   encode_a(z) -{ 0 }-> a(0) :|: x_1 >= 0, z = x_1
   encode_a(z) -{ 0 }-> a(1 + encArg(x_119)) :|: z = 1 + x_119, x_119 >= 0
   encode_a(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_b(z) -{ 0 }-> b(d(encArg(x_114))) :|: x_114 >= 0, z = 1 + x_114
   encode_b(z) -{ 0 }-> b(b(encArg(x_112))) :|: z = 1 + x_112, x_112 >= 0
   encode_b(z) -{ 0 }-> b(a(encArg(x_113))) :|: z = 1 + x_113, x_113 >= 0
   encode_b(z) -{ 0 }-> b(0) :|: x_1 >= 0, z = x_1
   encode_b(z) -{ 0 }-> b(1 + encArg(x_111)) :|: z = 1 + x_111, x_111 >= 0
   encode_b(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_c(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_c(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   encode_d(z) -{ 0 }-> d(d(encArg(x_118))) :|: z = 1 + x_118, x_118 >= 0
   encode_d(z) -{ 0 }-> d(b(encArg(x_116))) :|: x_116 >= 0, z = 1 + x_116
   encode_d(z) -{ 0 }-> d(a(encArg(x_117))) :|: x_117 >= 0, z = 1 + x_117
   encode_d(z) -{ 0 }-> d(0) :|: x_1 >= 0, z = x_1
   encode_d(z) -{ 0 }-> d(1 + encArg(x_115)) :|: x_115 >= 0, z = 1 + x_115
   encode_d(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


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

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

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

   a(z) -{ 1 }-> d(0) :|: z - 3 >= 0
   a(z) -{ 1 }-> d(1 + (1 + (1 + (z - 3)))) :|: z - 3 >= 0
   a(z) -{ 0 }-> 0 :|: z >= 0
   a(z) -{ 0 }-> 1 + z :|: z >= 0
   b(z) -{ 1 }-> b(0) :|: z - 5 >= 0
   b(z) -{ 1 }-> b(1 + (1 + (1 + (z - 5)))) :|: z - 5 >= 0
   b(z) -{ 1 }-> a(a(b(0))) :|: z - 5 >= 0
   b(z) -{ 1 }-> a(a(b(1 + (1 + (1 + (z - 5)))))) :|: z - 5 >= 0
   b(z) -{ 0 }-> 0 :|: z >= 0
   b(z) -{ 0 }-> 1 + z :|: z >= 0
   b(z) -{ 2 }-> 1 + (1 + d(d(b(b(b(1 + (1 + (z - 10)))))))) :|: z - 10 >= 0
   b(z) -{ 2 }-> 1 + (1 + d(d(b(a(a(b(b(1 + (1 + (z - 10)))))))))) :|: z - 10 >= 0
   b(z) -{ 1 }-> 1 + (1 + d(d(b(0)))) :|: z - 5 >= 0
   b(z) -{ 1 }-> 1 + (1 + d(d(b(1 + (z - 5))))) :|: z - 5 >= 0
   b(z) -{ 2 }-> 1 + (1 + d(d(b(1 + (1 + d(d(b(b(z - 10))))))))) :|: z - 10 >= 0
   d(z) -{ 2 }-> d(d(b(b(d(d(d(b(b(d(d(z - 6))))))))))) :|: z - 6 >= 0
   d(z) -{ 2 }-> d(d(b(b(d(b(b(d(d(z - 6))))))))) :|: z - 6 >= 0
   d(z) -{ 2 }-> d(d(b(b(d(b(b(b(b(z - 8))))))))) :|: z - 8 >= 0
   d(z) -{ 1 }-> d(d(b(b(d(0))))) :|: z - 3 >= 0
   d(z) -{ 1 }-> d(d(b(b(d(1 + (z - 3)))))) :|: z - 3 >= 0
   d(z) -{ 2 }-> b(b(d(d(d(b(b(d(d(z - 6))))))))) :|: z - 6 >= 0
   d(z) -{ 2 }-> b(b(d(b(b(d(d(z - 6))))))) :|: z - 6 >= 0
   d(z) -{ 2 }-> b(b(d(b(b(b(b(z - 8))))))) :|: z - 8 >= 0
   d(z) -{ 1 }-> b(b(d(0))) :|: z - 3 >= 0
   d(z) -{ 1 }-> b(b(d(1 + (z - 3)))) :|: z - 3 >= 0
   d(z) -{ 2 }-> b(b(b(b(b(1 + (1 + (z - 10))))))) :|: z - 10 >= 0
   d(z) -{ 2 }-> b(b(b(a(a(b(b(1 + (1 + (z - 10))))))))) :|: z - 10 >= 0
   d(z) -{ 1 }-> b(b(b(0))) :|: z - 5 >= 0
   d(z) -{ 1 }-> b(b(b(1 + (z - 5)))) :|: z - 5 >= 0
   d(z) -{ 2 }-> b(b(b(1 + (1 + d(d(b(b(z - 10)))))))) :|: z - 10 >= 0
   d(z) -{ 0 }-> 0 :|: z >= 0
   d(z) -{ 0 }-> 1 + z :|: z >= 0
   encArg(z) -{ 0 }-> d(d(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> d(b(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> d(a(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> d(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> d(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> b(d(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 }-> b(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> a(d(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 }-> a(1 + encArg(z - 2)) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_a(z) -{ 0 }-> a(d(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 }-> a(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_a(z) -{ 0 }-> 0 :|: z >= 0
   encode_b(z) -{ 0 }-> b(d(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 }-> b(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_b(z) -{ 0 }-> 0 :|: z >= 0
   encode_c(z) -{ 0 }-> 0 :|: z >= 0
   encode_c(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_d(z) -{ 0 }-> d(d(encArg(z - 1))) :|: z - 1 >= 0
   encode_d(z) -{ 0 }-> d(b(encArg(z - 1))) :|: z - 1 >= 0
   encode_d(z) -{ 0 }-> d(a(encArg(z - 1))) :|: z - 1 >= 0
   encode_d(z) -{ 0 }-> d(0) :|: z >= 0
   encode_d(z) -{ 0 }-> d(1 + encArg(z - 1)) :|: z - 1 >= 0
   encode_d(z) -{ 0 }-> 0 :|: z >= 0


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

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

   encArg(v0) -> null_encArg [0]
   encode_b(v0) -> null_encode_b [0]
   encode_d(v0) -> null_encode_d [0]
   encode_c(v0) -> null_encode_c [0]
   encode_a(v0) -> null_encode_a [0]
   a(v0) -> null_a [0]
   b(v0) -> null_b [0]
   d(v0) -> null_d [0]

And the following fresh constants:    null_encArg, null_encode_b, null_encode_d, null_encode_c, null_encode_a, null_a, null_b, null_d

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

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

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

   a(c_a(c_d(c_d(x1)))) -> d(d(c(c(x1)))) [1]
   b(c_b(c_b(c_b(c_b(c_b(x1)))))) -> a(a(b(b(c(c(x1)))))) [1]
   d(c_d(c_a(c_a(c(c(x1)))))) -> b(b(b(b(x1)))) [1]
   d(c_d(c(c(x1)))) -> d(d(b(b(d(d(x1)))))) [1]
   b(c_b(c_d(c_d(c_b(c_b(x1)))))) -> c(c(d(d(b(b(x1)))))) [1]
   b(c_b(c_a(c_a(c(c(x1)))))) -> b(b(c(c(x1)))) [1]
   d(c_d(c(c(x1)))) -> b(b(d(d(x1)))) [1]
   encArg(c(x_1)) -> c(encArg(x_1)) [0]
   encArg(cons_b(x_1)) -> b(encArg(x_1)) [0]
   encArg(cons_a(x_1)) -> a(encArg(x_1)) [0]
   encArg(cons_d(x_1)) -> d(encArg(x_1)) [0]
   encode_b(x_1) -> b(encArg(x_1)) [0]
   encode_d(x_1) -> d(encArg(x_1)) [0]
   encode_c(x_1) -> c(encArg(x_1)) [0]
   encode_a(x_1) -> a(encArg(x_1)) [0]
   a(x0) -> c_a(x0) [0]
   b(x0) -> c_b(x0) [0]
   d(x0) -> c_d(x0) [0]
   encArg(v0) -> null_encArg [0]
   encode_b(v0) -> null_encode_b [0]
   encode_d(v0) -> null_encode_d [0]
   encode_c(v0) -> null_encode_c [0]
   encode_a(v0) -> null_encode_a [0]
   a(v0) -> null_a [0]
   b(v0) -> null_b [0]
   d(v0) -> null_d [0]

