/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 41 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 0 ms]
    (10) typed CpxTrs
    (11) RewriteLemmaProof [LOWER BOUND(ID), 435 ms]
    (12) BOUNDS(1, INF)
(13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(14) TRS for Loop Detection
(15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(16) CpxTRS
(17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
    (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (22) CpxWeightedTrs
    (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (24) CpxTypedWeightedTrs
    (25) CompletionProof [UPPER BOUND(ID), 0 ms]
    (26) CpxTypedWeightedCompleteTrs
        (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (28) CpxRNTS
    (29) CompletionProof [UPPER BOUND(ID), 0 ms]
    (30) CpxTypedWeightedCompleteTrs
        (31) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
        (34) CpxRNTS
        (35) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
        (36) CpxRNTS
(37) CpxTrsToCdtProof [UPPER BOUND(ID), 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), 0 ms]
    (46) CdtProblem
    (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CdtProblem
    (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CdtProblem
    (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (52) CdtProblem
    (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (54) CdtProblem
    (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (56) CdtProblem
    (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (58) CdtProblem
    (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (60) CdtProblem
    (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (62) CdtProblem
    (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (64) CdtProblem
    (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (66) CdtProblem
    (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CdtProblem
    (69) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (70) CdtProblem
    (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) 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:

   0(0(0(0(x1)))) -> 0(1(1(1(x1))))
   1(1(0(1(x1)))) -> 0(0(0(0(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(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(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:

   0(0(0(0(x1)))) -> 0(1(1(1(x1))))
   1(1(0(1(x1)))) -> 0(0(0(0(x1))))

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

   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(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:

   0(0(0(0(x1)))) -> 0(1(1(1(x1))))
   1(1(0(1(x1)))) -> 0(0(0(0(x1))))

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

   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))

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

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

(6)
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:

   0(0(0(0(x1)))) -> 0(1(1(1(x1))))
   1(1(0(1(x1)))) -> 0(0(0(0(x1))))

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

   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))

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

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

(8)
Obligation:
Innermost TRS:
Rules:
0(0(0(0(x1)))) -> 0(1(1(1(x1))))
1(1(0(1(x1)))) -> 0(0(0(0(x1))))
encArg(cons_0(x_1)) -> 0(encArg(x_1))
encArg(cons_1(x_1)) -> 1(encArg(x_1))
encode_0(x_1) -> 0(encArg(x_1))
encode_1(x_1) -> 1(encArg(x_1))

Types:
0 :: 0:1:encArg:encode_0:encode_1 -> 0:1:encArg:encode_0:encode_1
1 :: 0:1:encArg:encode_0:encode_1 -> 0:1:encArg:encode_0:encode_1
encArg :: cons_0:cons_1 -> 0:1:encArg:encode_0:encode_1
cons_0 :: cons_0:cons_1 -> cons_0:cons_1
cons_1 :: cons_0:cons_1 -> cons_0:cons_1
encode_0 :: cons_0:cons_1 -> 0:1:encArg:encode_0:encode_1
encode_1 :: cons_0:cons_1 -> 0:1:encArg:encode_0:encode_1
hole_0:1:encArg:encode_0:encode_11_2 :: 0:1:encArg:encode_0:encode_1
hole_cons_0:cons_12_2 :: cons_0:cons_1
gen_cons_0:cons_13_2 :: Nat -> cons_0:cons_1

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

(9) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
0, 1, encArg

They will be analysed ascendingly in the following order:
0 = 1
0 < encArg
1 < encArg

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

(10)
Obligation:
Innermost TRS:
Rules:
0(0(0(0(x1)))) -> 0(1(1(1(x1))))
1(1(0(1(x1)))) -> 0(0(0(0(x1))))
encArg(cons_0(x_1)) -> 0(encArg(x_1))
encArg(cons_1(x_1)) -> 1(encArg(x_1))
encode_0(x_1) -> 0(encArg(x_1))
encode_1(x_1) -> 1(encArg(x_1))

Types:
0 :: 0:1:encArg:encode_0:encode_1 -> 0:1:encArg:encode_0:encode_1
1 :: 0:1:encArg:encode_0:encode_1 -> 0:1:encArg:encode_0:encode_1
encArg :: cons_0:cons_1 -> 0:1:encArg:encode_0:encode_1
cons_0 :: cons_0:cons_1 -> cons_0:cons_1
cons_1 :: cons_0:cons_1 -> cons_0:cons_1
encode_0 :: cons_0:cons_1 -> 0:1:encArg:encode_0:encode_1
encode_1 :: cons_0:cons_1 -> 0:1:encArg:encode_0:encode_1
hole_0:1:encArg:encode_0:encode_11_2 :: 0:1:encArg:encode_0:encode_1
hole_cons_0:cons_12_2 :: cons_0:cons_1
gen_cons_0:cons_13_2 :: Nat -> cons_0:cons_1


