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


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (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), 35 ms]
(4) CpxRelTRS
(5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(6) TRS for Loop Detection
(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxRelTRS
    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) typed CpxTrs
    (11) OrderProof [LOWER BOUND(ID), 0 ms]
    (12) typed CpxTrs
    (13) RewriteLemmaProof [LOWER BOUND(ID), 470 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), 3 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) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (40) CdtProblem
    (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (42) CdtProblem
    (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (44) CdtProblem
    (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 19 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) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) CdtProblem
    (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (64) CdtProblem
    (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (66) CdtProblem
    (67) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (70) CdtProblem
    (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
    (73) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (74) CdtProblem
    (75) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (76) CdtProblem
    (77) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (78) CdtProblem
    (79) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (80) CdtProblem
    (81) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 27 ms]
    (82) CdtProblem
    (83) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (84) CdtProblem
    (85) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (86) CdtProblem
    (87) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 3 ms]
    (88) CdtProblem
    (89) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (90) CdtProblem
    (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (92) CdtProblem
    (93) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (94) CdtProblem
    (95) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (96) CdtProblem
    (97) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (98) CdtProblem
    (99) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (100) CdtProblem
    (101) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (102) CdtProblem
    (103) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 38 ms]
    (104) CdtProblem
    (105) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (106) CdtProblem
    (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (108) CdtProblem
    (109) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (110) CdtProblem
    (111) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (112) CdtProblem
    (113) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 40 ms]
    (114) CdtProblem
    (115) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 50 ms]
    (116) CdtProblem
    (117) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 24 ms]
    (118) CdtProblem
    (119) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 63 ms]
    (120) CdtProblem
    (121) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (122) CdtProblem
    (123) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 73 ms]
    (124) CdtProblem
    (125) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
    (126) CdtProblem
    (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (128) CdtProblem
    (129) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 49 ms]
    (130) CdtProblem
    (131) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 13 ms]
    (132) CdtProblem
    (133) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 28 ms]
    (134) CdtProblem
    (135) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 98 ms]
    (136) CdtProblem
    (137) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 60 ms]
    (138) CdtProblem
    (139) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 39 ms]
    (140) CdtProblem
    (141) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 153 ms]
    (142) CdtProblem
    (143) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 110 ms]
    (144) CdtProblem
    (145) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 121 ms]
    (146) 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(a(b(x1))) -> b(a(a(a(b(x1)))))
   b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1))))))))))))
   b(a(a(a(b(a(a(a(b(x1))))))))) -> b(x1)
   b(a(a(a(b(b(b(x1))))))) -> b(b(b(a(a(a(b(x1)))))))
   b(a(a(b(b(x1))))) -> b(x1)
   b(b(a(a(b(x1))))) -> b(x1)
   b(a(a(a(b(a(b(x1))))))) -> b(x1)
   b(a(b(a(a(a(b(x1))))))) -> 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(a(x_1)) -> a(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encode_b(x_1) -> b(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(a(b(x1))) -> b(a(a(a(b(x1)))))
   b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1))))))))))))
   b(a(a(a(b(a(a(a(b(x1))))))))) -> b(x1)
   b(a(a(a(b(b(b(x1))))))) -> b(b(b(a(a(a(b(x1)))))))
   b(a(a(b(b(x1))))) -> b(x1)
   b(b(a(a(b(x1))))) -> b(x1)
   b(a(a(a(b(a(b(x1))))))) -> b(x1)
   b(a(b(a(a(a(b(x1))))))) -> b(x1)

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

   encArg(a(x_1)) -> a(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encode_b(x_1) -> b(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(a(b(x1))) -> b(a(a(a(b(x1)))))
   b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1))))))))))))
   b(a(a(a(b(a(a(a(b(x1))))))))) -> b(x1)
   b(a(a(a(b(b(b(x1))))))) -> b(b(b(a(a(a(b(x1)))))))
   b(a(a(b(b(x1))))) -> b(x1)
   b(b(a(a(b(x1))))) -> b(x1)
   b(a(a(a(b(a(b(x1))))))) -> b(x1)
   b(a(b(a(a(a(b(x1))))))) -> b(x1)

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

   encArg(a(x_1)) -> a(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encode_b(x_1) -> b(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(a(b(x1))) -> b(a(a(a(b(x1)))))
   b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1))))))))))))
   b(a(a(a(b(a(a(a(b(x1))))))))) -> b(x1)
   b(a(a(a(b(b(b(x1))))))) -> b(b(b(a(a(a(b(x1)))))))
   b(a(a(b(b(x1))))) -> b(x1)
   b(b(a(a(b(x1))))) -> b(x1)
   b(a(a(a(b(a(b(x1))))))) -> b(x1)
   b(a(b(a(a(a(b(x1))))))) -> b(x1)

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

   encArg(a(x_1)) -> a(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encode_b(x_1) -> b(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(a(b(x1))) -> b(a(a(a(b(x1)))))
   b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1))))))))))))
   b(a(a(a(b(a(a(a(b(x1))))))))) -> b(x1)
   b(a(a(a(b(b(b(x1))))))) -> b(b(b(a(a(a(b(x1)))))))
   b(a(a(b(b(x1))))) -> b(x1)
   b(b(a(a(b(x1))))) -> b(x1)
   b(a(a(a(b(a(b(x1))))))) -> b(x1)
   b(a(b(a(a(a(b(x1))))))) -> b(x1)

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

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

Types:
b :: a:cons_b -> a:cons_b
a :: a:cons_b -> a:cons_b
encArg :: a:cons_b -> a:cons_b
cons_b :: a:cons_b -> a:cons_b
encode_b :: a:cons_b -> a:cons_b
encode_a :: a:cons_b -> a:cons_b
hole_a:cons_b1_0 :: a:cons_b
gen_a:cons_b2_0 :: Nat -> a:cons_b

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

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

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

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

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

Types:
b :: a:cons_b -> a:cons_b
a :: a:cons_b -> a:cons_b
encArg :: a:cons_b -> a:cons_b
cons_b :: a:cons_b -> a:cons_b
encode_b :: a:cons_b -> a:cons_b
encode_a :: a:cons_b -> a:cons_b
hole_a:cons_b1_0 :: a:cons_b
gen_a:cons_b2_0 :: Nat -> a:cons_b


Generator Equations:
gen_a:cons_b2_0(0) <=> hole_a:cons_b1_0
gen_a:cons_b2_0(+(x, 1)) <=> a(gen_a:cons_b2_0(x))


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

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

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

(13) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_a:cons_b2_0(+(1, n615_0))) -> *3_0, rt in Omega(0)

Induction Base:
encArg(gen_a:cons_b2_0(+(1, 0)))

Induction Step:
encArg(gen_a:cons_b2_0(+(1, +(n615_0, 1)))) ->_R^Omega(0)
a(encArg(gen_a:cons_b2_0(+(1, n615_0)))) ->_IH
a(*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(a(b(x1))) -> b(a(a(a(b(x1)))))
   b(a(a(a(b(a(a(b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1))))))))))))
   b(a(a(a(b(a(a(a(b(x1))))))))) -> b(x1)
   b(a(a(a(b(b(b(x1))))))) -> b(b(b(a(a(a(b(x1)))))))
   b(a(a(b(b(x1))))) -> b(x1)
   b(b(a(a(b(x1))))) -> b(x1)
   b(a(a(a(b(a(b(x1))))))) -> b(x1)
   b(a(b(a(a(a(b(x1))))))) -> b(x1)
   encArg(a(x_1)) -> a(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encode_b(x_1) -> b(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:

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

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

   encArg(a(x_1)) -> a(encArg(x_1))
   encArg(cons_b(x_1)) -> b(encArg(x_1))
   encode_b(x_1) -> b(encArg(x_1))
   encode_a(x_1) -> a(encArg(x_1))
   b(x0) -> c_b(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:

   b(c_b(a(a(c_b(x1))))) -> b(x1) [1]
   b(a(a(c_b(c_b(x1))))) -> b(x1) [1]
   b(a(a(a(c_b(a(a(c_b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1)))))))))))) [1]
   b(a(a(a(c_b(a(c_b(x1))))))) -> b(x1) [1]
   b(a(c_b(x1))) -> b(a(a(a(b(x1))))) [1]
   b(a(a(a(c_b(a(a(a(c_b(x1))))))))) -> b(x1) [1]
   b(a(c_b(a(a(a(c_b(x1))))))) -> b(x1) [1]
   b(a(a(a(c_b(c_b(c_b(x1))))))) -> b(b(b(a(a(a(b(x1))))))) [1]
   encArg(a(x_1)) -> a(encArg(x_1)) [0]
   encArg(cons_b(x_1)) -> b(encArg(x_1)) [0]
   encode_b(x_1) -> b(encArg(x_1)) [0]
   encode_a(x_1) -> a(encArg(x_1)) [0]
   b(x0) -> c_b(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:

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

The TRS has the following type information:
b :: c_b:a:cons_b -> c_b:a:cons_b
c_b :: c_b:a:cons_b -> c_b:a:cons_b
a :: c_b:a:cons_b -> c_b:a:cons_b
encArg :: c_b:a:cons_b -> c_b:a:cons_b
cons_b :: c_b:a:cons_b -> c_b:a:cons_b
encode_b :: c_b:a:cons_b -> c_b:a:cons_b
encode_a :: c_b:a:cons_b -> c_b:a:cons_b

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_a_1
   b_1

Due to the following rules being added:

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

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

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

   b(c_b(a(a(c_b(x1))))) -> b(x1) [1]
   b(a(a(c_b(c_b(x1))))) -> b(x1) [1]
   b(a(a(a(c_b(a(a(c_b(c_b(a(a(c_b(x1')))))))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1')))))))))))) [2]
   b(a(a(a(c_b(a(a(c_b(a(a(c_b(c_b(x1'')))))))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1'')))))))))))) [2]
   b(a(a(a(c_b(a(a(c_b(a(a(a(c_b(a(a(c_b(x11))))))))))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(a(a(b(a(a(b(a(a(a(b(b(x11))))))))))))))))))))))) [2]
   b(a(a(a(c_b(a(a(c_b(a(a(a(c_b(a(c_b(x12)))))))))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x12)))))))))))) [2]
   b(a(a(a(c_b(a(a(c_b(a(c_b(x13)))))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(a(a(a(b(x13)))))))))))))))) [2]
   b(a(a(a(c_b(a(a(c_b(a(a(a(c_b(a(a(a(c_b(x14)))))))))))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x14)))))))))))) [2]
   b(a(a(a(c_b(a(a(c_b(a(c_b(a(a(a(c_b(x15)))))))))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x15)))))))))))) [2]
   b(a(a(a(c_b(a(a(c_b(a(a(a(c_b(c_b(c_b(x16)))))))))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(b(b(a(a(a(b(x16)))))))))))))))))) [2]
   b(a(a(a(c_b(a(a(c_b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(c_b(x1)))))))))))) [1]
   b(a(a(a(c_b(a(a(c_b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(const))))))))))) [1]
   b(a(a(a(c_b(a(c_b(x1))))))) -> b(x1) [1]
   b(a(c_b(c_b(a(a(c_b(x17))))))) -> b(a(a(a(b(x17))))) [2]
   b(a(c_b(a(a(c_b(c_b(x18))))))) -> b(a(a(a(b(x18))))) [2]
   b(a(c_b(a(a(a(c_b(a(a(c_b(x19)))))))))) -> b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(b(x19)))))))))))))))) [2]
   b(a(c_b(a(a(a(c_b(a(c_b(x110))))))))) -> b(a(a(a(b(x110))))) [2]
   b(a(c_b(a(c_b(x111))))) -> b(a(a(a(b(a(a(a(b(x111))))))))) [2]
   b(a(c_b(a(a(a(c_b(a(a(a(c_b(x112))))))))))) -> b(a(a(a(b(x112))))) [2]
   b(a(c_b(a(c_b(a(a(a(c_b(x113))))))))) -> b(a(a(a(b(x113))))) [2]
   b(a(c_b(a(a(a(c_b(c_b(c_b(x114))))))))) -> b(a(a(a(b(b(b(a(a(a(b(x114))))))))))) [2]
   b(a(c_b(x1))) -> b(a(a(a(c_b(x1))))) [1]
   b(a(c_b(x1))) -> b(a(a(a(const)))) [1]
   b(a(a(a(c_b(a(a(a(c_b(x1))))))))) -> b(x1) [1]
   b(a(c_b(a(a(a(c_b(x1))))))) -> b(x1) [1]
   b(a(a(a(c_b(c_b(c_b(c_b(a(a(c_b(x115))))))))))) -> b(b(b(a(a(a(b(x115))))))) [2]
   b(a(a(a(c_b(c_b(c_b(a(a(c_b(c_b(x116))))))))))) -> b(b(b(a(a(a(b(x116))))))) [2]
   b(a(a(a(c_b(c_b(c_b(a(a(a(c_b(a(a(c_b(x117)))))))))))))) -> b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(b(x117)))))))))))))))))) [2]
   b(a(a(a(c_b(c_b(c_b(a(a(a(c_b(a(c_b(x118))))))))))))) -> b(b(b(a(a(a(b(x118))))))) [2]
   b(a(a(a(c_b(c_b(c_b(a(c_b(x119))))))))) -> b(b(b(a(a(a(b(a(a(a(b(x119))))))))))) [2]
   b(a(a(a(c_b(c_b(c_b(a(a(a(c_b(a(a(a(c_b(x120))))))))))))))) -> b(b(b(a(a(a(b(x120))))))) [2]
   b(a(a(a(c_b(c_b(c_b(a(c_b(a(a(a(c_b(x121))))))))))))) -> b(b(b(a(a(a(b(x121))))))) [2]
   b(a(a(a(c_b(c_b(c_b(a(a(a(c_b(c_b(c_b(x122))))))))))))) -> b(b(b(a(a(a(b(b(b(a(a(a(b(x122))))))))))))) [2]
   b(a(a(a(c_b(c_b(c_b(x1))))))) -> b(b(b(a(a(a(c_b(x1))))))) [1]
   b(a(a(a(c_b(c_b(c_b(x1))))))) -> b(b(b(a(a(a(const)))))) [1]
   encArg(a(x_1)) -> a(encArg(x_1)) [0]
   encArg(cons_b(a(x_1'))) -> b(a(encArg(x_1'))) [0]
   encArg(cons_b(cons_b(x_1''))) -> b(b(encArg(x_1''))) [0]
   encArg(cons_b(x_1)) -> b(const) [0]
   encode_b(a(x_11)) -> b(a(encArg(x_11))) [0]
   encode_b(cons_b(x_12)) -> b(b(encArg(x_12))) [0]
   encode_b(x_1) -> b(const) [0]
   encode_a(x_1) -> a(encArg(x_1)) [0]
   b(x0) -> c_b(x0) [0]
   encArg(v0) -> const [0]
   encode_b(v0) -> const [0]
   encode_a(v0) -> const [0]
   b(v0) -> const [0]