The TRS has the following type information:
a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
c_a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
c_d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
c :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
c_b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
encArg :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
cons_b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
cons_a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
cons_d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
encode_b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
encode_d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
encode_c :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
encode_a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d -> c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
null_encArg :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
null_encode_b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
null_encode_d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
null_encode_c :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
null_encode_a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
null_a :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
null_b :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d
null_d :: c_d:c_a:c:c_b:cons_b:cons_a:cons_d:null_encArg:null_encode_b:null_encode_d:null_encode_c:null_encode_a:null_a:null_b:null_d

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

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

   null_encArg => 0
   null_encode_b => 0
   null_encode_d => 0
   null_encode_c => 0
   null_encode_a => 0
   null_a => 0
   null_b => 0
   null_d => 0

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

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

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

Only complete derivations are relevant for the runtime complexity.

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

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

(36)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_d(z0) -> d(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_b(z0)) -> c2(B(encArg(z0)), ENCARG(z0))
   ENCARG(cons_a(z0)) -> c3(A(encArg(z0)), ENCARG(z0))
   ENCARG(cons_d(z0)) -> c4(D(encArg(z0)), ENCARG(z0))
   ENCODE_B(z0) -> c5(B(encArg(z0)), ENCARG(z0))
   ENCODE_D(z0) -> c6(D(encArg(z0)), ENCARG(z0))
   ENCODE_C(z0) -> c7(ENCARG(z0))
   ENCODE_A(z0) -> c8(A(encArg(z0)), ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(D(d(b(b(z0)))), D(b(b(z0))), B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10(B(b(c(c(z0)))), B(c(c(z0))))
   B(b(b(b(b(b(z0)))))) -> c11(A(a(b(b(c(c(z0)))))), A(b(b(c(c(z0))))), B(b(c(c(z0)))), B(c(c(z0))))
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))), D(c(c(z0))))
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(a(a(c(c(z0)))))) -> c15(B(b(b(b(z0)))), B(b(b(z0))), B(b(z0)), B(z0))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(D(d(b(b(z0)))), D(b(b(z0))), B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10(B(b(c(c(z0)))), B(c(c(z0))))
   B(b(b(b(b(b(z0)))))) -> c11(A(a(b(b(c(c(z0)))))), A(b(b(c(c(z0))))), B(b(c(c(z0)))), B(c(c(z0))))
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))), D(c(c(z0))))
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(a(a(c(c(z0)))))) -> c15(B(b(b(b(z0)))), B(b(b(z0))), B(b(z0)), B(z0))
K tuples:none
Defined Rule Symbols:   b_1, a_1, d_1, encArg_1, encode_b_1, encode_d_1, encode_c_1, encode_a_1

Defined Pair Symbols:   ENCARG_1, ENCODE_B_1, ENCODE_D_1, ENCODE_C_1, ENCODE_A_1, B_1, A_1, D_1

Compound Symbols:   c1_1, c2_2, c3_2, c4_2, c5_2, c6_2, c7_1, c8_2, c9_4, c10_2, c11_4, c12_2, c13_4, c14_6, c15_4


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

(37) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   ENCODE_C(z0) -> c7(ENCARG(z0))

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_d(z0) -> d(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_b(z0)) -> c2(B(encArg(z0)), ENCARG(z0))
   ENCARG(cons_a(z0)) -> c3(A(encArg(z0)), ENCARG(z0))
   ENCARG(cons_d(z0)) -> c4(D(encArg(z0)), ENCARG(z0))
   ENCODE_B(z0) -> c5(B(encArg(z0)), ENCARG(z0))
   ENCODE_D(z0) -> c6(D(encArg(z0)), ENCARG(z0))
   ENCODE_A(z0) -> c8(A(encArg(z0)), ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(D(d(b(b(z0)))), D(b(b(z0))), B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10(B(b(c(c(z0)))), B(c(c(z0))))
   B(b(b(b(b(b(z0)))))) -> c11(A(a(b(b(c(c(z0)))))), A(b(b(c(c(z0))))), B(b(c(c(z0)))), B(c(c(z0))))
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))), D(c(c(z0))))
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(a(a(c(c(z0)))))) -> c15(B(b(b(b(z0)))), B(b(b(z0))), B(b(z0)), B(z0))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(D(d(b(b(z0)))), D(b(b(z0))), B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10(B(b(c(c(z0)))), B(c(c(z0))))
   B(b(b(b(b(b(z0)))))) -> c11(A(a(b(b(c(c(z0)))))), A(b(b(c(c(z0))))), B(b(c(c(z0)))), B(c(c(z0))))
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))), D(c(c(z0))))
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(a(a(c(c(z0)))))) -> c15(B(b(b(b(z0)))), B(b(b(z0))), B(b(z0)), B(z0))
K tuples:none
Defined Rule Symbols:   b_1, a_1, d_1, encArg_1, encode_b_1, encode_d_1, encode_c_1, encode_a_1

Defined Pair Symbols:   ENCARG_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1, B_1, A_1, D_1

Compound Symbols:   c1_1, c2_2, c3_2, c4_2, c5_2, c6_2, c8_2, c9_4, c10_2, c11_4, c12_2, c13_4, c14_6, c15_4


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

(39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 9 trailing tuple parts
----------------------------------------

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_d(z0) -> d(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_b(z0)) -> c2(B(encArg(z0)), ENCARG(z0))
   ENCARG(cons_a(z0)) -> c3(A(encArg(z0)), ENCARG(z0))
   ENCARG(cons_d(z0)) -> c4(D(encArg(z0)), ENCARG(z0))
   ENCODE_B(z0) -> c5(B(encArg(z0)), ENCARG(z0))
   ENCODE_D(z0) -> c6(D(encArg(z0)), ENCARG(z0))
   ENCODE_A(z0) -> c8(A(encArg(z0)), ENCARG(z0))
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(a(a(c(c(z0)))))) -> c15(B(b(b(b(z0)))), B(b(b(z0))), B(b(z0)), B(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
S tuples:
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(a(a(c(c(z0)))))) -> c15(B(b(b(b(z0)))), B(b(b(z0))), B(b(z0)), B(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
K tuples:none
Defined Rule Symbols:   b_1, a_1, d_1, encArg_1, encode_b_1, encode_d_1, encode_c_1, encode_a_1

Defined Pair Symbols:   ENCARG_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1, D_1, B_1, A_1

Compound Symbols:   c1_1, c2_2, c3_2, c4_2, c5_2, c6_2, c8_2, c13_4, c14_6, c15_4, c9_2, c10, c11, c12_1


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

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_d(z0) -> d(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_b(z0)) -> c2(B(encArg(z0)), ENCARG(z0))
   ENCARG(cons_a(z0)) -> c3(A(encArg(z0)), ENCARG(z0))
   ENCARG(cons_d(z0)) -> c4(D(encArg(z0)), ENCARG(z0))
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_B(z0) -> c7(ENCARG(z0))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_D(z0) -> c7(ENCARG(z0))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   ENCODE_A(z0) -> c7(ENCARG(z0))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
S tuples:
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
K tuples:none
Defined Rule Symbols:   b_1, a_1, d_1, encArg_1, encode_b_1, encode_d_1, encode_c_1, encode_a_1