Generator Equations:
gen_cons_0:cons_13_2(0) <=> hole_cons_0:cons_12_2
gen_cons_0:cons_13_2(+(x, 1)) <=> cons_0(gen_cons_0:cons_13_2(x))


The following defined symbols remain to be analysed:
1, 0, encArg

They will be analysed ascendingly in the following order:
0 = 1
0 < encArg
1 < encArg

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

(11) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
encArg(gen_cons_0:cons_13_2(+(1, n11_2))) -> *4_2, rt in Omega(0)

Induction Base:
encArg(gen_cons_0:cons_13_2(+(1, 0)))

Induction Step:
encArg(gen_cons_0:cons_13_2(+(1, +(n11_2, 1)))) ->_R^Omega(0)
0(encArg(gen_cons_0:cons_13_2(+(1, n11_2)))) ->_IH
0(*4_2)

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

(12)
BOUNDS(1, INF)

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

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

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

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


The TRS R consists of the following rules:

   0(0(0(0(x1)))) -> 0(1(1(1(x1))))
   1(1(0(1(x1)))) -> 0(0(0(0(x1))))

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

   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))

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

(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:

   0(0(0(0(x1)))) -> 0(1(1(1(x1))))
   1(1(0(1(x1)))) -> 0(0(0(0(x1))))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(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:

   0(c_0(c_0(c_0(x1)))) -> 0(1(1(1(x1))))
   1(c_1(c_0(c_1(x1)))) -> 0(0(0(0(x1))))

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

   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   0(x0) -> c_0(x0)
   1(x0) -> c_1(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:

   0(c_0(c_0(c_0(x1)))) -> 0(1(1(1(x1)))) [1]
   1(c_1(c_0(c_1(x1)))) -> 0(0(0(0(x1)))) [1]
   encArg(cons_0(x_1)) -> 0(encArg(x_1)) [0]
   encArg(cons_1(x_1)) -> 1(encArg(x_1)) [0]
   encode_0(x_1) -> 0(encArg(x_1)) [0]
   encode_1(x_1) -> 1(encArg(x_1)) [0]
   0(x0) -> c_0(x0) [0]
   1(x0) -> c_1(x0) [0]

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

(21) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID))
Renamed defined symbols to avoid conflicts with arithmetic symbols:

0 => 0'
1 => 1'

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

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


The TRS R consists of the following rules:

   0'(c_0(c_0(c_0(x1)))) -> 0'(1'(1'(1'(x1)))) [1]
   1'(c_1(c_0(c_1(x1)))) -> 0'(0'(0'(0'(x1)))) [1]
   encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0]
   encArg(cons_1(x_1)) -> 1'(encArg(x_1)) [0]
   encode_0(x_1) -> 0'(encArg(x_1)) [0]
   encode_1(x_1) -> 1'(encArg(x_1)) [0]
   0'(x0) -> c_0(x0) [0]
   1'(x0) -> c_1(x0) [0]

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

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

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

   0'(c_0(c_0(c_0(x1)))) -> 0'(1'(1'(1'(x1)))) [1]
   1'(c_1(c_0(c_1(x1)))) -> 0'(0'(0'(0'(x1)))) [1]
   encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0]
   encArg(cons_1(x_1)) -> 1'(encArg(x_1)) [0]
   encode_0(x_1) -> 0'(encArg(x_1)) [0]
   encode_1(x_1) -> 1'(encArg(x_1)) [0]
   0'(x0) -> c_0(x0) [0]
   1'(x0) -> c_1(x0) [0]

The TRS has the following type information:
0' :: c_0:c_1 -> c_0:c_1
c_0 :: c_0:c_1 -> c_0:c_1
1' :: c_0:c_1 -> c_0:c_1
c_1 :: c_0:c_1 -> c_0:c_1
encArg :: cons_0:cons_1 -> c_0:c_1
cons_0 :: cons_0:cons_1 -> cons_0:cons_1
cons_1 :: cons_0:cons_1 -> cons_0:cons_1
encode_0 :: cons_0:cons_1 -> c_0:c_1
encode_1 :: cons_0:cons_1 -> c_0:c_1

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

(25) 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_0(v0) -> null_encode_0 [0]
   encode_1(v0) -> null_encode_1 [0]
   0'(v0) -> null_0' [0]
   1'(v0) -> null_1' [0]

And the following fresh constants:    null_encArg, null_encode_0, null_encode_1, null_0', null_1', const

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

(26)
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:

   0'(c_0(c_0(c_0(x1)))) -> 0'(1'(1'(1'(x1)))) [1]
   1'(c_1(c_0(c_1(x1)))) -> 0'(0'(0'(0'(x1)))) [1]
   encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0]
   encArg(cons_1(x_1)) -> 1'(encArg(x_1)) [0]
   encode_0(x_1) -> 0'(encArg(x_1)) [0]
   encode_1(x_1) -> 1'(encArg(x_1)) [0]
   0'(x0) -> c_0(x0) [0]
   1'(x0) -> c_1(x0) [0]
   encArg(v0) -> null_encArg [0]
   encode_0(v0) -> null_encode_0 [0]
   encode_1(v0) -> null_encode_1 [0]
   0'(v0) -> null_0' [0]
   1'(v0) -> null_1' [0]