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

   b(z) -{ 1 }-> b(x1) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   b(z) -{ 1 }-> b(x1) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x1)))))
   b(z) -{ 1 }-> b(x1) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))
   b(z) -{ 2 }-> b(b(b(1 + (1 + (1 + b(x115)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x115))))))))), x115 >= 0
   b(z) -{ 2 }-> b(b(b(1 + (1 + (1 + b(x116)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x116))))))))), x116 >= 0
   b(z) -{ 2 }-> b(b(b(1 + (1 + (1 + b(x118)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x118))))))))))), x118 >= 0
   b(z) -{ 2 }-> b(b(b(1 + (1 + (1 + b(x120)))))) :|: x120 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x120)))))))))))))
   b(z) -{ 2 }-> b(b(b(1 + (1 + (1 + b(x121)))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x121))))))))))), x121 >= 0
   b(z) -{ 2 }-> b(b(b(1 + (1 + (1 + b(b(b(1 + (1 + (1 + b(x122))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x122))))))))))), x122 >= 0
   b(z) -{ 2 }-> b(b(b(1 + (1 + (1 + b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(x117)))))))))))))) :|: x117 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x117))))))))))))
   b(z) -{ 2 }-> b(b(b(1 + (1 + (1 + b(1 + (1 + (1 + b(x119))))))))) :|: x119 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x119)))))))
   b(z) -{ 1 }-> b(b(b(1 + (1 + (1 + 0))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x1)))))
   b(z) -{ 1 }-> b(b(b(1 + (1 + (1 + (1 + x1)))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x1)))))
   b(z) -{ 2 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(x1'))))))))) :|: x1' >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1'))))))))))
   b(z) -{ 2 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(x1''))))))))) :|: x1'' >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1''))))))))))
   b(z) -{ 2 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(x12))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x12)))))))))))), x12 >= 0
   b(z) -{ 2 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(x14))))))))) :|: x14 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x14))))))))))))))
   b(z) -{ 2 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(x15))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x15)))))))))))), x15 >= 0
   b(z) -{ 2 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(b(b(1 + (1 + (1 + b(x16)))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x16)))))))))))), x16 >= 0
   b(z) -{ 2 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(x11))))))))))))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x11))))))))))))), x11 >= 0
   b(z) -{ 2 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(1 + (1 + (1 + b(x13)))))))))))) :|: x13 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x13))))))))
   b(z) -{ 1 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(0)))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))
   b(z) -{ 1 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + x1)))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))
   b(z) -{ 2 }-> b(1 + (1 + (1 + b(x110)))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x110))))))), x110 >= 0
   b(z) -{ 2 }-> b(1 + (1 + (1 + b(x112)))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x112))))))))), x112 >= 0
   b(z) -{ 2 }-> b(1 + (1 + (1 + b(x113)))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x113))))))), x113 >= 0
   b(z) -{ 2 }-> b(1 + (1 + (1 + b(x17)))) :|: x17 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x17)))))
   b(z) -{ 2 }-> b(1 + (1 + (1 + b(x18)))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x18))))), x18 >= 0
   b(z) -{ 2 }-> b(1 + (1 + (1 + b(b(b(1 + (1 + (1 + b(x114))))))))) :|: x114 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x114)))))))
   b(z) -{ 2 }-> b(1 + (1 + (1 + b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(x19)))))))))))) :|: x19 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x19))))))))
   b(z) -{ 2 }-> b(1 + (1 + (1 + b(1 + (1 + (1 + b(x111))))))) :|: z = 1 + (1 + (1 + (1 + x111))), x111 >= 0
   b(z) -{ 1 }-> b(1 + (1 + (1 + 0))) :|: z = 1 + (1 + x1), x1 >= 0
   b(z) -{ 1 }-> b(1 + (1 + (1 + (1 + x1)))) :|: z = 1 + (1 + x1), x1 >= 0
   b(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   b(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   encArg(z) -{ 0 }-> b(b(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0
   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 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 1 + encArg(x_1) :|: z = 1 + x_1, x_1 >= 0
   encode_a(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_a(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   encode_b(z) -{ 0 }-> b(b(encArg(x_12))) :|: z = 1 + x_12, x_12 >= 0
   encode_b(z) -{ 0 }-> b(0) :|: x_1 >= 0, z = x_1
   encode_b(z) -{ 0 }-> b(1 + encArg(x_11)) :|: x_11 >= 0, z = 1 + x_11
   encode_b(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:

   b(z) -{ 2 }-> b(b(b(1 + (1 + (1 + b(b(b(1 + (1 + (1 + b(z - 12))))))))))) :|: z - 12 >= 0
   b(z) -{ 2 }-> b(b(b(1 + (1 + (1 + b(z - 14)))))) :|: z - 14 >= 0
   b(z) -{ 2 }-> b(b(b(1 + (1 + (1 + b(z - 12)))))) :|: z - 12 >= 0
   b(z) -{ 2 }-> b(b(b(1 + (1 + (1 + b(z - 10)))))) :|: z - 10 >= 0
   b(z) -{ 2 }-> b(b(b(1 + (1 + (1 + b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(z - 13)))))))))))))) :|: z - 13 >= 0
   b(z) -{ 2 }-> b(b(b(1 + (1 + (1 + b(1 + (1 + (1 + b(z - 8))))))))) :|: z - 8 >= 0
   b(z) -{ 1 }-> b(b(b(1 + (1 + (1 + 0))))) :|: z - 6 >= 0
   b(z) -{ 1 }-> b(b(b(1 + (1 + (1 + (1 + (z - 6))))))) :|: z - 6 >= 0
   b(z) -{ 1 }-> b(z - 8) :|: z - 8 >= 0
   b(z) -{ 1 }-> b(z - 6) :|: z - 6 >= 0
   b(z) -{ 1 }-> b(z - 4) :|: z - 4 >= 0
   b(z) -{ 2 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(b(b(1 + (1 + (1 + b(z - 13)))))))))))))) :|: z - 13 >= 0
   b(z) -{ 2 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(z - 15))))))))) :|: z - 15 >= 0
   b(z) -{ 2 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(z - 13))))))))) :|: z - 13 >= 0
   b(z) -{ 2 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(z - 11))))))))) :|: z - 11 >= 0
   b(z) -{ 2 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(z - 14))))))))))))))))) :|: z - 14 >= 0
   b(z) -{ 2 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(1 + (1 + (1 + b(z - 9)))))))))))) :|: z - 9 >= 0
   b(z) -{ 1 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(0)))))))) :|: z - 7 >= 0
   b(z) -{ 1 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(1 + (z - 7))))))))) :|: z - 7 >= 0
   b(z) -{ 2 }-> b(1 + (1 + (1 + b(b(b(1 + (1 + (1 + b(z - 8))))))))) :|: z - 8 >= 0
   b(z) -{ 2 }-> b(1 + (1 + (1 + b(z - 8)))) :|: z - 8 >= 0
   b(z) -{ 2 }-> b(1 + (1 + (1 + b(z - 6)))) :|: z - 6 >= 0
   b(z) -{ 2 }-> b(1 + (1 + (1 + b(z - 10)))) :|: z - 10 >= 0
   b(z) -{ 2 }-> b(1 + (1 + (1 + b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(z - 9)))))))))))) :|: z - 9 >= 0
   b(z) -{ 2 }-> b(1 + (1 + (1 + b(1 + (1 + (1 + b(z - 4))))))) :|: z - 4 >= 0
   b(z) -{ 1 }-> b(1 + (1 + (1 + 0))) :|: z - 2 >= 0
   b(z) -{ 1 }-> b(1 + (1 + (1 + (1 + (z - 2))))) :|: z - 2 >= 0
   b(z) -{ 0 }-> 0 :|: z >= 0
   b(z) -{ 0 }-> 1 + z :|: z >= 0
   encArg(z) -{ 0 }-> b(b(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 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 1 + encArg(z - 1) :|: z - 1 >= 0
   encode_a(z) -{ 0 }-> 0 :|: z >= 0
   encode_a(z) -{ 0 }-> 1 + encArg(z) :|: z >= 0
   encode_b(z) -{ 0 }-> b(b(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


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

(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_a(v0) -> null_encode_a [0]
   b(v0) -> null_b [0]

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

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

(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:

   b(c_b(a(a(c_b(x1))))) -> b(x1) [1]
   b(a(a(c_b(c_b(x1))))) -> b(x1) [1]
   b(a(a(a(c_b(a(a(c_b(x1)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(x1)))))))))))) [1]
   b(a(a(a(c_b(a(c_b(x1))))))) -> b(x1) [1]
   b(a(c_b(x1))) -> b(a(a(a(b(x1))))) [1]
   b(a(a(a(c_b(a(a(a(c_b(x1))))))))) -> b(x1) [1]
   b(a(c_b(a(a(a(c_b(x1))))))) -> b(x1) [1]
   b(a(a(a(c_b(c_b(c_b(x1))))))) -> b(b(b(a(a(a(b(x1))))))) [1]
   encArg(a(x_1)) -> a(encArg(x_1)) [0]
   encArg(cons_b(x_1)) -> b(encArg(x_1)) [0]
   encode_b(x_1) -> b(encArg(x_1)) [0]
   encode_a(x_1) -> a(encArg(x_1)) [0]
   b(x0) -> c_b(x0) [0]
   encArg(v0) -> null_encArg [0]
   encode_b(v0) -> null_encode_b [0]
   encode_a(v0) -> null_encode_a [0]
   b(v0) -> null_b [0]

The TRS has the following type information:
b :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b -> c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b
c_b :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b -> c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b
a :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b -> c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b
encArg :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b -> c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b
cons_b :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b -> c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b
encode_b :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b -> c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b
encode_a :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b -> c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b
null_encArg :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b
null_encode_b :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b
null_encode_a :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b
null_b :: c_b:a:cons_b:null_encArg:null_encode_b:null_encode_a:null_b