Defined Pair Symbols:   ENCARG_1, D_1, B_1, A_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c2_2, c3_2, c4_2, c13_4, c14_6, c9_2, c10, c11, c12_1, c7_1


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

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

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_d(z0) -> d(encArg(z0))
   encode_c(z0) -> c(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_b(z0)) -> c2(B(encArg(z0)), ENCARG(z0))
   ENCARG(cons_a(z0)) -> c3(A(encArg(z0)), ENCARG(z0))
   ENCARG(cons_d(z0)) -> c4(D(encArg(z0)), ENCARG(z0))
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
S tuples:
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
K tuples:none
Defined Rule Symbols:   b_1, a_1, d_1, encArg_1, encode_b_1, encode_d_1, encode_c_1, encode_a_1

Defined Pair Symbols:   ENCARG_1, D_1, B_1, A_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c2_2, c3_2, c4_2, c13_4, c14_6, c9_2, c10, c11, c12_1, c7_1


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

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

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_b(z0)) -> c2(B(encArg(z0)), ENCARG(z0))
   ENCARG(cons_a(z0)) -> c3(A(encArg(z0)), ENCARG(z0))
   ENCARG(cons_d(z0)) -> c4(D(encArg(z0)), ENCARG(z0))
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
S tuples:
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, D_1, B_1, A_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c2_2, c3_2, c4_2, c13_4, c14_6, c9_2, c10, c11, c12_1, c7_1


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

(47) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1)))
Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S.
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
We considered the (Usable) Rules:none
And the Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_b(z0)) -> c2(B(encArg(z0)), ENCARG(z0))
   ENCARG(cons_a(z0)) -> c3(A(encArg(z0)), ENCARG(z0))
   ENCARG(cons_d(z0)) -> c4(D(encArg(z0)), ENCARG(z0))
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
The order we found is given by the following interpretation:

Polynomial interpretation :

   POL(A(x_1)) = [1]
   POL(B(x_1)) = 0
   POL(D(x_1)) = 0
   POL(ENCARG(x_1)) = x_1
   POL(ENCODE_A(x_1)) = [1]
   POL(ENCODE_B(x_1)) = 0
   POL(ENCODE_D(x_1)) = 0
   POL(a(x_1)) = 0
   POL(b(x_1)) = 0
   POL(c(x_1)) = [1] + x_1
   POL(c1(x_1)) = x_1
   POL(c10) = 0
   POL(c11) = 0
   POL(c12(x_1)) = x_1
   POL(c13(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4
   POL(c14(x_1, x_2, x_3, x_4, x_5, x_6)) = x_1 + x_2 + x_3 + x_4 + x_5 + x_6
   POL(c2(x_1, x_2)) = x_1 + x_2
   POL(c3(x_1, x_2)) = x_1 + x_2
   POL(c4(x_1, x_2)) = x_1 + x_2
   POL(c7(x_1)) = x_1
   POL(c9(x_1, x_2)) = x_1 + x_2
   POL(cons_a(x_1)) = [1] + x_1
   POL(cons_b(x_1)) = [1] + x_1
   POL(cons_d(x_1)) = [1] + x_1
   POL(d(x_1)) = 0
   POL(encArg(x_1)) = [1] + x_1

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_b(z0)) -> c2(B(encArg(z0)), ENCARG(z0))
   ENCARG(cons_a(z0)) -> c3(A(encArg(z0)), ENCARG(z0))
   ENCARG(cons_d(z0)) -> c4(D(encArg(z0)), ENCARG(z0))
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
S tuples:
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, D_1, B_1, A_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c2_2, c3_2, c4_2, c13_4, c14_6, c9_2, c10, c11, c12_1, c7_1


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

(49) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_b(z0)) -> c2(B(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_b(c(z0))) -> c2(B(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_a(z0)) -> c3(A(encArg(z0)), ENCARG(z0))
   ENCARG(cons_d(z0)) -> c4(D(encArg(z0)), ENCARG(z0))
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(B(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
S tuples:
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, D_1, B_1, A_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c3_2, c4_2, c13_4, c14_6, c9_2, c10, c11, c12_1, c7_1, c2_2


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

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_a(z0)) -> c3(A(encArg(z0)), ENCARG(z0))
   ENCARG(cons_d(z0)) -> c4(D(encArg(z0)), ENCARG(z0))
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
S tuples:
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, D_1, B_1, A_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c3_2, c4_2, c13_4, c14_6, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1


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

(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_a(z0)) -> c3(A(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_a(c(z0))) -> c3(A(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_d(z0)) -> c4(D(encArg(z0)), ENCARG(z0))
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(A(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
S tuples:
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, D_1, B_1, A_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c4_2, c13_4, c14_6, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2


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

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   ENCARG(cons_d(z0)) -> c4(D(encArg(z0)), ENCARG(z0))
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
S tuples:
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, D_1, B_1, A_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c4_2, c13_4, c14_6, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1


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

(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_d(z0)) -> c4(D(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_d(c(z0))) -> c4(D(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(D(c(encArg(z0))), ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
S tuples:
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, D_1, B_1, A_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c13_4, c14_6, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2


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

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
S tuples:
   D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, D_1, B_1, A_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c13_4, c14_6, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2, c4_1


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

(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace D(d(c(c(z0)))) -> c13(B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0)) by 
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))), D(c(c(z0))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))), D(c(c(z0))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c13(B(b(d(d(a(a(c(c(z0)))))))), B(b(b(b(b(z0))))), D(d(a(a(c(c(z0)))))), D(a(a(c(c(z0))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))), D(c(c(z0))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))), D(c(c(z0))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c13(B(b(d(d(a(a(c(c(z0)))))))), B(b(b(b(b(z0))))), D(d(a(a(c(c(z0)))))), D(a(a(c(c(z0))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
S tuples:
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))), D(c(c(z0))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))), D(c(c(z0))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c13(B(b(d(d(a(a(c(c(z0)))))))), B(b(b(b(b(z0))))), D(d(a(a(c(c(z0)))))), D(a(a(c(c(z0))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, D_1, B_1, A_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c14_6, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1


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

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c13(B(b(d(d(a(a(c(c(z0)))))))), B(b(b(b(b(z0))))), D(d(a(a(c(c(z0)))))))
S tuples:
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c13(B(b(d(d(a(a(c(c(z0)))))))), B(b(b(b(b(z0))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, D_1, B_1, A_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c14_6, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3


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

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
S tuples:
   D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, D_1, B_1, A_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c14_6, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1


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

(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace D(d(c(c(z0)))) -> c14(D(d(b(b(d(d(z0)))))), D(b(b(d(d(z0))))), B(b(d(d(z0)))), B(d(d(z0))), D(d(z0)), D(z0)) by 
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))), B(d(d(b(b(z0))))), D(d(b(b(z0)))), D(b(b(z0))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))), D(c(c(z0))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))), D(c(c(z0))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))), D(a(a(c(c(z0))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))), B(d(d(b(b(z0))))), D(d(b(b(z0)))), D(b(b(z0))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))), D(c(c(z0))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))), D(c(c(z0))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))), D(a(a(c(c(z0))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))), B(d(d(b(b(z0))))), D(d(b(b(z0)))), D(b(b(z0))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))), D(c(c(z0))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))), D(c(c(z0))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))), D(a(a(c(c(z0))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1, D_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6


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

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_B(z0) -> c7(B(encArg(z0)))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1, D_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5


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

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

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(c(z0)) -> c7(B(c(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, ENCODE_D_1, ENCODE_A_1, D_1, ENCODE_B_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5


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

(73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   ENCODE_B(c(z0)) -> c7(B(c(encArg(z0))))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_D(z0) -> c7(D(encArg(z0)))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, ENCODE_D_1, ENCODE_A_1, D_1, ENCODE_B_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_D(z0) -> c7(D(encArg(z0))) by 
   ENCODE_D(c(z0)) -> c7(D(c(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(c(z0)) -> c7(D(c(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, ENCODE_A_1, D_1, ENCODE_B_1, ENCODE_D_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5