The TRS has the following type information:
0' :: c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_0':null_1' -> c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_0':null_1'
c_0 :: c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_0':null_1' -> c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_0':null_1'
1' :: c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_0':null_1' -> c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_0':null_1'
c_1 :: c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_0':null_1' -> c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_0':null_1'
encArg :: cons_0:cons_1 -> c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_0':null_1'
cons_0 :: cons_0:cons_1 -> cons_0:cons_1
cons_1 :: cons_0:cons_1 -> cons_0:cons_1
encode_0 :: cons_0:cons_1 -> c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_0':null_1'
encode_1 :: cons_0:cons_1 -> c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_0':null_1'
null_encArg :: c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_0':null_1'
null_encode_0 :: c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_0':null_1'
null_encode_1 :: c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_0':null_1'
null_0' :: c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_0':null_1'
null_1' :: c_0:c_1:null_encArg:null_encode_0:null_encode_1:null_0':null_1'
const :: cons_0:cons_1

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:

   null_encArg => 0
   null_encode_0 => 0
   null_encode_1 => 0
   null_0' => 0
   null_1' => 0
   const => 0

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

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

   0'(z) -{ 1 }-> 0'(1'(1'(1'(x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   0'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   0'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   1'(z) -{ 1 }-> 0'(0'(0'(0'(x1)))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   1'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   1'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1'(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> 0'(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_0(z) -{ 0 }-> 0'(encArg(x_1)) :|: x_1 >= 0, z = x_1
   encode_0(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_1(z) -{ 0 }-> 1'(encArg(x_1)) :|: x_1 >= 0, z = x_1
   encode_1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0

Only complete derivations are relevant for the runtime complexity.

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

(29) 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_0_1
   encode_1_1
   0'_1
   1'_1

Due to the following rules being added:

   encArg(v0) -> const [0]
   encode_0(v0) -> const [0]
   encode_1(v0) -> const [0]
   0'(v0) -> const [0]
   1'(v0) -> const [0]

And the following fresh constants:    const, const1

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

(30)
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:

   0'(c_0(c_0(c_0(x1)))) -> 0'(1'(1'(1'(x1)))) [1]
   1'(c_1(c_0(c_1(x1)))) -> 0'(0'(0'(0'(x1)))) [1]
   encArg(cons_0(x_1)) -> 0'(encArg(x_1)) [0]
   encArg(cons_1(x_1)) -> 1'(encArg(x_1)) [0]
   encode_0(x_1) -> 0'(encArg(x_1)) [0]
   encode_1(x_1) -> 1'(encArg(x_1)) [0]
   0'(x0) -> c_0(x0) [0]
   1'(x0) -> c_1(x0) [0]
   encArg(v0) -> const [0]
   encode_0(v0) -> const [0]
   encode_1(v0) -> const [0]
   0'(v0) -> const [0]
   1'(v0) -> const [0]

The TRS has the following type information:
0' :: c_0:c_1:const -> c_0:c_1:const
c_0 :: c_0:c_1:const -> c_0:c_1:const
1' :: c_0:c_1:const -> c_0:c_1:const
c_1 :: c_0:c_1:const -> c_0:c_1:const
encArg :: cons_0:cons_1 -> c_0:c_1:const
cons_0 :: cons_0:cons_1 -> cons_0:cons_1
cons_1 :: cons_0:cons_1 -> cons_0:cons_1
encode_0 :: cons_0:cons_1 -> c_0:c_1:const
encode_1 :: cons_0:cons_1 -> c_0:c_1:const
const :: c_0:c_1:const
const1 :: cons_0:cons_1

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

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

(32)
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:

   0'(c_0(c_0(c_0(c_1(c_0(c_1(x1'))))))) -> 0'(1'(1'(0'(0'(0'(0'(x1'))))))) [2]
   0'(c_0(c_0(c_0(x1)))) -> 0'(1'(1'(c_1(x1)))) [1]
   0'(c_0(c_0(c_0(x1)))) -> 0'(1'(1'(const))) [1]
   1'(c_1(c_0(c_1(c_0(c_0(c_0(x1''))))))) -> 0'(0'(0'(0'(1'(1'(1'(x1''))))))) [2]
   1'(c_1(c_0(c_1(x1)))) -> 0'(0'(0'(c_0(x1)))) [1]
   1'(c_1(c_0(c_1(x1)))) -> 0'(0'(0'(const))) [1]
   encArg(cons_0(cons_0(x_1'))) -> 0'(0'(encArg(x_1'))) [0]
   encArg(cons_0(cons_1(x_1''))) -> 0'(1'(encArg(x_1''))) [0]
   encArg(cons_0(x_1)) -> 0'(const) [0]
   encArg(cons_1(cons_0(x_11))) -> 1'(0'(encArg(x_11))) [0]
   encArg(cons_1(cons_1(x_12))) -> 1'(1'(encArg(x_12))) [0]
   encArg(cons_1(x_1)) -> 1'(const) [0]
   encode_0(cons_0(x_13)) -> 0'(0'(encArg(x_13))) [0]
   encode_0(cons_1(x_14)) -> 0'(1'(encArg(x_14))) [0]
   encode_0(x_1) -> 0'(const) [0]
   encode_1(cons_0(x_15)) -> 1'(0'(encArg(x_15))) [0]
   encode_1(cons_1(x_16)) -> 1'(1'(encArg(x_16))) [0]
   encode_1(x_1) -> 1'(const) [0]
   0'(x0) -> c_0(x0) [0]
   1'(x0) -> c_1(x0) [0]
   encArg(v0) -> const [0]
   encode_0(v0) -> const [0]
   encode_1(v0) -> const [0]
   0'(v0) -> const [0]
   1'(v0) -> const [0]

The TRS has the following type information:
0' :: c_0:c_1:const -> c_0:c_1:const
c_0 :: c_0:c_1:const -> c_0:c_1:const
1' :: c_0:c_1:const -> c_0:c_1:const
c_1 :: c_0:c_1:const -> c_0:c_1:const
encArg :: cons_0:cons_1 -> c_0:c_1:const
cons_0 :: cons_0:cons_1 -> cons_0:cons_1
cons_1 :: cons_0:cons_1 -> cons_0:cons_1
encode_0 :: cons_0:cons_1 -> c_0:c_1:const
encode_1 :: cons_0:cons_1 -> c_0:c_1:const
const :: c_0:c_1:const
const1 :: cons_0:cons_1

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:

   const => 0
   const1 => 0

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

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

   0'(z) -{ 2 }-> 0'(1'(1'(0'(0'(0'(0'(x1'))))))) :|: z = 1 + (1 + (1 + (1 + (1 + (1 + x1'))))), x1' >= 0
   0'(z) -{ 1 }-> 0'(1'(1'(0))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   0'(z) -{ 1 }-> 0'(1'(1'(1 + x1))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   0'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   0'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   1'(z) -{ 2 }-> 0'(0'(0'(0'(1'(1'(1'(x1''))))))) :|: x1'' >= 0, z = 1 + (1 + (1 + (1 + (1 + (1 + x1'')))))
   1'(z) -{ 1 }-> 0'(0'(0'(0))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   1'(z) -{ 1 }-> 0'(0'(0'(1 + x1))) :|: x1 >= 0, z = 1 + (1 + (1 + x1))
   1'(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   1'(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1'(1'(encArg(x_12))) :|: z = 1 + (1 + x_12), x_12 >= 0
   encArg(z) -{ 0 }-> 1'(0'(encArg(x_11))) :|: x_11 >= 0, z = 1 + (1 + x_11)
   encArg(z) -{ 0 }-> 1'(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> 0'(1'(encArg(x_1''))) :|: z = 1 + (1 + x_1''), x_1'' >= 0
   encArg(z) -{ 0 }-> 0'(0'(encArg(x_1'))) :|: z = 1 + (1 + x_1'), x_1' >= 0
   encArg(z) -{ 0 }-> 0'(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_0(z) -{ 0 }-> 0'(1'(encArg(x_14))) :|: x_14 >= 0, z = 1 + x_14
   encode_0(z) -{ 0 }-> 0'(0'(encArg(x_13))) :|: z = 1 + x_13, x_13 >= 0
   encode_0(z) -{ 0 }-> 0'(0) :|: x_1 >= 0, z = x_1
   encode_0(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_1(z) -{ 0 }-> 1'(1'(encArg(x_16))) :|: z = 1 + x_16, x_16 >= 0
   encode_1(z) -{ 0 }-> 1'(0'(encArg(x_15))) :|: x_15 >= 0, z = 1 + x_15
   encode_1(z) -{ 0 }-> 1'(0) :|: x_1 >= 0, z = x_1
   encode_1(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