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_a => 0
   null_b => 0

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

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

   b(z) -{ 1 }-> b(x1) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + x1)))
   b(z) -{ 1 }-> b(x1) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x1)))))
   b(z) -{ 1 }-> b(x1) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + (1 + x1)))))))
   b(z) -{ 1 }-> b(b(b(1 + (1 + (1 + b(x1)))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x1)))))
   b(z) -{ 1 }-> b(1 + (1 + b(1 + (1 + b(1 + (1 + (1 + b(b(x1))))))))) :|: x1 >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + (1 + x1))))))
   b(z) -{ 1 }-> b(1 + (1 + (1 + b(x1)))) :|: z = 1 + (1 + x1), x1 >= 0
   b(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   b(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   encArg(z) -{ 0 }-> b(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 }-> 0 :|: v0 >= 0, z = v0
   encode_a(z) -{ 0 }-> 1 + encArg(x_1) :|: x_1 >= 0, z = x_1
   encode_b(z) -{ 0 }-> b(encArg(x_1)) :|: x_1 >= 0, z = x_1
   encode_b(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(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(a(a(b(a(b(z0))))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   ENCARG(cons_b(z0)) -> c1(B(encArg(z0)), ENCARG(z0))
   ENCODE_B(z0) -> c2(B(encArg(z0)), ENCARG(z0))
   ENCODE_A(z0) -> c3(ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(b(z0)))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))), B(a(a(b(a(a(a(b(b(z0))))))))), B(a(a(a(b(b(z0)))))), B(b(z0)), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(a(b(b(b(z0))))))) -> c7(B(b(b(a(a(a(b(z0))))))), B(b(a(a(a(b(z0)))))), B(a(a(a(b(z0))))), B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(a(a(b(a(b(z0))))))) -> c10(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(b(z0)))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))), B(a(a(b(a(a(a(b(b(z0))))))))), B(a(a(a(b(b(z0)))))), B(b(z0)), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(a(b(b(b(z0))))))) -> c7(B(b(b(a(a(a(b(z0))))))), B(b(a(a(a(b(z0)))))), B(a(a(a(b(z0))))), B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(a(a(b(a(b(z0))))))) -> c10(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
K tuples:none
Defined Rule Symbols:   b_1, encArg_1, encode_b_1, encode_a_1

Defined Pair Symbols:   ENCARG_1, ENCODE_B_1, ENCODE_A_1, B_1

Compound Symbols:   c_1, c1_2, c2_2, c3_1, c4_2, c5_5, c6_1, c7_4, c8_1, c9_1, c10_1, c11_1


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

(37) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 2 leading nodes:
   ENCODE_A(z0) -> c3(ENCARG(z0))
   B(a(a(a(b(a(b(z0))))))) -> c10(B(z0))

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(a(a(b(a(b(z0))))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   ENCARG(cons_b(z0)) -> c1(B(encArg(z0)), ENCARG(z0))
   ENCODE_B(z0) -> c2(B(encArg(z0)), ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(b(z0)))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))), B(a(a(b(a(a(a(b(b(z0))))))))), B(a(a(a(b(b(z0)))))), B(b(z0)), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(a(b(b(b(z0))))))) -> c7(B(b(b(a(a(a(b(z0))))))), B(b(a(a(a(b(z0)))))), B(a(a(a(b(z0))))), B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(b(z0)))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))), B(a(a(b(a(a(a(b(b(z0))))))))), B(a(a(a(b(b(z0)))))), B(b(z0)), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(a(b(b(b(z0))))))) -> c7(B(b(b(a(a(a(b(z0))))))), B(b(a(a(a(b(z0)))))), B(a(a(a(b(z0))))), B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
K tuples:none
Defined Rule Symbols:   b_1, encArg_1, encode_b_1, encode_a_1

Defined Pair Symbols:   ENCARG_1, ENCODE_B_1, B_1

Compound Symbols:   c_1, c1_2, c2_2, c4_2, c5_5, c6_1, c7_4, c8_1, c9_1, c11_1


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

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(a(a(b(a(b(z0))))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   ENCARG(cons_b(z0)) -> c1(B(encArg(z0)), ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(b(z0)))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))), B(a(a(b(a(a(a(b(b(z0))))))))), B(a(a(a(b(b(z0)))))), B(b(z0)), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(a(b(b(b(z0))))))) -> c7(B(b(b(a(a(a(b(z0))))))), B(b(a(a(a(b(z0)))))), B(a(a(a(b(z0))))), B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   ENCODE_B(z0) -> c3(B(encArg(z0)))
   ENCODE_B(z0) -> c3(ENCARG(z0))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(b(z0)))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))), B(a(a(b(a(a(a(b(b(z0))))))))), B(a(a(a(b(b(z0)))))), B(b(z0)), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(a(b(b(b(z0))))))) -> c7(B(b(b(a(a(a(b(z0))))))), B(b(a(a(a(b(z0)))))), B(a(a(a(b(z0))))), B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
K tuples:none
Defined Rule Symbols:   b_1, encArg_1, encode_b_1, encode_a_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c1_2, c4_2, c5_5, c6_1, c7_4, c8_1, c9_1, c11_1, c3_1


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

(41) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 1 leading nodes:
   ENCODE_B(z0) -> c3(ENCARG(z0))

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   encode_b(z0) -> b(encArg(z0))
   encode_a(z0) -> a(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(a(a(b(a(b(z0))))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   ENCARG(cons_b(z0)) -> c1(B(encArg(z0)), ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(b(z0)))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))), B(a(a(b(a(a(a(b(b(z0))))))))), B(a(a(a(b(b(z0)))))), B(b(z0)), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(a(b(b(b(z0))))))) -> c7(B(b(b(a(a(a(b(z0))))))), B(b(a(a(a(b(z0)))))), B(a(a(a(b(z0))))), B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   ENCODE_B(z0) -> c3(B(encArg(z0)))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(b(z0)))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))), B(a(a(b(a(a(a(b(b(z0))))))))), B(a(a(a(b(b(z0)))))), B(b(z0)), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(a(b(b(b(z0))))))) -> c7(B(b(b(a(a(a(b(z0))))))), B(b(a(a(a(b(z0)))))), B(a(a(a(b(z0))))), B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
K tuples:none
Defined Rule Symbols:   b_1, encArg_1, encode_b_1, encode_a_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c1_2, c4_2, c5_5, c6_1, c7_4, c8_1, c9_1, c11_1, c3_1


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

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

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   ENCARG(cons_b(z0)) -> c1(B(encArg(z0)), ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(b(z0)))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))), B(a(a(b(a(a(a(b(b(z0))))))))), B(a(a(a(b(b(z0)))))), B(b(z0)), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(a(b(b(b(z0))))))) -> c7(B(b(b(a(a(a(b(z0))))))), B(b(a(a(a(b(z0)))))), B(a(a(a(b(z0))))), B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   ENCODE_B(z0) -> c3(B(encArg(z0)))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(b(z0)))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))), B(a(a(b(a(a(a(b(b(z0))))))))), B(a(a(a(b(b(z0)))))), B(b(z0)), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(a(b(b(b(z0))))))) -> c7(B(b(b(a(a(a(b(z0))))))), B(b(a(a(a(b(z0)))))), B(a(a(a(b(z0))))), B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c1_2, c4_2, c5_5, c6_1, c7_4, c8_1, c9_1, c11_1, c3_1


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

(45) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_b(z0)) -> c1(B(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0)))

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(b(z0)))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))), B(a(a(b(a(a(a(b(b(z0))))))))), B(a(a(a(b(b(z0)))))), B(b(z0)), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(a(b(b(b(z0))))))) -> c7(B(b(b(a(a(a(b(z0))))))), B(b(a(a(a(b(z0)))))), B(a(a(a(b(z0))))), B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   ENCODE_B(z0) -> c3(B(encArg(z0)))
   ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0)))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(b(z0)))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))), B(a(a(b(a(a(a(b(b(z0))))))))), B(a(a(a(b(b(z0)))))), B(b(z0)), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(a(b(b(b(z0))))))) -> c7(B(b(b(a(a(a(b(z0))))))), B(b(a(a(a(b(z0)))))), B(a(a(a(b(z0))))), B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c4_2, c5_5, c6_1, c7_4, c8_1, c9_1, c11_1, c3_1, c1_2


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

(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(a(a(a(b(a(a(b(z0)))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))), B(a(a(b(a(a(a(b(b(z0))))))))), B(a(a(a(b(b(z0)))))), B(b(z0)), B(z0)) by 
   B(a(a(a(b(a(a(b(a(a(b(z0))))))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(z0))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), B(a(a(a(b(b(a(a(b(z0))))))))), B(b(a(a(b(z0))))), B(a(a(b(z0)))))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(a(b(b(b(z0))))))) -> c7(B(b(b(a(a(a(b(z0))))))), B(b(a(a(a(b(z0)))))), B(a(a(a(b(z0))))), B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   ENCODE_B(z0) -> c3(B(encArg(z0)))
   ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   B(a(a(a(b(a(a(b(a(a(b(z0))))))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(z0))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), B(a(a(a(b(b(a(a(b(z0))))))))), B(b(a(a(b(z0))))), B(a(a(b(z0)))))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(a(b(b(b(z0))))))) -> c7(B(b(b(a(a(a(b(z0))))))), B(b(a(a(a(b(z0)))))), B(a(a(a(b(z0))))), B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(a(a(b(z0))))))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(z0))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), B(a(a(a(b(b(a(a(b(z0))))))))), B(b(a(a(b(z0))))), B(a(a(b(z0)))))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c4_2, c6_1, c7_4, c8_1, c9_1, c11_1, c3_1, c1_2, c5_5, c5_2


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

(49) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(a(a(a(b(b(b(z0))))))) -> c7(B(b(b(a(a(a(b(z0))))))), B(b(a(a(a(b(z0)))))), B(a(a(a(b(z0))))), B(z0)) by 
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(b(z0))), B(b(a(a(a(b(a(a(a(b(z0)))))))))), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))), B(b(b(z0))))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   ENCODE_B(z0) -> c3(B(encArg(z0)))
   ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   B(a(a(a(b(a(a(b(a(a(b(z0))))))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(z0))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), B(a(a(a(b(b(a(a(b(z0))))))))), B(b(a(a(b(z0))))), B(a(a(b(z0)))))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(b(z0))), B(b(a(a(a(b(a(a(a(b(z0)))))))))), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))), B(b(b(z0))))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(a(a(b(z0))))))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(z0))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), B(a(a(a(b(b(a(a(b(z0))))))))), B(b(a(a(b(z0))))), B(a(a(b(z0)))))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(b(z0))), B(b(a(a(a(b(a(a(a(b(z0)))))))))), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))), B(b(b(z0))))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c4_2, c6_1, c8_1, c9_1, c11_1, c3_1, c1_2, c5_5, c5_2, c7_4, c7_2


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

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   ENCODE_B(z0) -> c3(B(encArg(z0)))
   ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   B(a(a(a(b(a(a(b(a(a(b(z0))))))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(z0))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), B(a(a(a(b(b(a(a(b(z0))))))))), B(b(a(a(b(z0))))), B(a(a(b(z0)))))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(a(a(a(b(a(a(a(b(z0)))))))))), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(a(a(b(z0))))))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(z0))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), B(a(a(a(b(b(a(a(b(z0))))))))), B(b(a(a(b(z0))))), B(a(a(b(z0)))))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(a(a(a(b(a(a(a(b(z0)))))))))), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c4_2, c6_1, c8_1, c9_1, c11_1, c3_1, c1_2, c5_5, c5_2, c7_2, c7_3


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

(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_B(z0) -> c3(B(encArg(z0))) by 
   ENCODE_B(a(z0)) -> c3(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0))))

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0)))
   ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   B(a(a(a(b(a(a(b(a(a(b(z0))))))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(z0))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), B(a(a(a(b(b(a(a(b(z0))))))))), B(b(a(a(b(z0))))), B(a(a(b(z0)))))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(a(a(a(b(a(a(a(b(z0)))))))))), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))))
   ENCODE_B(a(z0)) -> c3(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0))))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(a(a(b(z0))))))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(z0))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), B(a(a(a(b(b(a(a(b(z0))))))))), B(b(a(a(b(z0))))), B(a(a(b(z0)))))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(a(a(a(b(a(a(a(b(z0)))))))))), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c4_2, c6_1, c8_1, c9_1, c11_1, c1_2, c5_5, c5_2, c7_2, c7_3, c3_1


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_b(a(z0))) -> c1(B(a(encArg(z0))), ENCARG(a(z0))) by 
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0)))
   B(a(a(a(b(a(a(b(a(a(b(z0))))))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(z0))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), B(a(a(a(b(b(a(a(b(z0))))))))), B(b(a(a(b(z0))))), B(a(a(b(z0)))))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(a(a(a(b(a(a(a(b(z0)))))))))), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))))
   ENCODE_B(a(z0)) -> c3(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0))))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(a(a(b(z0))))))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(z0))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), B(a(a(a(b(b(a(a(b(z0))))))))), B(b(a(a(b(z0))))), B(a(a(b(z0)))))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(a(a(a(b(a(a(a(b(z0)))))))))), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c4_2, c6_1, c8_1, c9_1, c11_1, c1_2, c5_5, c5_2, c7_2, c7_3, c3_1, c1_1