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

(77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   ENCODE_D(c(z0)) -> c7(D(c(encArg(z0))))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   ENCODE_A(z0) -> c7(A(encArg(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, ENCODE_A_1, D_1, ENCODE_B_1, ENCODE_D_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5


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

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

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(c(z0)) -> c7(A(c(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5


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

(81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   ENCODE_A(c(z0)) -> c7(A(c(encArg(z0))))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c2(B(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_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5


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

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

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(B(b(c(encArg(z0)))), ENCARG(cons_b(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_b(cons_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5


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

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_a(z0))) -> c2(B(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_b(cons_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(c(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5


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

(87) 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(c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(c(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(B(a(c(encArg(z0)))), ENCARG(cons_a(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5


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

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(cons_d(z0))) -> c2(B(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_2, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5


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

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

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(B(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2


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

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2


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

(95) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_a(cons_b(z0))) -> c3(A(b(encArg(z0))), ENCARG(cons_b(z0))) by 
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(A(b(c(encArg(z0)))), ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(A(b(c(encArg(z0)))), ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2


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

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2


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

(99) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_a(cons_a(z0))) -> c3(A(a(encArg(z0))), ENCARG(cons_a(z0))) by 
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(A(a(c(encArg(z0)))), ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(A(a(c(encArg(z0)))), ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2


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

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_2, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2


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

(103) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_a(cons_d(z0))) -> c3(A(d(encArg(z0))), ENCARG(cons_d(z0))) by 
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(A(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(A(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2, c3_2


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

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2, c3_2


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

(107) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_d(cons_b(z0))) -> c4(D(b(encArg(z0))), ENCARG(cons_b(z0))) by 
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(D(b(c(encArg(z0)))), ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(D(b(c(encArg(z0)))), ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2, c3_2


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

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2, c3_2


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

(111) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_d(cons_a(z0))) -> c4(D(a(encArg(z0))), ENCARG(cons_a(z0))) by 
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(D(a(c(encArg(z0)))), ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(D(a(c(encArg(z0)))), ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2, c3_2


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

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_2, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2, c3_2


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

(115) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_d(cons_d(z0))) -> c4(D(d(encArg(z0))), ENCARG(cons_d(z0))) by 
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2, c3_2, c4_2


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

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0))))) by 
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2, c3_2, c4_2


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

(119) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(c(c(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0))))) by 
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_4, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2, c3_2, c4_2


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

(121) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(d(d(a(a(c(c(z0))))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0))))))) by 
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2, c3_2, c4_2, c13_4


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

(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0))))) by 
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c13_3, c5_1, c14_6, c14_3, c14_5, c2_2, c3_2, c4_2, c13_4


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

(125) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(c(c(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0))))) by 
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0)))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c14_6, c14_3, c14_5, c2_2, c3_2, c4_2, c13_4, c13_3


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

(127) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(d(d(a(a(c(c(z0))))))))) by 
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c14_6, c14_3, c14_5, c2_2, c3_2, c4_2, c13_4, c13_3


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

(129) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(b(b(d(d(z0))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0))))) by 
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(c(c(d(d(b(b(z0))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(c(c(d(d(b(b(z0))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(c(c(d(d(b(b(z0))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c14_6, c14_3, c14_5, c2_2, c3_2, c4_2, c13_4, c13_3


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

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c14_6, c14_3, c14_5, c2_2, c3_2, c4_2, c13_4, c13_3


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

(133) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace D(d(c(c(d(c(c(z0))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(z0)))))))), B(b(d(d(d(c(c(z0))))))), B(d(d(d(c(c(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0))))) by 
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c14_6, c14_3, c14_5, c2_2, c3_2, c4_2, c13_4, c13_3


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

(135) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace D(d(c(c(d(a(a(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(z0))))))))), D(b(b(d(d(d(a(a(c(c(z0)))))))))), B(b(d(d(d(a(a(c(c(z0))))))))), B(d(d(d(a(a(c(c(z0)))))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0))))))) by 
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(d(b(b(d(a(a(b(b(c(c(z0))))))))))), D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(d(b(b(d(b(a(a(b(b(c(c(z0)))))))))))), D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(d(b(b(d(b(b(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(d(b(b(d(b(b(b(b(c(c(z0))))))))))), D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(d(b(b(d(b(b(a(a(b(b(c(c(z0))))))))))))), D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(d(b(b(d(b(b(b(c(c(d(d(b(b(z0)))))))))))))), D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(c(c(z0)))))))))))), D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(d(b(b(d(b(b(b(a(a(b(b(c(c(z0)))))))))))))), D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(d(b(b(d(a(a(b(b(c(c(z0))))))))))), D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(d(b(b(d(b(a(a(b(b(c(c(z0)))))))))))), D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(d(b(b(d(b(b(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(d(b(b(d(b(b(b(b(c(c(z0))))))))))), D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(d(b(b(d(b(b(a(a(b(b(c(c(z0))))))))))))), D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(d(b(b(d(b(b(b(c(c(d(d(b(b(z0)))))))))))))), D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(c(c(z0)))))))))))), D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(d(b(b(d(b(b(b(a(a(b(b(c(c(z0)))))))))))))), D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(d(b(b(d(a(a(b(b(c(c(z0))))))))))), D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(d(b(b(d(b(a(a(b(b(c(c(z0)))))))))))), D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(d(b(b(d(b(b(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(d(b(b(d(b(b(b(b(c(c(z0))))))))))), D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(d(b(b(d(b(b(a(a(b(b(c(c(z0))))))))))))), D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(d(b(b(d(b(b(b(c(c(d(d(b(b(z0)))))))))))))), D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(c(c(z0)))))))))))), D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(d(b(b(d(b(b(b(a(a(b(b(c(c(z0)))))))))))))), D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c14_3, c14_5, c2_2, c3_2, c4_2, c13_4, c13_3, c14_6


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

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c14_3, c14_5, c2_2, c3_2, c4_2, c13_4, c13_3, c14_6


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

(139) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(b(b(d(d(b(b(z0))))))), B(b(d(d(b(b(z0))))))) by 
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(c(c(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(c(c(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), D(c(c(d(d(b(b(z0))))))), B(b(d(d(b(b(z0)))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c14_5, c2_2, c3_2, c4_2, c13_4, c13_3, c14_6, c14_3, c14_1


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

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), B(b(d(d(b(b(z0)))))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c14(D(d(c(c(d(d(b(b(z0)))))))), B(b(d(d(b(b(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c14_5, c2_2, c3_2, c4_2, c13_4, c13_3, c14_6, c14_1, c14_2


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

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(D(d(c(c(d(d(b(b(z0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(B(b(d(d(b(b(z0)))))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(D(d(c(c(d(d(b(b(z0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(B(b(d(d(b(b(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c14_5, c2_2, c3_2, c4_2, c13_4, c13_3, c14_6, c14_1, c6_1


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

(145) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(b(b(d(d(z0)))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0))))) by 
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(d(b(b(c(c(d(d(b(b(z0)))))))))), D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(d(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(b(b(b(b(b(b(z0)))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(b(b(d(d(z0))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(b(b(d(b(b(b(b(z0))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(D(d(c(c(d(d(b(b(z0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(d(b(b(c(c(d(d(b(b(z0)))))))))), D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(d(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(b(b(b(b(b(b(z0)))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(b(b(d(d(z0))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(b(b(d(b(b(b(b(z0))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(D(d(c(c(d(d(b(b(z0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(d(b(b(c(c(d(d(b(b(z0)))))))))), D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(d(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(b(b(b(b(b(b(z0)))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(b(b(d(d(z0))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(b(b(d(b(b(b(b(z0))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c14_5, c2_2, c3_2, c4_2, c13_4, c13_3, c14_6, c14_1, c6_1, c14_4