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

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

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

   0'(z) -{ 2 }-> 0'(1'(1'(0'(0'(0'(0'(z - 6))))))) :|: z - 6 >= 0
   0'(z) -{ 1 }-> 0'(1'(1'(0))) :|: z - 3 >= 0
   0'(z) -{ 1 }-> 0'(1'(1'(1 + (z - 3)))) :|: z - 3 >= 0
   0'(z) -{ 0 }-> 0 :|: z >= 0
   0'(z) -{ 0 }-> 1 + z :|: z >= 0
   1'(z) -{ 2 }-> 0'(0'(0'(0'(1'(1'(1'(z - 6))))))) :|: z - 6 >= 0
   1'(z) -{ 1 }-> 0'(0'(0'(0))) :|: z - 3 >= 0
   1'(z) -{ 1 }-> 0'(0'(0'(1 + (z - 3)))) :|: z - 3 >= 0
   1'(z) -{ 0 }-> 0 :|: z >= 0
   1'(z) -{ 0 }-> 1 + z :|: z >= 0
   encArg(z) -{ 0 }-> 1'(1'(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1'(0'(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 1'(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> 0'(1'(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0'(0'(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> 0'(0) :|: z - 1 >= 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encode_0(z) -{ 0 }-> 0'(1'(encArg(z - 1))) :|: z - 1 >= 0
   encode_0(z) -{ 0 }-> 0'(0'(encArg(z - 1))) :|: z - 1 >= 0
   encode_0(z) -{ 0 }-> 0'(0) :|: z >= 0
   encode_0(z) -{ 0 }-> 0 :|: z >= 0
   encode_1(z) -{ 0 }-> 1'(1'(encArg(z - 1))) :|: z - 1 >= 0
   encode_1(z) -{ 0 }-> 1'(0'(encArg(z - 1))) :|: z - 1 >= 0
   encode_1(z) -{ 0 }-> 1'(0) :|: z >= 0
   encode_1(z) -{ 0 }-> 0 :|: z >= 0


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

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

(38)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   encode_0(z0) -> 0(encArg(z0))
   encode_1(z0) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0))
   ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0))
   ENCODE_0(z0) -> c2(0'(encArg(z0)), ENCARG(z0))
   ENCODE_1(z0) -> c3(1'(encArg(z0)), ENCARG(z0))
   0'(0(0(0(z0)))) -> c4(0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0))
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
S tuples:
   0'(0(0(0(z0)))) -> c4(0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0))
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
K tuples:none
Defined Rule Symbols:   0_1, 1_1, encArg_1, encode_0_1, encode_1_1

Defined Pair Symbols:   ENCARG_1, ENCODE_0_1, ENCODE_1_1, 0'_1, 1'_1

Compound Symbols:   c_2, c1_2, c2_2, c3_2, c4_4, c5_4


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

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

(40)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   encode_0(z0) -> 0(encArg(z0))
   encode_1(z0) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0))
   ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0))
   0'(0(0(0(z0)))) -> c4(0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0))
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   ENCODE_0(z0) -> c6(0'(encArg(z0)))
   ENCODE_0(z0) -> c6(ENCARG(z0))
   ENCODE_1(z0) -> c6(1'(encArg(z0)))
   ENCODE_1(z0) -> c6(ENCARG(z0))
S tuples:
   0'(0(0(0(z0)))) -> c4(0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0))
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
K tuples:none
Defined Rule Symbols:   0_1, 1_1, encArg_1, encode_0_1, encode_1_1

Defined Pair Symbols:   ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1

Compound Symbols:   c_2, c1_2, c4_4, c5_4, c6_1


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

(41) CdtLeafRemovalProof (ComplexityIfPolyImplication)
Removed 2 leading nodes:
   ENCODE_0(z0) -> c6(ENCARG(z0))
   ENCODE_1(z0) -> c6(ENCARG(z0))

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

(42)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   encode_0(z0) -> 0(encArg(z0))
   encode_1(z0) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0))
   ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0))
   0'(0(0(0(z0)))) -> c4(0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0))
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   ENCODE_0(z0) -> c6(0'(encArg(z0)))
   ENCODE_1(z0) -> c6(1'(encArg(z0)))
S tuples:
   0'(0(0(0(z0)))) -> c4(0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0))
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
K tuples:none
Defined Rule Symbols:   0_1, 1_1, encArg_1, encode_0_1, encode_1_1

Defined Pair Symbols:   ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1

Compound Symbols:   c_2, c1_2, c4_4, c5_4, c6_1


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

(43) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   encode_0(z0) -> 0(encArg(z0))
   encode_1(z0) -> 1(encArg(z0))

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0))
   ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0))
   0'(0(0(0(z0)))) -> c4(0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0))
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   ENCODE_0(z0) -> c6(0'(encArg(z0)))
   ENCODE_1(z0) -> c6(1'(encArg(z0)))
S tuples:
   0'(0(0(0(z0)))) -> c4(0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0))
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1, 1_1

Defined Pair Symbols:   ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1

Compound Symbols:   c_2, c1_2, c4_4, c5_4, c6_1


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

(45) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0)))
   ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0)))

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0))
   0'(0(0(0(z0)))) -> c4(0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0))
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   ENCODE_0(z0) -> c6(0'(encArg(z0)))
   ENCODE_1(z0) -> c6(1'(encArg(z0)))
   ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0)))
   ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0)))
S tuples:
   0'(0(0(0(z0)))) -> c4(0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0))
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1, 1_1

Defined Pair Symbols:   ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1

Compound Symbols:   c1_2, c4_4, c5_4, c6_1, c_2


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

(47) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) by 
   ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0)))
   ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0)))