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

(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_b(cons_b(z0))) -> c1(B(b(encArg(z0))), ENCARG(cons_b(z0))) by 
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(a(a(b(z0))))))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(z0))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), B(a(a(a(b(b(a(a(b(z0))))))))), B(b(a(a(b(z0))))), B(a(a(b(z0)))))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(a(a(a(b(a(a(a(b(z0)))))))))), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))))
   ENCODE_B(a(z0)) -> c3(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0))))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(a(a(b(z0))))))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(z0))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), B(a(a(a(b(b(a(a(b(z0))))))))), B(b(a(a(b(z0))))), B(a(a(b(z0)))))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(a(a(a(b(a(a(a(b(z0)))))))))), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c4_2, c6_1, c8_1, c9_1, c11_1, c5_5, c5_2, c7_2, c7_3, c3_1, c1_2, c1_1


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(a(a(a(b(a(a(b(a(a(b(z0))))))))))) -> c5(B(a(a(b(a(a(b(a(a(a(b(z0))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(z0)))))))))))), B(a(a(a(b(b(a(a(b(z0))))))))), B(b(a(a(b(z0))))), B(a(a(b(z0))))) by 
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))), B(a(a(b(a(a(b(z0))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))), B(a(a(b(a(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(a(a(a(b(a(a(a(b(z0)))))))))), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))))
   ENCODE_B(a(z0)) -> c3(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0))))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))), B(a(a(b(a(a(b(z0))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))), B(a(a(b(a(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(a(a(a(b(a(a(a(b(z0)))))))))), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))), B(a(a(b(a(a(b(z0))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))), B(a(a(b(a(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c4_2, c6_1, c8_1, c9_1, c11_1, c5_2, c7_2, c7_3, c3_1, c1_2, c1_1, c5_5, c5_4


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

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(a(a(a(b(a(a(a(b(z0)))))))))), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))))
   ENCODE_B(a(z0)) -> c3(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0))))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(a(a(a(b(a(a(a(b(z0)))))))))), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c4_2, c6_1, c8_1, c9_1, c11_1, c5_2, c7_2, c7_3, c3_1, c1_2, c1_1, c5_4


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(a(a(a(b(a(a(a(b(z0)))))))))), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0)))))) by 
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))))
   ENCODE_B(a(z0)) -> c3(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0))))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c4_2, c6_1, c8_1, c9_1, c11_1, c5_2, c7_2, c7_3, c3_1, c1_2, c1_1, c5_4


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

(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace B(a(a(a(b(b(b(b(b(z0))))))))) -> c7(B(b(b(b(b(a(a(a(b(z0))))))))), B(b(a(a(a(b(b(b(z0)))))))), B(a(a(a(b(b(b(z0)))))))) by 
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(b(b(b(z0))))), B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCODE_B(a(z0)) -> c3(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0))))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(b(b(b(z0))))), B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(b(b(b(z0))))), B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c4_2, c6_1, c8_1, c9_1, c11_1, c5_2, c7_2, c3_1, c1_2, c1_1, c5_4, c7_3


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

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCODE_B(a(z0)) -> c3(B(a(encArg(z0))))
   ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0))))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c4_2, c6_1, c8_1, c9_1, c11_1, c5_2, c7_2, c3_1, c1_2, c1_1, c5_4, c7_3


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

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_B(a(z0)) -> c3(B(a(encArg(z0)))) by 
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0))))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c4_2, c6_1, c8_1, c9_1, c11_1, c5_2, c7_2, c3_1, c1_2, c1_1, c5_4, c7_3


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_B(cons_b(z0)) -> c3(B(b(encArg(z0)))) by 
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   ENCARG(a(z0)) -> c(ENCARG(z0))
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   ENCARG_1, B_1, ENCODE_B_1

Compound Symbols:   c_1, c4_2, c6_1, c8_1, c9_1, c11_1, c5_2, c7_2, c1_2, c1_1, c5_4, c7_3, c3_1


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

(73) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(a(z0)) -> c(ENCARG(z0)) by 
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
S tuples:
   B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0))
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c4_2, c6_1, c8_1, c9_1, c11_1, c5_2, c7_2, c1_2, c1_1, c5_4, c7_3, c3_1, c_1


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

(75) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(a(b(z0))) -> c4(B(a(a(a(b(z0))))), B(z0)) by 
   B(a(b(a(b(y0))))) -> c4(B(a(a(a(b(a(b(y0))))))), B(a(b(y0))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(a(a(a(b(y0))))))))), B(a(a(a(b(y0))))))
   B(a(b(a(a(a(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(a(b(y0))))))))))))), B(a(a(a(b(a(a(a(b(y0))))))))))
   B(a(b(a(a(b(b(y0))))))) -> c4(B(a(a(a(b(a(a(b(b(y0))))))))), B(a(a(b(b(y0))))))
   B(a(b(b(a(a(b(y0))))))) -> c4(B(a(a(a(b(b(a(a(b(y0))))))))), B(b(a(a(b(y0))))))
   B(a(b(a(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(b(a(a(a(b(y0))))))))))), B(a(b(a(a(a(b(y0))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(a(a(a(b(a(a(b(y0)))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(b(y0)))))))))))), B(a(a(a(b(a(a(b(y0)))))))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))), B(b(b(y0))))
   B(a(b(a(a(a(b(b(b(y0))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(y0))))))))))), B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))), B(a(a(b(a(a(b(y0))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))), B(a(a(b(a(a(b(a(a(b(y0)))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))), B(a(a(b(a(a(b(a(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))), B(b(b(a(a(a(b(y0))))))))
   B(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))), B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))), B(b(b(b(b(b(b(y0))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))), B(b(b(b(b(y0))))))
   B(a(b(a(a(a(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))), B(b(b(b(b(a(a(a(b(y0))))))))))
   B(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(b(y0))))) -> c4(B(a(a(a(b(a(b(y0))))))), B(a(b(y0))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(a(a(a(b(y0))))))))), B(a(a(a(b(y0))))))
   B(a(b(a(a(a(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(a(b(y0))))))))))))), B(a(a(a(b(a(a(a(b(y0))))))))))
   B(a(b(a(a(b(b(y0))))))) -> c4(B(a(a(a(b(a(a(b(b(y0))))))))), B(a(a(b(b(y0))))))
   B(a(b(b(a(a(b(y0))))))) -> c4(B(a(a(a(b(b(a(a(b(y0))))))))), B(b(a(a(b(y0))))))
   B(a(b(a(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(b(a(a(a(b(y0))))))))))), B(a(b(a(a(a(b(y0))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(a(a(a(b(a(a(b(y0)))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(b(y0)))))))))))), B(a(a(a(b(a(a(b(y0)))))))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))), B(b(b(y0))))
   B(a(b(a(a(a(b(b(b(y0))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(y0))))))))))), B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))), B(a(a(b(a(a(b(y0))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))), B(a(a(b(a(a(b(a(a(b(y0)))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))), B(a(a(b(a(a(b(a(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))), B(b(b(a(a(a(b(y0))))))))
   B(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))), B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))), B(b(b(b(b(b(b(y0))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))), B(b(b(b(b(y0))))))
   B(a(b(a(a(a(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))), B(b(b(b(b(a(a(a(b(y0))))))))))
   B(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
S tuples:
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(a(b(y0))))) -> c4(B(a(a(a(b(a(b(y0))))))), B(a(b(y0))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(a(a(a(b(y0))))))))), B(a(a(a(b(y0))))))
   B(a(b(a(a(a(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(a(b(y0))))))))))))), B(a(a(a(b(a(a(a(b(y0))))))))))
   B(a(b(a(a(b(b(y0))))))) -> c4(B(a(a(a(b(a(a(b(b(y0))))))))), B(a(a(b(b(y0))))))
   B(a(b(b(a(a(b(y0))))))) -> c4(B(a(a(a(b(b(a(a(b(y0))))))))), B(b(a(a(b(y0))))))
   B(a(b(a(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(b(a(a(a(b(y0))))))))))), B(a(b(a(a(a(b(y0))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(a(a(a(b(a(a(b(y0)))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(b(y0)))))))))))), B(a(a(a(b(a(a(b(y0)))))))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))), B(b(b(y0))))
   B(a(b(a(a(a(b(b(b(y0))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(y0))))))))))), B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))), B(a(a(b(a(a(b(y0))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))), B(a(a(b(a(a(b(a(a(b(y0)))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))), B(a(a(b(a(a(b(a(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))), B(b(b(a(a(a(b(y0))))))))
   B(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))), B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))), B(b(b(b(b(b(b(y0))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))), B(b(b(b(b(y0))))))
   B(a(b(a(a(a(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))), B(b(b(b(b(a(a(a(b(y0))))))))))
   B(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c6_1, c8_1, c9_1, c11_1, c5_2, c7_2, c1_2, c1_1, c5_4, c7_3, c3_1, c_1, c4_2


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

(77) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 14 leading nodes:
   B(a(b(a(b(y0))))) -> c4(B(a(a(a(b(a(b(y0))))))), B(a(b(y0))))
   B(a(b(a(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(b(a(a(a(b(y0))))))))))), B(a(b(a(a(a(b(y0))))))))
   B(a(b(a(a(a(b(b(b(y0))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(y0))))))))))), B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(a(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))), B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(a(b(y0)))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(b(y0)))))))))))), B(a(a(a(b(a(a(b(y0)))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(b(a(a(b(y0))))))) -> c4(B(a(a(a(b(b(a(a(b(y0))))))))), B(b(a(a(b(y0))))))
   B(a(b(a(a(b(b(y0))))))) -> c4(B(a(a(a(b(a(a(b(b(y0))))))))), B(a(a(b(b(y0))))))
   B(a(b(a(a(a(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(a(a(a(b(a(a(a(b(y0))))))))))))), B(a(a(a(b(a(a(a(b(y0))))))))))

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(a(a(a(b(y0))))))))), B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))), B(b(b(y0))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))), B(a(a(b(a(a(b(y0))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))), B(a(a(b(a(a(b(a(a(b(y0)))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))), B(a(a(b(a(a(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))), B(b(b(a(a(a(b(y0))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))), B(b(b(b(b(b(b(y0))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))), B(b(b(b(b(y0))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))), B(b(b(b(b(a(a(a(b(y0))))))))))
S tuples:
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(a(a(a(b(y0))))))))), B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))), B(b(b(y0))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))), B(a(a(b(a(a(b(y0))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))), B(a(a(b(a(a(b(a(a(b(y0)))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))), B(a(a(b(a(a(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))), B(b(b(a(a(a(b(y0))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))), B(b(b(b(b(b(b(y0))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))), B(b(b(b(b(y0))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))), B(b(b(b(b(a(a(a(b(y0))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c6_1, c8_1, c9_1, c11_1, c5_2, c7_2, c1_2, c1_1, c5_4, c7_3, c3_1, c_1, c4_2


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

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(a(a(a(b(y0))))))))), B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
S tuples:
   B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0))
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(a(a(a(b(y0))))))))), B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c6_1, c8_1, c9_1, c11_1, c5_2, c7_2, c1_2, c1_1, c5_4, c7_3, c3_1, c_1, c4_2, c4_1