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

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(D(d(c(c(d(d(b(b(z0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(d(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(b(b(b(b(b(b(z0)))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(b(b(d(d(z0))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(b(b(d(b(b(b(b(z0))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(D(d(c(c(d(d(b(b(z0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(d(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(b(b(b(b(b(b(z0)))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(b(b(d(d(z0))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(b(b(d(b(b(b(b(z0))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c14_5, c2_2, c3_2, c4_2, c13_4, c13_3, c14_6, c14_1, c6_1, c14_4


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

(149) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace D(d(c(c(c(c(z0)))))) -> c14(D(d(b(b(d(d(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(z0))))))), B(b(d(d(c(c(z0)))))), B(d(d(c(c(z0))))), D(d(c(c(z0))))) by 
   D(d(c(c(c(c(x0)))))) -> c14(D(d(c(c(d(d(b(b(d(d(x0)))))))))), D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(d(b(b(d(d(c(c(d(d(b(b(z0)))))))))))), D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(b(b(b(b(b(b(z0)))))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(b(b(z0))))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(D(d(c(c(d(d(b(b(z0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(d(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(b(b(b(b(b(b(z0)))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(b(b(d(d(z0))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(b(b(d(b(b(b(b(z0))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(d(c(c(d(d(b(b(d(d(x0)))))))))), D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(d(b(b(d(d(c(c(d(d(b(b(z0)))))))))))), D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(b(b(b(b(b(b(z0)))))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(b(b(z0))))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(D(d(c(c(d(d(b(b(z0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(d(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(b(b(b(b(b(b(z0)))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(b(b(d(d(z0))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(b(b(d(b(b(b(b(z0))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(d(c(c(d(d(b(b(d(d(x0)))))))))), D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(d(b(b(d(d(c(c(d(d(b(b(z0)))))))))))), D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(b(b(b(b(b(b(z0)))))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(b(b(z0))))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c14_5, c2_2, c3_2, c4_2, c13_4, c13_3, c14_6, c14_1, c6_1, c14_4


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

(151) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0))))))) by 
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(a(a(b(b(c(c(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(a(a(c(c(b(z0))))))))) -> c14(D(d(b(a(a(b(b(c(c(z0))))))))), D(b(b(d(d(a(a(c(c(b(z0)))))))))), B(b(d(d(a(a(c(c(b(z0))))))))), B(d(d(a(a(c(c(b(z0)))))))), D(d(a(a(c(c(b(z0))))))))
   D(d(c(c(a(a(c(c(b(b(z0)))))))))) -> c14(D(d(b(b(a(a(b(b(c(c(z0)))))))))), D(b(b(d(d(a(a(c(c(b(b(z0))))))))))), B(b(d(d(a(a(c(c(b(b(z0)))))))))), B(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(a(a(c(c(b(b(b(z0))))))))))) -> c14(D(d(b(b(b(a(a(b(b(c(c(z0))))))))))), D(b(b(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(b(d(d(a(a(c(c(b(b(b(z0))))))))))), B(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(a(a(c(c(d(d(b(b(z0)))))))))))) -> c14(D(d(b(b(b(b(c(c(d(d(b(b(z0)))))))))))), D(b(b(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), B(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(b(b(b(b(c(c(z0)))))))))), D(b(b(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(b(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), B(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(z0)))))))))))) -> c14(D(d(b(b(b(b(a(a(b(b(c(c(z0)))))))))))), D(b(b(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), B(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(b(d(d(b(b(z0))))))))))))) -> c14(D(d(b(b(b(b(b(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(a(a(c(c(b(a(a(c(c(z0))))))))))))) -> c14(D(d(b(b(b(b(b(b(b(c(c(z0))))))))))), D(b(b(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(b(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), B(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(b(z0))))))))))))) -> c14(D(d(b(b(b(b(b(a(a(b(b(c(c(z0))))))))))))), D(b(b(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(D(d(c(c(d(d(b(b(z0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(d(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(b(b(b(b(b(b(z0)))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(b(b(d(d(z0))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(b(b(d(b(b(b(b(z0))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(d(c(c(d(d(b(b(d(d(x0)))))))))), D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(d(b(b(d(d(c(c(d(d(b(b(z0)))))))))))), D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(b(b(b(b(b(b(z0)))))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(b(b(z0))))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(a(a(b(b(c(c(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(a(a(c(c(b(z0))))))))) -> c14(D(d(b(a(a(b(b(c(c(z0))))))))), D(b(b(d(d(a(a(c(c(b(z0)))))))))), B(b(d(d(a(a(c(c(b(z0))))))))), B(d(d(a(a(c(c(b(z0)))))))), D(d(a(a(c(c(b(z0))))))))
   D(d(c(c(a(a(c(c(b(b(z0)))))))))) -> c14(D(d(b(b(a(a(b(b(c(c(z0)))))))))), D(b(b(d(d(a(a(c(c(b(b(z0))))))))))), B(b(d(d(a(a(c(c(b(b(z0)))))))))), B(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(a(a(c(c(b(b(b(z0))))))))))) -> c14(D(d(b(b(b(a(a(b(b(c(c(z0))))))))))), D(b(b(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(b(d(d(a(a(c(c(b(b(b(z0))))))))))), B(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(a(a(c(c(d(d(b(b(z0)))))))))))) -> c14(D(d(b(b(b(b(c(c(d(d(b(b(z0)))))))))))), D(b(b(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), B(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(b(b(b(b(c(c(z0)))))))))), D(b(b(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(b(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), B(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(z0)))))))))))) -> c14(D(d(b(b(b(b(a(a(b(b(c(c(z0)))))))))))), D(b(b(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), B(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(b(d(d(b(b(z0))))))))))))) -> c14(D(d(b(b(b(b(b(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(a(a(c(c(b(a(a(c(c(z0))))))))))))) -> c14(D(d(b(b(b(b(b(b(b(c(c(z0))))))))))), D(b(b(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(b(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), B(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(b(z0))))))))))))) -> c14(D(d(b(b(b(b(b(a(a(b(b(c(c(z0))))))))))))), D(b(b(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(D(d(c(c(d(d(b(b(z0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(d(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(b(b(b(b(b(b(z0)))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(b(b(d(d(z0))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(b(b(d(b(b(b(b(z0))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(d(c(c(d(d(b(b(d(d(x0)))))))))), D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(d(b(b(d(d(c(c(d(d(b(b(z0)))))))))))), D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(b(b(b(b(b(b(z0)))))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(b(b(z0))))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(d(a(a(b(b(c(c(z0)))))))), D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(a(a(c(c(b(z0))))))))) -> c14(D(d(b(a(a(b(b(c(c(z0))))))))), D(b(b(d(d(a(a(c(c(b(z0)))))))))), B(b(d(d(a(a(c(c(b(z0))))))))), B(d(d(a(a(c(c(b(z0)))))))), D(d(a(a(c(c(b(z0))))))))
   D(d(c(c(a(a(c(c(b(b(z0)))))))))) -> c14(D(d(b(b(a(a(b(b(c(c(z0)))))))))), D(b(b(d(d(a(a(c(c(b(b(z0))))))))))), B(b(d(d(a(a(c(c(b(b(z0)))))))))), B(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(a(a(c(c(b(b(b(z0))))))))))) -> c14(D(d(b(b(b(a(a(b(b(c(c(z0))))))))))), D(b(b(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(b(d(d(a(a(c(c(b(b(b(z0))))))))))), B(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(a(a(c(c(d(d(b(b(z0)))))))))))) -> c14(D(d(b(b(b(b(c(c(d(d(b(b(z0)))))))))))), D(b(b(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), B(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(b(b(b(b(c(c(z0)))))))))), D(b(b(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(b(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), B(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(z0)))))))))))) -> c14(D(d(b(b(b(b(a(a(b(b(c(c(z0)))))))))))), D(b(b(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), B(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(b(d(d(b(b(z0))))))))))))) -> c14(D(d(b(b(b(b(b(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(a(a(c(c(b(a(a(c(c(z0))))))))))))) -> c14(D(d(b(b(b(b(b(b(b(c(c(z0))))))))))), D(b(b(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(b(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), B(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(b(z0))))))))))))) -> c14(D(d(b(b(b(b(b(a(a(b(b(c(c(z0))))))))))))), D(b(b(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c2_2, c3_2, c4_2, c13_4, c13_3, c14_6, c14_5, c14_1, c6_1, c14_4