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   0'(0(0(0(z0)))) -> c4(0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0))
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   ENCODE_0(z0) -> c6(0'(encArg(z0)))
   ENCODE_1(z0) -> c6(1'(encArg(z0)))
   ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0)))
   ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0)))
   ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0)))
   ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0)))
S tuples:
   0'(0(0(0(z0)))) -> c4(0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0))
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1, 1_1

Defined Pair Symbols:   0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1, ENCARG_1

Compound Symbols:   c4_4, c5_4, c6_1, c_2, c1_2


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

(49) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace 0'(0(0(0(z0)))) -> c4(0'(1(1(1(z0)))), 1'(1(1(z0))), 1'(1(z0)), 1'(z0)) by 
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(0(0(0(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))

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

(50)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   ENCODE_0(z0) -> c6(0'(encArg(z0)))
   ENCODE_1(z0) -> c6(1'(encArg(z0)))
   ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0)))
   ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0)))
   ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0)))
   ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0)))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(0(0(0(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
S tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(0(0(0(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1, 1_1

Defined Pair Symbols:   1'_1, ENCODE_0_1, ENCODE_1_1, ENCARG_1, 0'_1

Compound Symbols:   c5_4, c6_1, c_2, c1_2, c4_4, c4_1


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

(51) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_0(z0) -> c6(0'(encArg(z0))) by 
   ENCODE_0(cons_0(z0)) -> c6(0'(0(encArg(z0))))
   ENCODE_0(cons_1(z0)) -> c6(0'(1(encArg(z0))))

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

(52)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   ENCODE_1(z0) -> c6(1'(encArg(z0)))
   ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0)))
   ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0)))
   ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0)))
   ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0)))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(0(0(0(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
   ENCODE_0(cons_0(z0)) -> c6(0'(0(encArg(z0))))
   ENCODE_0(cons_1(z0)) -> c6(0'(1(encArg(z0))))
S tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(0(0(0(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1, 1_1

Defined Pair Symbols:   1'_1, ENCODE_1_1, ENCARG_1, 0'_1, ENCODE_0_1

Compound Symbols:   c5_4, c6_1, c_2, c1_2, c4_4, c4_1


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

(53) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_1(z0) -> c6(1'(encArg(z0))) by 
   ENCODE_1(cons_0(z0)) -> c6(1'(0(encArg(z0))))
   ENCODE_1(cons_1(z0)) -> c6(1'(1(encArg(z0))))

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

(54)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0)))
   ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0)))
   ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0)))
   ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0)))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(0(0(0(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
   ENCODE_0(cons_0(z0)) -> c6(0'(0(encArg(z0))))
   ENCODE_0(cons_1(z0)) -> c6(0'(1(encArg(z0))))
   ENCODE_1(cons_0(z0)) -> c6(1'(0(encArg(z0))))
   ENCODE_1(cons_1(z0)) -> c6(1'(1(encArg(z0))))
S tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(0(0(0(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1, 1_1

Defined Pair Symbols:   1'_1, ENCARG_1, 0'_1, ENCODE_0_1, ENCODE_1_1

Compound Symbols:   c5_4, c_2, c1_2, c4_4, c4_1, c6_1


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

(55) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0))) by 
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))

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

(56)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0)))
   ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0)))
   ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0)))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(0(0(0(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
   ENCODE_0(cons_0(z0)) -> c6(0'(0(encArg(z0))))
   ENCODE_0(cons_1(z0)) -> c6(0'(1(encArg(z0))))
   ENCODE_1(cons_0(z0)) -> c6(1'(0(encArg(z0))))
   ENCODE_1(cons_1(z0)) -> c6(1'(1(encArg(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))
S tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(0(0(0(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1, 1_1

Defined Pair Symbols:   1'_1, ENCARG_1, 0'_1, ENCODE_0_1, ENCODE_1_1

Compound Symbols:   c5_4, c_2, c1_2, c4_4, c4_1, c6_1


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

(57) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) by 
   ENCARG(cons_0(cons_1(cons_0(z0)))) -> c(0'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0))))
   ENCARG(cons_0(cons_1(cons_1(z0)))) -> c(0'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0))))

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

(58)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0)))
   ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0)))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(0(0(0(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
   ENCODE_0(cons_0(z0)) -> c6(0'(0(encArg(z0))))
   ENCODE_0(cons_1(z0)) -> c6(0'(1(encArg(z0))))
   ENCODE_1(cons_0(z0)) -> c6(1'(0(encArg(z0))))
   ENCODE_1(cons_1(z0)) -> c6(1'(1(encArg(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))
   ENCARG(cons_0(cons_1(cons_0(z0)))) -> c(0'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0))))
   ENCARG(cons_0(cons_1(cons_1(z0)))) -> c(0'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0))))
S tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(0(0(0(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1, 1_1

Defined Pair Symbols:   1'_1, ENCARG_1, 0'_1, ENCODE_0_1, ENCODE_1_1

Compound Symbols:   c5_4, c1_2, c4_4, c4_1, c6_1, c_2


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

(59) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0))) by 
   ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))