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

(81) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(a(a(a(b(a(a(a(b(z0))))))))) -> c6(B(z0)) by 
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(a(b(y0))))))))))))))))) -> c6(B(a(a(a(b(a(a(a(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(a(b(b(y0))))))))))))) -> c6(B(a(a(b(b(y0))))))
   B(a(a(a(b(a(a(a(b(b(a(a(b(y0))))))))))))) -> c6(B(b(a(a(b(y0))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(a(b(y0))))))))))))))) -> c6(B(a(b(a(a(a(b(y0))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(b(y0)))))))))))))))) -> c6(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(y0))))))))))))))) -> c6(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))))))) -> c6(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))))) -> c6(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))))) -> c6(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c6(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c6(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))))))) -> c6(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c6(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(b(y0)))))))))))))) -> c6(B(a(b(a(a(b(y0)))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(y0))))))))))))) -> c6(B(a(b(b(b(y0))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(b(a(a(b(y0))))))))))))))))) -> c6(B(a(b(a(a(b(a(a(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))) -> c6(B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))) -> c6(B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(a(a(a(b(y0))))))))))))))))) -> c6(B(a(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(b(b(b(b(y0))))))))))))))))) -> c6(B(a(b(b(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(b(b(y0))))))))))))))) -> c6(B(a(b(b(b(b(b(y0))))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c6(B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(a(a(a(b(y0))))))))), B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(a(b(y0))))))))))))))))) -> c6(B(a(a(a(b(a(a(a(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(a(b(b(y0))))))))))))) -> c6(B(a(a(b(b(y0))))))
   B(a(a(a(b(a(a(a(b(b(a(a(b(y0))))))))))))) -> c6(B(b(a(a(b(y0))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(a(b(y0))))))))))))))) -> c6(B(a(b(a(a(a(b(y0))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(b(y0)))))))))))))))) -> c6(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(y0))))))))))))))) -> c6(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))))))) -> c6(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))))) -> c6(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))))) -> c6(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c6(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c6(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))))))) -> c6(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c6(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(b(y0)))))))))))))) -> c6(B(a(b(a(a(b(y0)))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(y0))))))))))))) -> c6(B(a(b(b(b(y0))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(b(a(a(b(y0))))))))))))))))) -> c6(B(a(b(a(a(b(a(a(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))) -> c6(B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))) -> c6(B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(a(a(a(b(y0))))))))))))))))) -> c6(B(a(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(b(b(b(b(y0))))))))))))))))) -> c6(B(a(b(b(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(b(b(y0))))))))))))))) -> c6(B(a(b(b(b(b(b(y0))))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c6(B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
S tuples:
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(a(a(a(b(y0))))))))), B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(a(b(y0))))))))))))))))) -> c6(B(a(a(a(b(a(a(a(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(a(b(b(y0))))))))))))) -> c6(B(a(a(b(b(y0))))))
   B(a(a(a(b(a(a(a(b(b(a(a(b(y0))))))))))))) -> c6(B(b(a(a(b(y0))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(a(b(y0))))))))))))))) -> c6(B(a(b(a(a(a(b(y0))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(b(y0)))))))))))))))) -> c6(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(y0))))))))))))))) -> c6(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))))))) -> c6(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))))) -> c6(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))))) -> c6(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c6(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c6(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))))))) -> c6(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c6(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(b(y0)))))))))))))) -> c6(B(a(b(a(a(b(y0)))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(y0))))))))))))) -> c6(B(a(b(b(b(y0))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(b(a(a(b(y0))))))))))))))))) -> c6(B(a(b(a(a(b(a(a(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))) -> c6(B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))) -> c6(B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(a(a(a(b(y0))))))))))))))))) -> c6(B(a(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(b(b(b(b(y0))))))))))))))))) -> c6(B(a(b(b(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(b(b(y0))))))))))))))) -> c6(B(a(b(b(b(b(b(y0))))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c6(B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c8_1, c9_1, c11_1, c5_2, c7_2, c1_2, c1_1, c5_4, c7_3, c3_1, c_1, c4_2, c4_1, c6_1


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

(83) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 21 leading nodes:
   B(a(a(a(b(a(a(a(b(a(b(a(a(a(b(y0))))))))))))))) -> c6(B(a(b(a(a(a(b(y0))))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(y0))))))))))))) -> c6(B(a(b(b(b(y0))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(a(a(a(b(y0))))))))))))))))) -> c6(B(a(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(b(b(b(b(y0))))))))))))))))) -> c6(B(a(b(b(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(b(b(y0))))))))))))))) -> c6(B(a(b(b(b(b(b(y0))))))))
   B(a(a(a(b(a(a(a(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c6(B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(y0))))))))))))))) -> c6(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))))))) -> c6(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c6(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c6(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c6(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(b(y0)))))))))))))) -> c6(B(a(b(a(a(b(y0)))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(b(a(a(b(y0))))))))))))))))) -> c6(B(a(b(a(a(b(a(a(b(y0))))))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))) -> c6(B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(a(a(a(b(a(a(a(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))) -> c6(B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(b(y0)))))))))))))))) -> c6(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))))))) -> c6(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))))) -> c6(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))))) -> c6(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(a(a(b(a(a(a(b(b(a(a(b(y0))))))))))))) -> c6(B(b(a(a(b(y0))))))
   B(a(a(a(b(a(a(a(b(a(a(b(b(y0))))))))))))) -> c6(B(a(a(b(b(y0))))))
Removed 1 trailing nodes:
   B(a(a(a(b(a(a(a(b(a(a(a(b(a(a(a(b(y0))))))))))))))))) -> c6(B(a(a(a(b(a(a(a(b(y0))))))))))

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(a(a(a(b(y0))))))))), B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
S tuples:
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(a(a(a(b(z0))))))))), B(a(a(a(b(z0))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(a(a(a(b(y0))))))))), B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c8_1, c9_1, c11_1, c5_2, c7_2, c1_2, c1_1, c5_4, c7_3, c3_1, c_1, c4_2, c4_1


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

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(z0))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
S tuples:
   B(a(a(b(b(z0))))) -> c8(B(z0))
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(z0))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c8_1, c9_1, c11_1, c5_2, c7_2, c1_2, c1_1, c5_4, c7_3, c3_1, c_1, c4_2, c4_1


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

(87) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(a(a(b(b(z0))))) -> c8(B(z0)) by 
   B(a(a(b(b(a(a(b(b(y0))))))))) -> c8(B(a(a(b(b(y0))))))
   B(a(a(b(b(b(a(a(b(y0))))))))) -> c8(B(b(a(a(b(y0))))))
   B(a(a(b(b(a(b(a(a(a(b(y0))))))))))) -> c8(B(a(b(a(a(a(b(y0))))))))
   B(a(a(b(b(a(a(a(b(a(a(b(y0)))))))))))) -> c8(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(b(b(a(a(a(b(b(b(y0))))))))))) -> c8(B(a(a(a(b(b(b(y0))))))))
   B(a(a(b(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))) -> c8(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(a(b(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))) -> c8(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(a(b(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))) -> c8(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(a(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))) -> c8(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(b(b(a(a(a(b(b(b(b(b(y0))))))))))))) -> c8(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c8(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(b(b(a(b(a(a(b(y0)))))))))) -> c8(B(a(b(a(a(b(y0)))))))
   B(a(a(b(b(a(b(b(b(y0))))))))) -> c8(B(a(b(b(b(y0))))))
   B(a(a(b(b(a(b(a(a(b(a(a(b(y0))))))))))))) -> c8(B(a(b(a(a(b(a(a(b(y0))))))))))
   B(a(a(b(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c8(B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(a(a(b(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c8(B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(a(a(b(b(a(b(b(b(a(a(a(b(y0))))))))))))) -> c8(B(a(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(b(b(a(b(b(b(b(b(b(b(y0))))))))))))) -> c8(B(a(b(b(b(b(b(b(b(y0))))))))))
   B(a(a(b(b(a(b(b(b(b(b(y0))))))))))) -> c8(B(a(b(b(b(b(b(y0))))))))
   B(a(a(b(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c8(B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))) -> c8(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(z0))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(a(b(b(a(a(b(b(y0))))))))) -> c8(B(a(a(b(b(y0))))))
   B(a(a(b(b(b(a(a(b(y0))))))))) -> c8(B(b(a(a(b(y0))))))
   B(a(a(b(b(a(b(a(a(a(b(y0))))))))))) -> c8(B(a(b(a(a(a(b(y0))))))))
   B(a(a(b(b(a(a(a(b(a(a(b(y0)))))))))))) -> c8(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(b(b(a(a(a(b(b(b(y0))))))))))) -> c8(B(a(a(a(b(b(b(y0))))))))
   B(a(a(b(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))) -> c8(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(a(b(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))) -> c8(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(a(b(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))) -> c8(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(a(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))) -> c8(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(b(b(a(a(a(b(b(b(b(b(y0))))))))))))) -> c8(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c8(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(b(b(a(b(a(a(b(y0)))))))))) -> c8(B(a(b(a(a(b(y0)))))))
   B(a(a(b(b(a(b(b(b(y0))))))))) -> c8(B(a(b(b(b(y0))))))
   B(a(a(b(b(a(b(a(a(b(a(a(b(y0))))))))))))) -> c8(B(a(b(a(a(b(a(a(b(y0))))))))))
   B(a(a(b(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c8(B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(a(a(b(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c8(B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(a(a(b(b(a(b(b(b(a(a(a(b(y0))))))))))))) -> c8(B(a(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(b(b(a(b(b(b(b(b(b(b(y0))))))))))))) -> c8(B(a(b(b(b(b(b(b(b(y0))))))))))
   B(a(a(b(b(a(b(b(b(b(b(y0))))))))))) -> c8(B(a(b(b(b(b(b(y0))))))))
   B(a(a(b(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c8(B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))) -> c8(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
S tuples:
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(z0))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(a(b(b(a(a(b(b(y0))))))))) -> c8(B(a(a(b(b(y0))))))
   B(a(a(b(b(b(a(a(b(y0))))))))) -> c8(B(b(a(a(b(y0))))))
   B(a(a(b(b(a(b(a(a(a(b(y0))))))))))) -> c8(B(a(b(a(a(a(b(y0))))))))
   B(a(a(b(b(a(a(a(b(a(a(b(y0)))))))))))) -> c8(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(b(b(a(a(a(b(b(b(y0))))))))))) -> c8(B(a(a(a(b(b(b(y0))))))))
   B(a(a(b(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))) -> c8(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(a(b(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))) -> c8(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(a(b(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))) -> c8(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(a(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))) -> c8(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(b(b(a(a(a(b(b(b(b(b(y0))))))))))))) -> c8(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c8(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(b(b(a(b(a(a(b(y0)))))))))) -> c8(B(a(b(a(a(b(y0)))))))
   B(a(a(b(b(a(b(b(b(y0))))))))) -> c8(B(a(b(b(b(y0))))))
   B(a(a(b(b(a(b(a(a(b(a(a(b(y0))))))))))))) -> c8(B(a(b(a(a(b(a(a(b(y0))))))))))
   B(a(a(b(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c8(B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(a(a(b(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c8(B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(a(a(b(b(a(b(b(b(a(a(a(b(y0))))))))))))) -> c8(B(a(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(b(b(a(b(b(b(b(b(b(b(y0))))))))))))) -> c8(B(a(b(b(b(b(b(b(b(y0))))))))))
   B(a(a(b(b(a(b(b(b(b(b(y0))))))))))) -> c8(B(a(b(b(b(b(b(y0))))))))
   B(a(a(b(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c8(B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))) -> c8(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c9_1, c11_1, c5_2, c7_2, c1_2, c1_1, c5_4, c7_3, c3_1, c_1, c4_2, c4_1, c8_1


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

(89) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 20 leading nodes:
   B(a(a(b(b(a(b(b(b(y0))))))))) -> c8(B(a(b(b(b(y0))))))
   B(a(a(b(b(a(b(b(b(a(a(a(b(y0))))))))))))) -> c8(B(a(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(b(b(a(b(b(b(b(b(b(b(y0))))))))))))) -> c8(B(a(b(b(b(b(b(b(b(y0))))))))))
   B(a(a(b(b(a(b(b(b(b(b(y0))))))))))) -> c8(B(a(b(b(b(b(b(y0))))))))
   B(a(a(b(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c8(B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(b(b(a(b(a(a(a(b(y0))))))))))) -> c8(B(a(b(a(a(a(b(y0))))))))
   B(a(a(b(b(a(a(a(b(b(b(y0))))))))))) -> c8(B(a(a(a(b(b(b(y0))))))))
   B(a(a(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))) -> c8(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(b(b(a(a(a(b(b(b(b(b(y0))))))))))))) -> c8(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c8(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))) -> c8(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(b(b(a(b(a(a(b(y0)))))))))) -> c8(B(a(b(a(a(b(y0)))))))
   B(a(a(b(b(a(b(a(a(b(a(a(b(y0))))))))))))) -> c8(B(a(b(a(a(b(a(a(b(y0))))))))))
   B(a(a(b(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c8(B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(a(a(b(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c8(B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(a(a(b(b(a(a(a(b(a(a(b(y0)))))))))))) -> c8(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(b(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))) -> c8(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(a(b(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))) -> c8(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(a(b(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))) -> c8(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(a(b(b(b(a(a(b(y0))))))))) -> c8(B(b(a(a(b(y0))))))
Removed 1 trailing nodes:
   B(a(a(b(b(a(a(b(b(y0))))))))) -> c8(B(a(a(b(b(y0))))))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(z0))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
S tuples:
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))), B(a(a(b(x0)))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(z0))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c9_1, c11_1, c5_2, c7_2, c1_2, c1_1, c5_4, c7_3, c3_1, c_1, c4_2, c4_1


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

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(z0))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
S tuples:
   B(b(a(a(b(z0))))) -> c9(B(z0))
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(z0))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c9_1, c11_1, c5_2, c7_2, c1_2, c1_1, c5_4, c7_3, c3_1, c_1, c4_1, c5_3