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

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_b(z0)) -> c7(B(b(encArg(z0))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(D(d(c(c(d(d(b(b(z0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(d(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(b(b(b(b(b(b(z0)))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(b(b(d(d(z0))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(b(b(d(b(b(b(b(z0))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(d(c(c(d(d(b(b(d(d(x0)))))))))), D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(d(b(b(d(d(c(c(d(d(b(b(z0)))))))))))), D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(b(b(b(b(b(b(z0)))))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(b(b(z0))))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(a(a(c(c(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(b(b(b(b(c(c(z0)))))))))), D(b(b(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(b(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), B(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(a(a(c(c(b(a(a(c(c(z0))))))))))))) -> c14(D(d(b(b(b(b(b(b(b(c(c(z0))))))))))), D(b(b(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(b(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), B(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(a(a(c(c(b(z0))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(z0)))))))))), B(b(d(d(a(a(c(c(b(z0))))))))), B(d(d(a(a(c(c(b(z0)))))))), D(d(a(a(c(c(b(z0))))))))
   D(d(c(c(a(a(c(c(b(b(z0)))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(z0))))))))))), B(b(d(d(a(a(c(c(b(b(z0)))))))))), B(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(a(a(c(c(b(b(b(z0))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(b(d(d(a(a(c(c(b(b(b(z0))))))))))), B(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(a(a(c(c(d(d(b(b(z0)))))))))))) -> c14(D(b(b(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), B(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), B(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(b(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(D(d(c(c(d(d(b(b(z0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(d(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(b(b(b(b(b(b(z0)))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(b(b(d(d(z0))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(b(b(d(b(b(b(b(z0))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(d(c(c(d(d(b(b(d(d(x0)))))))))), D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(d(b(b(d(d(c(c(d(d(b(b(z0)))))))))))), D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(b(b(b(b(b(b(z0)))))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(b(b(z0))))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(a(a(c(c(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(b(b(b(b(c(c(z0)))))))))), D(b(b(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(b(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), B(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(a(a(c(c(b(a(a(c(c(z0))))))))))))) -> c14(D(d(b(b(b(b(b(b(b(c(c(z0))))))))))), D(b(b(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(b(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), B(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(a(a(c(c(b(z0))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(z0)))))))))), B(b(d(d(a(a(c(c(b(z0))))))))), B(d(d(a(a(c(c(b(z0)))))))), D(d(a(a(c(c(b(z0))))))))
   D(d(c(c(a(a(c(c(b(b(z0)))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(z0))))))))))), B(b(d(d(a(a(c(c(b(b(z0)))))))))), B(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(a(a(c(c(b(b(b(z0))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(b(d(d(a(a(c(c(b(b(b(z0))))))))))), B(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(a(a(c(c(d(d(b(b(z0)))))))))))) -> c14(D(b(b(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), B(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), B(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(b(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c2_2, c3_2, c4_2, c13_4, c13_3, c14_6, c14_5, c14_1, c6_1, c14_4


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

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

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(D(d(c(c(d(d(b(b(z0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(d(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(b(b(b(b(b(b(z0)))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(b(b(d(d(z0))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(b(b(d(b(b(b(b(z0))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(d(c(c(d(d(b(b(d(d(x0)))))))))), D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(d(b(b(d(d(c(c(d(d(b(b(z0)))))))))))), D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(b(b(b(b(b(b(z0)))))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(b(b(z0))))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(a(a(c(c(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(b(b(b(b(c(c(z0)))))))))), D(b(b(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(b(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), B(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(a(a(c(c(b(a(a(c(c(z0))))))))))))) -> c14(D(d(b(b(b(b(b(b(b(c(c(z0))))))))))), D(b(b(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(b(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), B(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(a(a(c(c(b(z0))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(z0)))))))))), B(b(d(d(a(a(c(c(b(z0))))))))), B(d(d(a(a(c(c(b(z0)))))))), D(d(a(a(c(c(b(z0))))))))
   D(d(c(c(a(a(c(c(b(b(z0)))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(z0))))))))))), B(b(d(d(a(a(c(c(b(b(z0)))))))))), B(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(a(a(c(c(b(b(b(z0))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(b(d(d(a(a(c(c(b(b(b(z0))))))))))), B(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(a(a(c(c(d(d(b(b(z0)))))))))))) -> c14(D(b(b(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), B(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), B(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(b(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   ENCODE_B(cons_b(c(z0))) -> c7(B(b(c(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c7(B(b(b(encArg(z0)))))
   ENCODE_B(cons_b(cons_a(z0))) -> c7(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_d(z0))) -> c7(B(b(d(encArg(z0)))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(D(d(c(c(d(d(b(b(z0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(d(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(b(b(b(b(b(b(z0)))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(b(b(d(d(z0))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(b(b(d(b(b(b(b(z0))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(d(c(c(d(d(b(b(d(d(x0)))))))))), D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(d(b(b(d(d(c(c(d(d(b(b(z0)))))))))))), D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(b(b(b(b(b(b(z0)))))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(b(b(z0))))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(a(a(c(c(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(b(b(b(b(c(c(z0)))))))))), D(b(b(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(b(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), B(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(a(a(c(c(b(a(a(c(c(z0))))))))))))) -> c14(D(d(b(b(b(b(b(b(b(c(c(z0))))))))))), D(b(b(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(b(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), B(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(a(a(c(c(b(z0))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(z0)))))))))), B(b(d(d(a(a(c(c(b(z0))))))))), B(d(d(a(a(c(c(b(z0)))))))), D(d(a(a(c(c(b(z0))))))))
   D(d(c(c(a(a(c(c(b(b(z0)))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(z0))))))))))), B(b(d(d(a(a(c(c(b(b(z0)))))))))), B(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(a(a(c(c(b(b(b(z0))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(b(d(d(a(a(c(c(b(b(b(z0))))))))))), B(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(a(a(c(c(d(d(b(b(z0)))))))))))) -> c14(D(b(b(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), B(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), B(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(b(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c2_2, c3_2, c4_2, c13_4, c13_3, c14_6, c14_5, c14_1, c6_1, c14_4


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

(157) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   ENCODE_B(cons_b(c(z0))) -> c7(B(b(c(encArg(z0)))))