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

(60)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0)))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(0(0(0(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
   ENCODE_0(cons_0(z0)) -> c6(0'(0(encArg(z0))))
   ENCODE_0(cons_1(z0)) -> c6(0'(1(encArg(z0))))
   ENCODE_1(cons_0(z0)) -> c6(1'(0(encArg(z0))))
   ENCODE_1(cons_1(z0)) -> c6(1'(1(encArg(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))
   ENCARG(cons_0(cons_1(cons_0(z0)))) -> c(0'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0))))
   ENCARG(cons_0(cons_1(cons_1(z0)))) -> c(0'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0))))
   ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))
S tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(0(0(0(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1, 1_1

Defined Pair Symbols:   1'_1, ENCARG_1, 0'_1, ENCODE_0_1, ENCODE_1_1

Compound Symbols:   c5_4, c1_2, c4_4, c4_1, c6_1, c_2


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

(61) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) by 
   ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0))))
   ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0))))

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

(62)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(0(0(0(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
   ENCODE_0(cons_0(z0)) -> c6(0'(0(encArg(z0))))
   ENCODE_0(cons_1(z0)) -> c6(0'(1(encArg(z0))))
   ENCODE_1(cons_0(z0)) -> c6(1'(0(encArg(z0))))
   ENCODE_1(cons_1(z0)) -> c6(1'(1(encArg(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))
   ENCARG(cons_0(cons_1(cons_0(z0)))) -> c(0'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0))))
   ENCARG(cons_0(cons_1(cons_1(z0)))) -> c(0'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0))))
   ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))
   ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0))))
   ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0))))
S tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(0(0(0(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1, 1_1

Defined Pair Symbols:   1'_1, 0'_1, ENCODE_0_1, ENCODE_1_1, ENCARG_1

Compound Symbols:   c5_4, c4_4, c4_1, c6_1, c_2, c1_2


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

(63) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace 0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(0(0(0(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0))))) by 
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(1(1(1(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(1(0(1(0(z0)))))))) -> c4(0'(1(1(0(0(1(1(1(z0)))))))), 1'(1(1(1(0(1(0(z0))))))), 1'(1(1(0(1(0(z0)))))), 1'(1(0(1(0(z0))))))
   0'(0(0(0(1(0(1(0(0(z0))))))))) -> c4(0'(1(1(0(0(0(1(1(1(z0))))))))), 1'(1(1(1(0(1(0(0(z0)))))))), 1'(1(1(0(1(0(0(z0))))))), 1'(1(0(1(0(0(z0)))))))
   0'(0(0(0(1(0(1(0(0(0(z0)))))))))) -> c4(0'(1(1(0(0(0(0(1(1(1(z0)))))))))), 1'(1(1(1(0(1(0(0(0(z0))))))))), 1'(1(1(0(1(0(0(0(z0)))))))), 1'(1(0(1(0(0(0(z0))))))))

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

(64)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
   ENCODE_0(cons_0(z0)) -> c6(0'(0(encArg(z0))))
   ENCODE_0(cons_1(z0)) -> c6(0'(1(encArg(z0))))
   ENCODE_1(cons_0(z0)) -> c6(1'(0(encArg(z0))))
   ENCODE_1(cons_1(z0)) -> c6(1'(1(encArg(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))
   ENCARG(cons_0(cons_1(cons_0(z0)))) -> c(0'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0))))
   ENCARG(cons_0(cons_1(cons_1(z0)))) -> c(0'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0))))
   ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))
   ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0))))
   ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0))))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(1(1(1(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(1(0(1(0(z0)))))))) -> c4(0'(1(1(0(0(1(1(1(z0)))))))), 1'(1(1(1(0(1(0(z0))))))), 1'(1(1(0(1(0(z0)))))), 1'(1(0(1(0(z0))))))
   0'(0(0(0(1(0(1(0(0(z0))))))))) -> c4(0'(1(1(0(0(0(1(1(1(z0))))))))), 1'(1(1(1(0(1(0(0(z0)))))))), 1'(1(1(0(1(0(0(z0))))))), 1'(1(0(1(0(0(z0)))))))
   0'(0(0(0(1(0(1(0(0(0(z0)))))))))) -> c4(0'(1(1(0(0(0(0(1(1(1(z0)))))))))), 1'(1(1(1(0(1(0(0(0(z0))))))))), 1'(1(1(0(1(0(0(0(z0)))))))), 1'(1(0(1(0(0(0(z0))))))))
S tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(1(1(1(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(1(0(1(0(z0)))))))) -> c4(0'(1(1(0(0(1(1(1(z0)))))))), 1'(1(1(1(0(1(0(z0))))))), 1'(1(1(0(1(0(z0)))))), 1'(1(0(1(0(z0))))))
   0'(0(0(0(1(0(1(0(0(z0))))))))) -> c4(0'(1(1(0(0(0(1(1(1(z0))))))))), 1'(1(1(1(0(1(0(0(z0)))))))), 1'(1(1(0(1(0(0(z0))))))), 1'(1(0(1(0(0(z0)))))))
   0'(0(0(0(1(0(1(0(0(0(z0)))))))))) -> c4(0'(1(1(0(0(0(0(1(1(1(z0)))))))))), 1'(1(1(1(0(1(0(0(0(z0))))))))), 1'(1(1(0(1(0(0(0(z0)))))))), 1'(1(0(1(0(0(0(z0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1, 1_1