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

(93) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(b(a(a(b(z0))))) -> c9(B(z0)) by 
   B(b(a(a(b(b(a(a(b(y0))))))))) -> c9(B(b(a(a(b(y0))))))
   B(b(a(a(b(a(b(a(a(a(b(y0))))))))))) -> c9(B(a(b(a(a(a(b(y0))))))))
   B(b(a(a(b(a(a(a(b(a(a(b(y0)))))))))))) -> c9(B(a(a(a(b(a(a(b(y0)))))))))
   B(b(a(a(b(a(a(a(b(b(b(y0))))))))))) -> c9(B(a(a(a(b(b(b(y0))))))))
   B(b(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))) -> c9(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(b(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))) -> c9(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(b(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))) -> c9(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(b(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))) -> c9(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(b(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c9(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(b(a(a(b(a(b(b(b(y0))))))))) -> c9(B(a(b(b(b(y0))))))
   B(b(a(a(b(a(b(a(a(b(a(a(b(y0))))))))))))) -> c9(B(a(b(a(a(b(a(a(b(y0))))))))))
   B(b(a(a(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c9(B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(b(a(a(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c9(B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(b(a(a(b(a(b(b(b(a(a(a(b(y0))))))))))))) -> c9(B(a(b(b(b(a(a(a(b(y0))))))))))
   B(b(a(a(b(a(b(b(b(b(b(b(b(y0))))))))))))) -> c9(B(a(b(b(b(b(b(b(b(y0))))))))))
   B(b(a(a(b(a(b(b(b(b(b(y0))))))))))) -> c9(B(a(b(b(b(b(b(y0))))))))
   B(b(a(a(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c9(B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(b(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))) -> c9(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(b(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))) -> c9(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(b(a(a(b(a(b(a(a(b(y0)))))))))) -> c9(B(a(b(a(a(b(y0)))))))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(z0))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(b(a(a(b(b(a(a(b(y0))))))))) -> c9(B(b(a(a(b(y0))))))
   B(b(a(a(b(a(b(a(a(a(b(y0))))))))))) -> c9(B(a(b(a(a(a(b(y0))))))))
   B(b(a(a(b(a(a(a(b(a(a(b(y0)))))))))))) -> c9(B(a(a(a(b(a(a(b(y0)))))))))
   B(b(a(a(b(a(a(a(b(b(b(y0))))))))))) -> c9(B(a(a(a(b(b(b(y0))))))))
   B(b(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))) -> c9(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(b(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))) -> c9(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(b(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))) -> c9(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(b(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))) -> c9(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(b(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c9(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(b(a(a(b(a(b(b(b(y0))))))))) -> c9(B(a(b(b(b(y0))))))
   B(b(a(a(b(a(b(a(a(b(a(a(b(y0))))))))))))) -> c9(B(a(b(a(a(b(a(a(b(y0))))))))))
   B(b(a(a(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c9(B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(b(a(a(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c9(B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(b(a(a(b(a(b(b(b(a(a(a(b(y0))))))))))))) -> c9(B(a(b(b(b(a(a(a(b(y0))))))))))
   B(b(a(a(b(a(b(b(b(b(b(b(b(y0))))))))))))) -> c9(B(a(b(b(b(b(b(b(b(y0))))))))))
   B(b(a(a(b(a(b(b(b(b(b(y0))))))))))) -> c9(B(a(b(b(b(b(b(y0))))))))
   B(b(a(a(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c9(B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(b(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))) -> c9(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(b(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))) -> c9(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(b(a(a(b(a(b(a(a(b(y0)))))))))) -> c9(B(a(b(a(a(b(y0)))))))
S tuples:
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(z0))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(b(a(a(b(b(a(a(b(y0))))))))) -> c9(B(b(a(a(b(y0))))))
   B(b(a(a(b(a(b(a(a(a(b(y0))))))))))) -> c9(B(a(b(a(a(a(b(y0))))))))
   B(b(a(a(b(a(a(a(b(a(a(b(y0)))))))))))) -> c9(B(a(a(a(b(a(a(b(y0)))))))))
   B(b(a(a(b(a(a(a(b(b(b(y0))))))))))) -> c9(B(a(a(a(b(b(b(y0))))))))
   B(b(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))) -> c9(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(b(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))) -> c9(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(b(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))) -> c9(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(b(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))) -> c9(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(b(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c9(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(b(a(a(b(a(b(b(b(y0))))))))) -> c9(B(a(b(b(b(y0))))))
   B(b(a(a(b(a(b(a(a(b(a(a(b(y0))))))))))))) -> c9(B(a(b(a(a(b(a(a(b(y0))))))))))
   B(b(a(a(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c9(B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(b(a(a(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c9(B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(b(a(a(b(a(b(b(b(a(a(a(b(y0))))))))))))) -> c9(B(a(b(b(b(a(a(a(b(y0))))))))))
   B(b(a(a(b(a(b(b(b(b(b(b(b(y0))))))))))))) -> c9(B(a(b(b(b(b(b(b(b(y0))))))))))
   B(b(a(a(b(a(b(b(b(b(b(y0))))))))))) -> c9(B(a(b(b(b(b(b(y0))))))))
   B(b(a(a(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c9(B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(b(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))) -> c9(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(b(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))) -> c9(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(b(a(a(b(a(b(a(a(b(y0)))))))))) -> c9(B(a(b(a(a(b(y0)))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c11_1, c5_2, c7_2, c1_2, c1_1, c5_4, c7_3, c3_1, c_1, c4_1, c5_3, c9_1


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

(95) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 19 leading nodes:
   B(b(a(a(b(a(b(b(b(y0))))))))) -> c9(B(a(b(b(b(y0))))))
   B(b(a(a(b(a(b(b(b(a(a(a(b(y0))))))))))))) -> c9(B(a(b(b(b(a(a(a(b(y0))))))))))
   B(b(a(a(b(a(b(b(b(b(b(b(b(y0))))))))))))) -> c9(B(a(b(b(b(b(b(b(b(y0))))))))))
   B(b(a(a(b(a(b(b(b(b(b(y0))))))))))) -> c9(B(a(b(b(b(b(b(y0))))))))
   B(b(a(a(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c9(B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(b(a(a(b(a(b(a(a(a(b(y0))))))))))) -> c9(B(a(b(a(a(a(b(y0))))))))
   B(b(a(a(b(a(b(a(a(b(a(a(b(y0))))))))))))) -> c9(B(a(b(a(a(b(a(a(b(y0))))))))))
   B(b(a(a(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c9(B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(b(a(a(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c9(B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(b(a(a(b(a(b(a(a(b(y0)))))))))) -> c9(B(a(b(a(a(b(y0)))))))
   B(b(a(a(b(a(a(a(b(a(a(b(y0)))))))))))) -> c9(B(a(a(a(b(a(a(b(y0)))))))))
   B(b(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))) -> c9(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(b(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))) -> c9(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(b(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))) -> c9(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(b(a(a(b(a(a(a(b(b(b(y0))))))))))) -> c9(B(a(a(a(b(b(b(y0))))))))
   B(b(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))) -> c9(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(b(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))) -> c9(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(b(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c9(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(b(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))) -> c9(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
Removed 1 trailing nodes:
   B(b(a(a(b(b(a(a(b(y0))))))))) -> c9(B(b(a(a(b(y0))))))

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(z0))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
S tuples:
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))), B(b(a(a(b(a(a(b(z0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))), B(b(a(a(b(a(a(a(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(b(z0)), B(a(a(a(b(z0))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))), B(b(a(a(b(x0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c11_1, c5_2, c7_2, c1_2, c1_1, c5_4, c7_3, c3_1, c_1, c4_1, c5_3


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

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
S tuples:
   B(a(b(a(a(a(b(z0))))))) -> c11(B(z0))
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c11_1, c5_2, c7_2, c1_2, c1_1, c7_3, c3_1, c_1, c4_1, c5_3, c7_1


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

(99) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(a(b(a(a(a(b(z0))))))) -> c11(B(z0)) by 
   B(a(b(a(a(a(b(a(b(a(a(a(b(y0))))))))))))) -> c11(B(a(b(a(a(a(b(y0))))))))
   B(a(b(a(a(a(b(a(a(a(b(a(a(b(y0)))))))))))))) -> c11(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(y0))))))))))))) -> c11(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))) -> c11(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))))) -> c11(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c11(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(a(b(b(b(y0))))))))))) -> c11(B(a(b(b(b(y0))))))
   B(a(b(a(a(a(b(a(b(a(a(b(a(a(b(y0))))))))))))))) -> c11(B(a(b(a(a(b(a(a(b(y0))))))))))
   B(a(b(a(a(a(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))) -> c11(B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(a(b(a(a(a(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))) -> c11(B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(a(b(b(b(a(a(a(b(y0))))))))))))))) -> c11(B(a(b(b(b(a(a(a(b(y0))))))))))
   B(a(b(a(a(a(b(a(b(b(b(b(b(b(b(y0))))))))))))))) -> c11(B(a(b(b(b(b(b(b(b(y0))))))))))
   B(a(b(a(a(a(b(a(b(b(b(b(b(y0))))))))))))) -> c11(B(a(b(b(b(b(b(y0))))))))
   B(a(b(a(a(a(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c11(B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(b(a(a(b(y0)))))))))))) -> c11(B(a(b(a(a(b(y0)))))))
   B(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))) -> c11(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))) -> c11(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))) -> c11(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))))) -> c11(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(b(a(a(a(b(a(b(a(a(a(b(y0))))))))))))) -> c11(B(a(b(a(a(a(b(y0))))))))
   B(a(b(a(a(a(b(a(a(a(b(a(a(b(y0)))))))))))))) -> c11(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(y0))))))))))))) -> c11(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))) -> c11(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))))) -> c11(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c11(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(a(b(b(b(y0))))))))))) -> c11(B(a(b(b(b(y0))))))
   B(a(b(a(a(a(b(a(b(a(a(b(a(a(b(y0))))))))))))))) -> c11(B(a(b(a(a(b(a(a(b(y0))))))))))
   B(a(b(a(a(a(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))) -> c11(B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(a(b(a(a(a(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))) -> c11(B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(a(b(b(b(a(a(a(b(y0))))))))))))))) -> c11(B(a(b(b(b(a(a(a(b(y0))))))))))
   B(a(b(a(a(a(b(a(b(b(b(b(b(b(b(y0))))))))))))))) -> c11(B(a(b(b(b(b(b(b(b(y0))))))))))
   B(a(b(a(a(a(b(a(b(b(b(b(b(y0))))))))))))) -> c11(B(a(b(b(b(b(b(y0))))))))
   B(a(b(a(a(a(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c11(B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(b(a(a(b(y0)))))))))))) -> c11(B(a(b(a(a(b(y0)))))))
   B(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))) -> c11(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))) -> c11(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))) -> c11(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))))) -> c11(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(b(a(a(a(b(a(b(a(a(a(b(y0))))))))))))) -> c11(B(a(b(a(a(a(b(y0))))))))
   B(a(b(a(a(a(b(a(a(a(b(a(a(b(y0)))))))))))))) -> c11(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(y0))))))))))))) -> c11(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))) -> c11(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))))) -> c11(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c11(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(a(b(b(b(y0))))))))))) -> c11(B(a(b(b(b(y0))))))
   B(a(b(a(a(a(b(a(b(a(a(b(a(a(b(y0))))))))))))))) -> c11(B(a(b(a(a(b(a(a(b(y0))))))))))
   B(a(b(a(a(a(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))) -> c11(B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(a(b(a(a(a(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))) -> c11(B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(a(b(b(b(a(a(a(b(y0))))))))))))))) -> c11(B(a(b(b(b(a(a(a(b(y0))))))))))
   B(a(b(a(a(a(b(a(b(b(b(b(b(b(b(y0))))))))))))))) -> c11(B(a(b(b(b(b(b(b(b(y0))))))))))
   B(a(b(a(a(a(b(a(b(b(b(b(b(y0))))))))))))) -> c11(B(a(b(b(b(b(b(y0))))))))
   B(a(b(a(a(a(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c11(B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(b(a(a(b(y0)))))))))))) -> c11(B(a(b(a(a(b(y0)))))))
   B(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))) -> c11(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))) -> c11(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))) -> c11(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))))) -> c11(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c7_2, c1_2, c1_1, c7_3, c3_1, c_1, c4_1, c5_3, c7_1, c11_1


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

(101) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 19 leading nodes:
   B(a(b(a(a(a(b(a(b(b(b(y0))))))))))) -> c11(B(a(b(b(b(y0))))))
   B(a(b(a(a(a(b(a(b(b(b(a(a(a(b(y0))))))))))))))) -> c11(B(a(b(b(b(a(a(a(b(y0))))))))))
   B(a(b(a(a(a(b(a(b(b(b(b(b(b(b(y0))))))))))))))) -> c11(B(a(b(b(b(b(b(b(b(y0))))))))))
   B(a(b(a(a(a(b(a(b(b(b(b(b(y0))))))))))))) -> c11(B(a(b(b(b(b(b(y0))))))))
   B(a(b(a(a(a(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c11(B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(b(a(a(a(b(y0))))))))))))) -> c11(B(a(b(a(a(a(b(y0))))))))
   B(a(b(a(a(a(b(a(b(a(a(b(a(a(b(y0))))))))))))))) -> c11(B(a(b(a(a(b(a(a(b(y0))))))))))
   B(a(b(a(a(a(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))) -> c11(B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(a(b(a(a(a(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))) -> c11(B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(a(b(a(a(b(y0)))))))))))) -> c11(B(a(b(a(a(b(y0)))))))
   B(a(b(a(a(a(b(a(a(a(b(a(a(b(y0)))))))))))))) -> c11(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))) -> c11(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))) -> c11(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))))) -> c11(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(y0))))))))))))) -> c11(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))) -> c11(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))))) -> c11(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c11(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))) -> c11(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c7_2, c1_2, c1_1, c7_3, c3_1, c_1, c4_1, c5_3, c7_1