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(c(z0)) -> c(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encArg(cons_a(z0)) -> a(encArg(z0))
   encArg(cons_d(z0)) -> d(encArg(z0))
   b(b(d(d(b(b(z0)))))) -> c(c(d(d(b(b(z0))))))
   b(b(a(a(c(c(z0)))))) -> b(b(c(c(z0))))
   b(b(b(b(b(b(z0)))))) -> a(a(b(b(c(c(z0))))))
   a(a(d(d(z0)))) -> d(d(c(c(z0))))
   d(d(c(c(z0)))) -> b(b(d(d(z0))))
   d(d(c(c(z0)))) -> d(d(b(b(d(d(z0))))))
   d(d(a(a(c(c(z0)))))) -> b(b(b(b(z0))))
Tuples:
   ENCARG(c(z0)) -> c1(ENCARG(z0))
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   ENCARG(cons_b(c(z0))) -> c2(ENCARG(c(z0)))
   ENCARG(cons_a(c(z0))) -> c3(ENCARG(c(z0)))
   ENCARG(cons_d(c(z0))) -> c4(ENCARG(c(z0)))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   ENCODE_B(cons_a(z0)) -> c7(B(a(encArg(z0))))
   ENCODE_B(cons_d(z0)) -> c7(B(d(encArg(z0))))
   ENCODE_D(cons_b(z0)) -> c7(D(b(encArg(z0))))
   ENCODE_D(cons_a(z0)) -> c7(D(a(encArg(z0))))
   ENCODE_D(cons_d(z0)) -> c7(D(d(encArg(z0))))
   ENCODE_A(cons_b(z0)) -> c7(A(b(encArg(z0))))
   ENCODE_A(cons_a(z0)) -> c7(A(a(encArg(z0))))
   ENCODE_A(cons_d(z0)) -> c7(A(d(encArg(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_a(z0)))) -> c2(B(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_b(cons_b(cons_d(z0)))) -> c2(B(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_b(cons_b(c(z0)))) -> c2(ENCARG(cons_b(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(cons_a(z0)))) -> c2(B(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_b(cons_a(cons_d(z0)))) -> c2(B(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_b(cons_a(c(z0)))) -> c2(ENCARG(cons_a(c(z0))))
   ENCARG(cons_b(cons_d(cons_b(z0)))) -> c2(B(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_b(cons_d(cons_a(z0)))) -> c2(B(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_b(cons_d(cons_d(z0)))) -> c2(B(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_b(cons_d(c(z0)))) -> c2(ENCARG(cons_d(c(z0))))
   ENCARG(cons_a(cons_b(cons_b(z0)))) -> c3(A(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_a(cons_b(cons_a(z0)))) -> c3(A(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_a(cons_b(cons_d(z0)))) -> c3(A(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_a(cons_b(c(z0)))) -> c3(ENCARG(cons_b(c(z0))))
   ENCARG(cons_a(cons_a(cons_b(z0)))) -> c3(A(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_a(cons_a(cons_a(z0)))) -> c3(A(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_a(cons_a(cons_d(z0)))) -> c3(A(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_a(cons_a(c(z0)))) -> c3(ENCARG(cons_a(c(z0))))
   ENCARG(cons_a(cons_d(cons_b(z0)))) -> c3(A(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_a(cons_d(cons_a(z0)))) -> c3(A(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_a(cons_d(cons_d(z0)))) -> c3(A(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   ENCARG(cons_a(cons_d(c(z0)))) -> c3(ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_b(cons_b(z0)))) -> c4(D(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCARG(cons_d(cons_b(cons_a(z0)))) -> c4(D(b(a(encArg(z0)))), ENCARG(cons_b(cons_a(z0))))
   ENCARG(cons_d(cons_b(cons_d(z0)))) -> c4(D(b(d(encArg(z0)))), ENCARG(cons_b(cons_d(z0))))
   ENCARG(cons_d(cons_b(c(z0)))) -> c4(ENCARG(cons_b(c(z0))))
   ENCARG(cons_d(cons_a(cons_b(z0)))) -> c4(D(a(b(encArg(z0)))), ENCARG(cons_a(cons_b(z0))))
   ENCARG(cons_d(cons_a(cons_a(z0)))) -> c4(D(a(a(encArg(z0)))), ENCARG(cons_a(cons_a(z0))))
   ENCARG(cons_d(cons_a(cons_d(z0)))) -> c4(D(a(d(encArg(z0)))), ENCARG(cons_a(cons_d(z0))))
   ENCARG(cons_d(cons_a(c(z0)))) -> c4(ENCARG(cons_a(c(z0))))
   ENCARG(cons_d(cons_d(c(z0)))) -> c4(D(d(c(encArg(z0)))), ENCARG(cons_d(c(z0))))
   ENCARG(cons_d(cons_d(cons_b(z0)))) -> c4(D(d(b(encArg(z0)))), ENCARG(cons_d(cons_b(z0))))
   ENCARG(cons_d(cons_d(cons_a(z0)))) -> c4(D(d(a(encArg(z0)))), ENCARG(cons_d(cons_a(z0))))
   ENCARG(cons_d(cons_d(cons_d(z0)))) -> c4(D(d(d(encArg(z0)))), ENCARG(cons_d(cons_d(z0))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(D(d(c(c(d(d(b(b(z0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(d(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(b(b(b(b(b(b(z0)))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(b(b(d(d(z0))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(b(b(d(b(b(b(b(z0))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(d(c(c(d(d(b(b(d(d(x0)))))))))), D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(d(b(b(d(d(c(c(d(d(b(b(z0)))))))))))), D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(b(b(b(b(b(b(z0)))))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(b(b(z0))))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(a(a(c(c(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(b(b(b(b(c(c(z0)))))))))), D(b(b(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(b(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), B(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(a(a(c(c(b(a(a(c(c(z0))))))))))))) -> c14(D(d(b(b(b(b(b(b(b(c(c(z0))))))))))), D(b(b(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(b(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), B(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(a(a(c(c(b(z0))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(z0)))))))))), B(b(d(d(a(a(c(c(b(z0))))))))), B(d(d(a(a(c(c(b(z0)))))))), D(d(a(a(c(c(b(z0))))))))
   D(d(c(c(a(a(c(c(b(b(z0)))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(z0))))))))))), B(b(d(d(a(a(c(c(b(b(z0)))))))))), B(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(a(a(c(c(b(b(b(z0))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(b(d(d(a(a(c(c(b(b(b(z0))))))))))), B(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(a(a(c(c(d(d(b(b(z0)))))))))))) -> c14(D(b(b(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), B(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), B(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(b(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   ENCODE_B(cons_b(cons_b(z0))) -> c7(B(b(b(encArg(z0)))))
   ENCODE_B(cons_b(cons_a(z0))) -> c7(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_d(z0))) -> c7(B(b(d(encArg(z0)))))
S tuples:
   B(b(d(d(b(b(z0)))))) -> c9(B(b(z0)), B(z0))
   B(b(a(a(c(c(z0)))))) -> c10
   B(b(b(b(b(b(z0)))))) -> c11
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(b(z0)))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(b(z0))))
   D(d(a(a(c(c(z0)))))) -> c7(B(b(z0)))
   D(d(a(a(c(c(z0)))))) -> c7(B(z0))
   D(d(c(c(x0)))) -> c13(B(b(d(d(x0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(z0))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(D(d(a(a(c(c(z0)))))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(b(b(d(d(z0)))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(b(b(d(d(z0))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(c(c(z0))))))) -> c13(B(b(d(d(d(b(b(d(d(z0))))))))), B(d(d(d(b(b(d(d(z0)))))))), D(d(d(c(c(z0))))), D(d(c(c(z0)))))
   D(d(c(c(d(a(a(c(c(z0))))))))) -> c13(B(b(d(b(b(b(b(z0))))))), B(d(b(b(b(b(z0)))))), D(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(b(b(d(d(z0))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(b(b(d(d(z0)))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(c(c(z0)))))) -> c13(B(b(d(d(b(b(d(d(z0)))))))), B(d(d(b(b(d(d(z0))))))), D(d(c(c(z0)))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c5(B(b(b(b(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(b(b(d(d(z0))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(b(b(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(b(b(b(b(b(b(z0))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(b(b(d(b(b(b(b(z0)))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(c(c(x0))))))) -> c14(D(b(b(d(d(d(c(c(x0)))))))), B(b(d(d(d(c(c(x0))))))), B(d(d(d(c(c(x0)))))), D(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(b(b(z0))))))))) -> c14(D(d(b(b(d(d(d(c(c(d(d(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(b(b(z0)))))))))), B(b(d(d(d(c(c(b(b(z0))))))))), B(d(d(d(c(c(b(b(z0)))))))), D(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(d(d(z0))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(c(c(z0))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(d(c(c(c(c(z0)))))))))), B(b(d(d(d(c(c(c(c(z0))))))))), B(d(d(d(c(c(c(c(z0)))))))), D(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(d(c(c(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(d(b(b(b(b(b(b(z0))))))))))))), D(b(b(d(d(d(c(c(a(a(c(c(z0)))))))))))), B(b(d(d(d(c(c(a(a(c(c(z0))))))))))), B(d(d(d(c(c(a(a(c(c(z0)))))))))), D(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(d(d(b(b(d(d(z0)))))))))))))))), D(b(b(d(d(d(c(c(d(c(c(z0))))))))))), B(b(d(d(d(c(c(d(c(c(z0)))))))))), B(d(d(d(c(c(d(c(c(z0))))))))), D(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(d(c(c(d(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(d(d(d(b(b(d(b(b(b(b(z0)))))))))))))), D(b(b(d(d(d(c(c(d(a(a(c(c(z0))))))))))))), B(b(d(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(d(d(d(c(c(d(a(a(c(c(z0))))))))))), D(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(d(a(a(c(c(x0))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(x0)))))))))), B(b(d(d(d(a(a(c(c(x0))))))))), B(d(d(d(a(a(c(c(x0)))))))), D(d(d(a(a(c(c(x0))))))), D(d(a(a(c(c(x0)))))))
   D(d(c(c(d(a(a(c(c(b(b(z0))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(z0)))))))))))), B(b(d(d(d(a(a(c(c(b(b(z0))))))))))), B(d(d(d(a(a(c(c(b(b(z0)))))))))), D(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(z0))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(d(d(d(a(a(c(c(b(b(b(z0))))))))))), D(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(d(a(a(c(c(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), D(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(a(a(c(c(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))))), B(b(d(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(d(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), D(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), D(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(d(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), D(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))) -> c14(D(b(b(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))))), B(b(d(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(d(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), D(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
   D(d(c(c(b(b(x0)))))) -> c14(D(d(c(c(d(d(b(b(x0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(D(d(c(c(d(d(b(b(z0)))))))))
   D(d(c(c(b(b(z0)))))) -> c6(B(b(d(d(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(b(b(d(d(z0)))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(b(b(d(d(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(b(b(b(b(b(b(z0)))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(b(b(d(d(z0))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(b(b(d(d(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(b(b(d(b(b(b(b(z0))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(x0)))))) -> c14(D(d(c(c(d(d(b(b(d(d(x0)))))))))), D(b(b(d(d(c(c(x0))))))), B(b(d(d(c(c(x0)))))), B(d(d(c(c(x0))))), D(d(c(c(x0)))))
   D(d(c(c(c(c(b(b(z0)))))))) -> c14(D(d(b(b(d(d(c(c(d(d(b(b(z0)))))))))))), D(b(b(d(d(c(c(b(b(z0))))))))), B(b(d(d(c(c(b(b(z0)))))))), B(d(d(c(c(b(b(z0))))))), D(d(c(c(b(b(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(b(b(d(d(z0)))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(c(c(z0)))))))) -> c14(D(d(b(b(d(d(b(b(d(d(b(b(d(d(z0)))))))))))))), D(b(b(d(d(c(c(c(c(z0))))))))), B(b(d(d(c(c(c(c(z0)))))))), B(d(d(c(c(c(c(z0))))))), D(d(c(c(c(c(z0)))))))
   D(d(c(c(c(c(a(a(c(c(z0)))))))))) -> c14(D(d(b(b(d(d(b(b(b(b(b(b(z0)))))))))))), D(b(b(d(d(c(c(a(a(c(c(z0))))))))))), B(b(d(d(c(c(a(a(c(c(z0)))))))))), B(d(d(c(c(a(a(c(c(z0))))))))), D(d(c(c(a(a(c(c(z0)))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(d(d(z0))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(c(c(z0))))))))) -> c14(D(d(b(b(d(d(b(b(d(d(d(b(b(d(d(z0))))))))))))))), D(b(b(d(d(c(c(d(c(c(z0)))))))))), B(b(d(d(c(c(d(c(c(z0))))))))), B(d(d(c(c(d(c(c(z0)))))))), D(d(c(c(d(c(c(z0))))))))
   D(d(c(c(c(c(d(a(a(c(c(z0))))))))))) -> c14(D(d(b(b(d(d(b(b(d(b(b(b(b(z0))))))))))))), D(b(b(d(d(c(c(d(a(a(c(c(z0)))))))))))), B(b(d(d(c(c(d(a(a(c(c(z0))))))))))), B(d(d(c(c(d(a(a(c(c(z0)))))))))), D(d(c(c(d(a(a(c(c(z0))))))))))
   D(d(c(c(a(a(c(c(a(a(c(c(z0)))))))))))) -> c14(D(d(b(b(b(b(b(b(c(c(z0)))))))))), D(b(b(d(d(a(a(c(c(a(a(c(c(z0))))))))))))), B(b(d(d(a(a(c(c(a(a(c(c(z0)))))))))))), B(d(d(a(a(c(c(a(a(c(c(z0))))))))))), D(d(a(a(c(c(a(a(c(c(z0)))))))))))
   D(d(c(c(a(a(c(c(b(a(a(c(c(z0))))))))))))) -> c14(D(d(b(b(b(b(b(b(b(c(c(z0))))))))))), D(b(b(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))))), B(b(d(d(a(a(c(c(b(a(a(c(c(z0))))))))))))), B(d(d(a(a(c(c(b(a(a(c(c(z0)))))))))))), D(d(a(a(c(c(b(a(a(c(c(z0))))))))))))
   D(d(c(c(a(a(c(c(z0)))))))) -> c14(D(b(b(d(d(a(a(c(c(z0))))))))), B(b(d(d(a(a(c(c(z0)))))))), B(d(d(a(a(c(c(z0))))))), D(d(a(a(c(c(z0)))))))
   D(d(c(c(a(a(c(c(b(z0))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(z0)))))))))), B(b(d(d(a(a(c(c(b(z0))))))))), B(d(d(a(a(c(c(b(z0)))))))), D(d(a(a(c(c(b(z0))))))))
   D(d(c(c(a(a(c(c(b(b(z0)))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(z0))))))))))), B(b(d(d(a(a(c(c(b(b(z0)))))))))), B(d(d(a(a(c(c(b(b(z0))))))))), D(d(a(a(c(c(b(b(z0)))))))))
   D(d(c(c(a(a(c(c(b(b(b(z0))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(z0)))))))))))), B(b(d(d(a(a(c(c(b(b(b(z0))))))))))), B(d(d(a(a(c(c(b(b(b(z0)))))))))), D(d(a(a(c(c(b(b(b(z0))))))))))
   D(d(c(c(a(a(c(c(d(d(b(b(z0)))))))))))) -> c14(D(b(b(d(d(a(a(c(c(d(d(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(d(d(b(b(z0)))))))))))), B(d(d(a(a(c(c(d(d(b(b(z0))))))))))), D(d(a(a(c(c(d(d(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(z0)))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(b(z0))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(z0)))))))))))), B(d(d(a(a(c(c(b(b(b(b(z0))))))))))), D(d(a(a(c(c(b(b(b(b(z0)))))))))))
   D(d(c(c(a(a(c(c(b(d(d(b(b(z0))))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(d(d(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(d(d(b(b(z0)))))))))))), D(d(a(a(c(c(b(d(d(b(b(z0))))))))))))
   D(d(c(c(a(a(c(c(b(b(b(b(b(z0))))))))))))) -> c14(D(b(b(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))))), B(b(d(d(a(a(c(c(b(b(b(b(b(z0))))))))))))), B(d(d(a(a(c(c(b(b(b(b(b(z0)))))))))))), D(d(a(a(c(c(b(b(b(b(b(z0))))))))))))
K tuples:
   A(a(d(d(z0)))) -> c12(D(d(c(c(z0)))))
Defined Rule Symbols:   encArg_1, b_1, a_1, d_1

Defined Pair Symbols:   ENCARG_1, B_1, A_1, D_1, ENCODE_B_1, ENCODE_D_1, ENCODE_A_1

Compound Symbols:   c1_1, c9_2, c10, c11, c12_1, c7_1, c2_1, c3_1, c4_1, c13_1, c5_1, c2_2, c3_2, c4_2, c13_4, c13_3, c14_6, c14_5, c14_1, c6_1, c14_4