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

(103) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(a(a(a(b(b(b(x0))))))) -> c7(B(a(a(a(b(x0))))), B(x0)) by 
   B(a(a(a(b(b(b(a(a(b(y0)))))))))) -> c7(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(y0)))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(a(a(b(y0)))))))))))), B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))), B(b(b(y0))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(y0))))))))))), B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))), B(b(b(b(b(b(b(y0))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))), B(b(b(b(b(y0))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))), B(b(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(a(b(b(b(y0))))))))), B(a(b(b(b(y0))))))
   B(a(a(a(b(b(b(a(b(a(a(b(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(a(b(a(a(b(a(a(b(y0))))))))))))), B(a(b(a(a(b(a(a(b(y0))))))))))
   B(a(a(a(b(b(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))) -> c7(B(a(a(a(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))), B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(a(a(a(b(b(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))), B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(a(b(b(b(a(a(a(b(y0))))))))))))), B(a(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(a(b(b(b(a(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(a(b(b(b(b(b(b(b(y0))))))))))))), B(a(b(b(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(a(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(a(b(b(b(b(b(y0))))))))))), B(a(b(b(b(b(b(y0))))))))
   B(a(a(a(b(b(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))), B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(a(b(a(a(a(b(y0))))))))))), B(a(b(a(a(a(b(y0))))))))
   B(a(a(a(b(b(b(a(b(a(a(b(y0)))))))))))) -> c7(B(a(a(a(b(a(b(a(a(b(y0)))))))))), B(a(b(a(a(b(y0)))))))
   B(a(a(a(b(b(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))), B(a(a(b(a(a(b(a(a(b(y0)))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(a(a(b(b(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))), B(a(a(b(a(a(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))), B(b(b(a(a(a(b(y0))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))), B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(b(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))), B(a(a(b(a(a(b(y0))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))

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

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(a(a(b(y0)))))))))) -> c7(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(y0)))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(a(a(b(y0)))))))))))), B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))), B(b(b(y0))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(y0))))))))))), B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))), B(b(b(b(b(b(b(y0))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))), B(b(b(b(b(y0))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))), B(b(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(a(b(b(b(y0))))))))), B(a(b(b(b(y0))))))
   B(a(a(a(b(b(b(a(b(a(a(b(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(a(b(a(a(b(a(a(b(y0))))))))))))), B(a(b(a(a(b(a(a(b(y0))))))))))
   B(a(a(a(b(b(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))) -> c7(B(a(a(a(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))), B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(a(a(a(b(b(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))), B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(a(b(b(b(a(a(a(b(y0))))))))))))), B(a(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(a(b(b(b(a(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(a(b(b(b(b(b(b(b(y0))))))))))))), B(a(b(b(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(a(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(a(b(b(b(b(b(y0))))))))))), B(a(b(b(b(b(b(y0))))))))
   B(a(a(a(b(b(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))), B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(a(b(a(a(a(b(y0))))))))))), B(a(b(a(a(a(b(y0))))))))
   B(a(a(a(b(b(b(a(b(a(a(b(y0)))))))))))) -> c7(B(a(a(a(b(a(b(a(a(b(y0)))))))))), B(a(b(a(a(b(y0)))))))
   B(a(a(a(b(b(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))), B(a(a(b(a(a(b(a(a(b(y0)))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(a(a(b(b(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))), B(a(a(b(a(a(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))), B(b(b(a(a(a(b(y0))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))), B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(b(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))), B(a(a(b(a(a(b(y0))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(a(a(b(y0)))))))))) -> c7(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(y0)))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(a(a(b(y0)))))))))))), B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))), B(b(b(y0))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(y0))))))))))), B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))), B(b(b(b(b(b(b(y0))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))), B(b(b(b(b(y0))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))), B(b(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(a(b(b(b(y0))))))))), B(a(b(b(b(y0))))))
   B(a(a(a(b(b(b(a(b(a(a(b(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(a(b(a(a(b(a(a(b(y0))))))))))))), B(a(b(a(a(b(a(a(b(y0))))))))))
   B(a(a(a(b(b(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))) -> c7(B(a(a(a(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))), B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(a(a(a(b(b(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))), B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(a(b(b(b(a(a(a(b(y0))))))))))))), B(a(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(a(b(b(b(a(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(a(b(b(b(b(b(b(b(y0))))))))))))), B(a(b(b(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(a(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(a(b(b(b(b(b(y0))))))))))), B(a(b(b(b(b(b(y0))))))))
   B(a(a(a(b(b(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))), B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(a(b(a(a(a(b(y0))))))))))), B(a(b(a(a(a(b(y0))))))))
   B(a(a(a(b(b(b(a(b(a(a(b(y0)))))))))))) -> c7(B(a(a(a(b(a(b(a(a(b(y0)))))))))), B(a(b(a(a(b(y0)))))))
   B(a(a(a(b(b(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))), B(a(a(b(a(a(b(a(a(b(y0)))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(a(a(b(b(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))), B(a(a(b(a(a(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))), B(b(b(a(a(a(b(y0))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))), B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(b(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))), B(a(a(b(a(a(b(y0))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c1_1, c7_3, c7_2, c3_1, c_1, c4_1, c5_3, c7_1


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

(105) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 23 leading nodes:
   B(a(a(a(b(b(b(a(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(a(b(b(b(y0))))))))), B(a(b(b(b(y0))))))
   B(a(a(a(b(b(b(a(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(a(b(b(b(a(a(a(b(y0))))))))))))), B(a(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(a(b(b(b(a(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(a(b(b(b(b(b(b(b(y0))))))))))))), B(a(b(b(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(a(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(a(b(b(b(b(b(y0))))))))))), B(a(b(b(b(b(b(y0))))))))
   B(a(a(a(b(b(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))), B(a(b(b(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(a(b(a(a(a(b(y0))))))))))), B(a(b(a(a(a(b(y0))))))))
   B(a(a(a(b(b(b(a(b(a(a(b(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(a(b(a(a(b(a(a(b(y0))))))))))))), B(a(b(a(a(b(a(a(b(y0))))))))))
   B(a(a(a(b(b(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))) -> c7(B(a(a(a(b(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))), B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))
   B(a(a(a(b(b(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))), B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(b(a(a(b(y0)))))))))))) -> c7(B(a(a(a(b(a(b(a(a(b(y0)))))))))), B(a(b(a(a(b(y0)))))))
   B(a(a(a(b(b(b(a(a(b(y0)))))))))) -> c7(B(a(a(a(b(a(a(b(y0)))))))), B(a(a(b(y0)))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(y0)))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(a(a(b(y0)))))))))))), B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(b(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))), B(a(a(b(a(a(b(a(a(b(y0)))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(a(a(b(b(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))), B(a(a(b(a(a(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(a(a(b(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))), B(a(a(b(a(a(b(y0))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))), B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(y0))))))))))), B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(b(b(y0))))))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))), B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))), B(b(b(y0))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))), B(b(b(b(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))), B(b(b(b(b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))), B(b(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))), B(b(b(a(a(a(b(y0))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))), B(b(b(y0))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))), B(b(b(b(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))), B(b(b(b(b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))), B(b(b(b(b(a(a(a(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))), B(b(b(a(a(a(b(y0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c1_1, c7_3, c7_2, c3_1, c_1, c4_1, c5_3, c7_1


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

(107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing tuple parts
----------------------------------------

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0)))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c1_1, c7_3, c7_2, c3_1, c_1, c4_1, c5_3, c7_1


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

(109) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(cons_b(a(x0))) -> c1(ENCARG(a(x0))) by 
   ENCARG(cons_b(a(a(y0)))) -> c1(ENCARG(a(a(y0))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0)))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   ENCARG(cons_b(a(a(y0)))) -> c1(ENCARG(a(a(y0))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0)))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c7_3, c7_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1


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

(111) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(a(a(a(b(b(b(b(b(x0))))))))) -> c7(B(b(a(a(a(b(b(b(x0)))))))), B(a(a(a(b(b(b(x0)))))))) by 
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(y0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(a(y0))) -> c(ENCARG(a(y0)))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   ENCARG(cons_b(a(a(y0)))) -> c1(ENCARG(a(a(y0))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0)))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c7_3, c7_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1


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

(113) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(a(a(y0))) -> c(ENCARG(a(y0))) by 
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   ENCARG(cons_b(a(a(y0)))) -> c1(ENCARG(a(a(y0))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0)))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c7_3, c7_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1


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

(115) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(a(cons_b(a(y0)))) -> c(ENCARG(cons_b(a(y0)))) by 
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   ENCARG(cons_b(a(a(y0)))) -> c1(ENCARG(a(a(y0))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0)))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c7_3, c7_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1


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

(117) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(a(b(b(b(y0))))) -> c4(B(a(a(a(b(b(b(y0)))))))) by 
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   ENCARG(cons_b(a(a(y0)))) -> c1(ENCARG(a(a(y0))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0)))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c7_3, c7_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1


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

(119) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(a(b(a(a(a(b(y0))))))) -> c4(B(a(a(a(b(y0)))))) by 
   B(a(b(a(a(a(b(a(a(b(y0)))))))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   ENCARG(cons_b(a(a(y0)))) -> c1(ENCARG(a(a(y0))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0)))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(b(a(a(a(b(a(a(b(y0)))))))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(b(a(a(a(b(a(a(b(y0)))))))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c7_3, c7_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1


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

(121) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 12 leading nodes:
   B(a(b(a(a(a(b(a(a(b(y0)))))))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   ENCARG(cons_b(a(a(y0)))) -> c1(ENCARG(a(a(y0))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0)))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c7_3, c7_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1


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

(123) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(a(a(a(b(b(b(a(a(a(b(z0))))))))))) -> c7(B(a(a(a(b(z0)))))) by 
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(y0)))))))))))))) -> c7(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   ENCARG(cons_b(a(a(y0)))) -> c1(ENCARG(a(a(y0))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0)))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(y0)))))))))))))) -> c7(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(y0)))))))))))))) -> c7(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c7_3, c7_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1


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(125) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 11 leading nodes:
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(y0)))))))))))))) -> c7(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(a(a(a(b(a(a(b(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
Removed 1 trailing nodes:
   B(a(a(a(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   ENCARG(cons_b(a(a(y0)))) -> c1(ENCARG(a(a(y0))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0)))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))), B(a(a(a(b(b(b(a(a(a(b(z0))))))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(a(a(a(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c7_3, c7_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1


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

(127) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing tuple parts
----------------------------------------

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   ENCARG(cons_b(a(a(y0)))) -> c1(ENCARG(a(a(y0))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0)))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c7_3, c3_1, c_1, c4_1, c5_3, c7_1, c1_1, c7_2, c4, c7


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

(129) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(a(a(a(b(b(b(b(b(y0))))))))) -> c7(B(a(a(a(b(b(b(y0)))))))) by 
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   ENCARG(cons_b(a(a(y0)))) -> c1(ENCARG(a(a(y0))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0)))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0))))))))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c7_3, c3_1, c_1, c4_1, c5_3, c7_1, c1_1, c7_2, c4, c7


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

(131) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(a(a(a(b(b(b(b(b(b(b(z0))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(z0))))))))))), B(b(a(a(a(b(b(b(b(b(z0)))))))))), B(a(a(a(b(b(b(b(b(z0)))))))))) by 
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   ENCARG(cons_b(a(a(y0)))) -> c1(ENCARG(a(a(y0))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0)))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1, c7_2, c4, c7, c7_3


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

(133) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0)))))))))) by 
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   ENCARG(cons_b(a(a(y0)))) -> c1(ENCARG(a(a(y0))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0)))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1, c7_2, c4, c7, c7_3


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

(135) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0)))))))))) by 
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   ENCARG(cons_b(a(a(y0)))) -> c1(ENCARG(a(a(y0))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0)))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1, c7_2, c4, c7, c7_3


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

(137) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(cons_b(a(a(y0)))) -> c1(ENCARG(a(a(y0)))) by 
   ENCARG(cons_b(a(a(a(y0))))) -> c1(ENCARG(a(a(a(y0)))))
   ENCARG(cons_b(a(a(cons_b(a(a(y0))))))) -> c1(ENCARG(a(a(cons_b(a(a(y0)))))))
   ENCARG(cons_b(a(a(cons_b(a(cons_b(y0))))))) -> c1(ENCARG(a(a(cons_b(a(cons_b(y0)))))))
   ENCARG(cons_b(a(a(cons_b(a(y0)))))) -> c1(ENCARG(a(a(cons_b(a(y0))))))
   ENCARG(cons_b(a(a(cons_b(cons_b(a(y0))))))) -> c1(ENCARG(a(a(cons_b(cons_b(a(y0)))))))
   ENCARG(cons_b(a(a(cons_b(cons_b(cons_b(y0))))))) -> c1(ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0)))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   ENCARG(cons_b(a(a(a(y0))))) -> c1(ENCARG(a(a(a(y0)))))
   ENCARG(cons_b(a(a(cons_b(a(a(y0))))))) -> c1(ENCARG(a(a(cons_b(a(a(y0)))))))
   ENCARG(cons_b(a(a(cons_b(a(cons_b(y0))))))) -> c1(ENCARG(a(a(cons_b(a(cons_b(y0)))))))
   ENCARG(cons_b(a(a(cons_b(a(y0)))))) -> c1(ENCARG(a(a(cons_b(a(y0))))))
   ENCARG(cons_b(a(a(cons_b(cons_b(a(y0))))))) -> c1(ENCARG(a(a(cons_b(cons_b(a(y0)))))))
   ENCARG(cons_b(a(a(cons_b(cons_b(cons_b(y0))))))) -> c1(ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1, c7_2, c4, c7, c7_3


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

(139) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace ENCARG(cons_b(a(cons_b(a(y0))))) -> c1(ENCARG(a(cons_b(a(y0))))) by 
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(a(a(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(a(a(y0))))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(a(cons_b(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(a(y0))))))) -> c1(ENCARG(a(cons_b(a(cons_b(a(y0)))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(cons_b(a(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(cons_b(cons_b(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))))

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   ENCARG(cons_b(a(a(a(y0))))) -> c1(ENCARG(a(a(a(y0)))))
   ENCARG(cons_b(a(a(cons_b(a(a(y0))))))) -> c1(ENCARG(a(a(cons_b(a(a(y0)))))))
   ENCARG(cons_b(a(a(cons_b(a(cons_b(y0))))))) -> c1(ENCARG(a(a(cons_b(a(cons_b(y0)))))))
   ENCARG(cons_b(a(a(cons_b(a(y0)))))) -> c1(ENCARG(a(a(cons_b(a(y0))))))
   ENCARG(cons_b(a(a(cons_b(cons_b(a(y0))))))) -> c1(ENCARG(a(a(cons_b(cons_b(a(y0)))))))
   ENCARG(cons_b(a(a(cons_b(cons_b(cons_b(y0))))))) -> c1(ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(a(a(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(a(a(y0))))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(a(cons_b(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(a(y0))))))) -> c1(ENCARG(a(cons_b(a(cons_b(a(y0)))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(cons_b(a(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(cons_b(cons_b(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1, c7_2, c4, c7, c7_3


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

(141) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(y0)))))))))), B(a(a(a(b(b(b(b(b(y0)))))))))) by 
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   ENCARG(cons_b(a(a(a(y0))))) -> c1(ENCARG(a(a(a(y0)))))
   ENCARG(cons_b(a(a(cons_b(a(a(y0))))))) -> c1(ENCARG(a(a(cons_b(a(a(y0)))))))
   ENCARG(cons_b(a(a(cons_b(a(cons_b(y0))))))) -> c1(ENCARG(a(a(cons_b(a(cons_b(y0)))))))
   ENCARG(cons_b(a(a(cons_b(a(y0)))))) -> c1(ENCARG(a(a(cons_b(a(y0))))))
   ENCARG(cons_b(a(a(cons_b(cons_b(a(y0))))))) -> c1(ENCARG(a(a(cons_b(cons_b(a(y0)))))))
   ENCARG(cons_b(a(a(cons_b(cons_b(cons_b(y0))))))) -> c1(ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(a(a(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(a(a(y0))))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(a(cons_b(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(a(y0))))))) -> c1(ENCARG(a(cons_b(a(cons_b(a(y0)))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(cons_b(a(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(cons_b(cons_b(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1, c7_2, c4, c7, c7_3


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

(143) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0))))))))))))) by none

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(a(a(a(b(z0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(z0)))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   ENCARG(cons_b(a(a(a(y0))))) -> c1(ENCARG(a(a(a(y0)))))
   ENCARG(cons_b(a(a(cons_b(a(a(y0))))))) -> c1(ENCARG(a(a(cons_b(a(a(y0)))))))
   ENCARG(cons_b(a(a(cons_b(a(cons_b(y0))))))) -> c1(ENCARG(a(a(cons_b(a(cons_b(y0)))))))
   ENCARG(cons_b(a(a(cons_b(a(y0)))))) -> c1(ENCARG(a(a(cons_b(a(y0))))))
   ENCARG(cons_b(a(a(cons_b(cons_b(a(y0))))))) -> c1(ENCARG(a(a(cons_b(cons_b(a(y0)))))))
   ENCARG(cons_b(a(a(cons_b(cons_b(cons_b(y0))))))) -> c1(ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(a(a(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(a(a(y0))))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(a(cons_b(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(a(y0))))))) -> c1(ENCARG(a(cons_b(a(cons_b(a(y0)))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(cons_b(a(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(cons_b(cons_b(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1, c7_2, c4, c7, c7_3


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

(145) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID))
Use forward instantiation to replace B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))) by none

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(a(z0)) -> a(encArg(z0))
   encArg(cons_b(z0)) -> b(encArg(z0))
   b(a(b(z0))) -> b(a(a(a(b(z0)))))
   b(a(a(a(b(a(a(b(z0)))))))) -> b(a(a(b(a(a(b(a(a(a(b(b(z0))))))))))))
   b(a(a(a(b(a(a(a(b(z0))))))))) -> b(z0)
   b(a(a(a(b(b(b(z0))))))) -> b(b(b(a(a(a(b(z0)))))))
   b(a(a(b(b(z0))))) -> b(z0)
   b(b(a(a(b(z0))))) -> b(z0)
   b(a(b(a(a(a(b(z0))))))) -> b(z0)
Tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   ENCARG(cons_b(a(a(z0)))) -> c1(B(a(a(encArg(z0)))), ENCARG(a(a(z0))))
   ENCARG(cons_b(a(cons_b(z0)))) -> c1(B(a(b(encArg(z0)))), ENCARG(a(cons_b(z0))))
   ENCARG(cons_b(cons_b(a(z0)))) -> c1(B(b(a(encArg(z0)))), ENCARG(cons_b(a(z0))))
   ENCARG(cons_b(cons_b(cons_b(z0)))) -> c1(B(b(b(encArg(z0)))), ENCARG(cons_b(cons_b(z0))))
   ENCODE_B(a(a(z0))) -> c3(B(a(a(encArg(z0)))))
   ENCODE_B(a(cons_b(z0))) -> c3(B(a(b(encArg(z0)))))
   ENCODE_B(cons_b(a(z0))) -> c3(B(b(a(encArg(z0)))))
   ENCODE_B(cons_b(cons_b(z0))) -> c3(B(b(b(encArg(z0)))))
   ENCARG(a(cons_b(a(a(y0))))) -> c(ENCARG(cons_b(a(a(y0)))))
   ENCARG(a(cons_b(a(cons_b(y0))))) -> c(ENCARG(cons_b(a(cons_b(y0)))))
   ENCARG(a(cons_b(cons_b(a(y0))))) -> c(ENCARG(cons_b(cons_b(a(y0)))))
   ENCARG(a(cons_b(cons_b(cons_b(y0))))) -> c(ENCARG(cons_b(cons_b(cons_b(y0)))))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(y0))))))) -> c4(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(y0))))))))))) -> c7(B(a(a(a(b(b(b(b(b(y0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   ENCARG(cons_b(a(cons_b(a(a(y0)))))) -> c1(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))) -> c1(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   ENCARG(a(a(a(y0)))) -> c(ENCARG(a(a(y0))))
   ENCARG(a(a(cons_b(a(a(y0)))))) -> c(ENCARG(a(cons_b(a(a(y0))))))
   ENCARG(a(a(cons_b(a(cons_b(y0)))))) -> c(ENCARG(a(cons_b(a(cons_b(y0))))))
   ENCARG(a(a(cons_b(a(y0))))) -> c(ENCARG(a(cons_b(a(y0)))))
   ENCARG(a(a(cons_b(cons_b(a(y0)))))) -> c(ENCARG(a(cons_b(cons_b(a(y0))))))
   ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))) -> c(ENCARG(a(cons_b(cons_b(cons_b(y0))))))
   ENCARG(a(cons_b(a(cons_b(a(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(a(cons_b(y0)))))))
   ENCARG(a(cons_b(a(cons_b(a(y0)))))) -> c(ENCARG(cons_b(a(cons_b(a(y0))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(a(y0)))))))
   ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))) -> c(ENCARG(cons_b(a(cons_b(cons_b(cons_b(y0)))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   ENCARG(cons_b(a(a(a(y0))))) -> c1(ENCARG(a(a(a(y0)))))
   ENCARG(cons_b(a(a(cons_b(a(a(y0))))))) -> c1(ENCARG(a(a(cons_b(a(a(y0)))))))
   ENCARG(cons_b(a(a(cons_b(a(cons_b(y0))))))) -> c1(ENCARG(a(a(cons_b(a(cons_b(y0)))))))
   ENCARG(cons_b(a(a(cons_b(a(y0)))))) -> c1(ENCARG(a(a(cons_b(a(y0))))))
   ENCARG(cons_b(a(a(cons_b(cons_b(a(y0))))))) -> c1(ENCARG(a(a(cons_b(cons_b(a(y0)))))))
   ENCARG(cons_b(a(a(cons_b(cons_b(cons_b(y0))))))) -> c1(ENCARG(a(a(cons_b(cons_b(cons_b(y0)))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(a(a(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(a(a(y0))))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(a(cons_b(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(a(cons_b(y0))))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(a(y0))))))) -> c1(ENCARG(a(cons_b(a(cons_b(a(y0)))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(cons_b(a(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(cons_b(a(y0))))))))
   ENCARG(cons_b(a(cons_b(a(cons_b(cons_b(cons_b(y0)))))))) -> c1(ENCARG(a(cons_b(a(cons_b(cons_b(cons_b(y0))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))))
S tuples:
   B(a(a(a(b(a(a(b(x0)))))))) -> c5(B(a(a(a(b(b(x0)))))), B(x0))
   B(a(b(a(a(b(a(a(b(y0))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(y0))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(b(y0)))))))))))))))
   B(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(y0))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(b(b(b(b(b(a(a(a(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(b(a(a(b(y0)))))) -> c4(B(a(a(a(b(a(a(b(y0)))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(b(z0)))))))))))))) -> c5(B(a(a(b(a(a(b(a(a(b(a(a(b(a(a(a(b(b(z0)))))))))))))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(b(z0))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(b(z0)))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(a(a(a(b(z0))))))))))))))) -> c5(B(a(a(b(a(a(b(z0))))))), B(a(a(b(a(a(a(b(b(a(a(b(a(a(a(b(z0)))))))))))))))), B(a(a(a(b(b(a(a(b(a(a(a(b(z0))))))))))))))
   B(a(a(a(b(a(a(b(a(a(b(x0))))))))))) -> c5(B(a(a(b(a(a(a(b(b(a(a(b(x0)))))))))))), B(a(a(a(b(b(a(a(b(x0))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(y0))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(b(b(b(a(a(a(b(y0))))))))) -> c4
   B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))) -> c7
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(y0))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(y0)))))))))))), B(a(a(a(b(b(b(b(b(b(b(y0))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(a(a(a(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(y0))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(a(a(a(b(y0))))))))))))))), B(b(a(a(a(b(b(b(b(b(a(a(a(b(y0)))))))))))))), B(a(a(a(b(b(b(b(b(a(a(a(b(y0))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(b(b(b(b(b(a(a(a(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))), B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c4(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0)))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(y0))))))))))))))))))))))
   B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))))) -> c7(B(b(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0)))))))))))))))))))))))), B(a(a(a(b(b(b(b(b(b(b(b(b(b(b(b(b(b(b(a(a(a(b(y0))))))))))))))))))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, b_1

Defined Pair Symbols:   B_1, ENCARG_1, ENCODE_B_1

Compound Symbols:   c5_2, c1_2, c3_1, c_1, c4_1, c5_3, c7_1, c1_1, c7_2, c4, c7, c7_3