Defined Pair Symbols:   1'_1, 0'_1, ENCODE_0_1, ENCODE_1_1, ENCARG_1

Compound Symbols:   c5_4, c4_1, c6_1, c_2, c1_2, c4_4


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

(65) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_0(cons_0(z0)) -> c6(0'(0(encArg(z0)))) by 
   ENCODE_0(cons_0(cons_0(z0))) -> c6(0'(0(0(encArg(z0)))))
   ENCODE_0(cons_0(cons_1(z0))) -> c6(0'(0(1(encArg(z0)))))

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

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
   ENCODE_0(cons_1(z0)) -> c6(0'(1(encArg(z0))))
   ENCODE_1(cons_0(z0)) -> c6(1'(0(encArg(z0))))
   ENCODE_1(cons_1(z0)) -> c6(1'(1(encArg(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))
   ENCARG(cons_0(cons_1(cons_0(z0)))) -> c(0'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0))))
   ENCARG(cons_0(cons_1(cons_1(z0)))) -> c(0'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0))))
   ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))
   ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0))))
   ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0))))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(1(1(1(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(1(0(1(0(z0)))))))) -> c4(0'(1(1(0(0(1(1(1(z0)))))))), 1'(1(1(1(0(1(0(z0))))))), 1'(1(1(0(1(0(z0)))))), 1'(1(0(1(0(z0))))))
   0'(0(0(0(1(0(1(0(0(z0))))))))) -> c4(0'(1(1(0(0(0(1(1(1(z0))))))))), 1'(1(1(1(0(1(0(0(z0)))))))), 1'(1(1(0(1(0(0(z0))))))), 1'(1(0(1(0(0(z0)))))))
   0'(0(0(0(1(0(1(0(0(0(z0)))))))))) -> c4(0'(1(1(0(0(0(0(1(1(1(z0)))))))))), 1'(1(1(1(0(1(0(0(0(z0))))))))), 1'(1(1(0(1(0(0(0(z0)))))))), 1'(1(0(1(0(0(0(z0))))))))
   ENCODE_0(cons_0(cons_0(z0))) -> c6(0'(0(0(encArg(z0)))))
   ENCODE_0(cons_0(cons_1(z0))) -> c6(0'(0(1(encArg(z0)))))
S tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(1(1(1(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(1(0(1(0(z0)))))))) -> c4(0'(1(1(0(0(1(1(1(z0)))))))), 1'(1(1(1(0(1(0(z0))))))), 1'(1(1(0(1(0(z0)))))), 1'(1(0(1(0(z0))))))
   0'(0(0(0(1(0(1(0(0(z0))))))))) -> c4(0'(1(1(0(0(0(1(1(1(z0))))))))), 1'(1(1(1(0(1(0(0(z0)))))))), 1'(1(1(0(1(0(0(z0))))))), 1'(1(0(1(0(0(z0)))))))
   0'(0(0(0(1(0(1(0(0(0(z0)))))))))) -> c4(0'(1(1(0(0(0(0(1(1(1(z0)))))))))), 1'(1(1(1(0(1(0(0(0(z0))))))))), 1'(1(1(0(1(0(0(0(z0)))))))), 1'(1(0(1(0(0(0(z0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1, 1_1

Defined Pair Symbols:   1'_1, 0'_1, ENCODE_0_1, ENCODE_1_1, ENCARG_1

Compound Symbols:   c5_4, c4_1, c6_1, c_2, c1_2, c4_4


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

(67) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_0(cons_1(z0)) -> c6(0'(1(encArg(z0)))) by 
   ENCODE_0(cons_1(cons_0(z0))) -> c6(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_1(cons_1(z0))) -> c6(0'(1(1(encArg(z0)))))

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

(68)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
   ENCODE_1(cons_0(z0)) -> c6(1'(0(encArg(z0))))
   ENCODE_1(cons_1(z0)) -> c6(1'(1(encArg(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))
   ENCARG(cons_0(cons_1(cons_0(z0)))) -> c(0'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0))))
   ENCARG(cons_0(cons_1(cons_1(z0)))) -> c(0'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0))))
   ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))
   ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0))))
   ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0))))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(1(1(1(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(1(0(1(0(z0)))))))) -> c4(0'(1(1(0(0(1(1(1(z0)))))))), 1'(1(1(1(0(1(0(z0))))))), 1'(1(1(0(1(0(z0)))))), 1'(1(0(1(0(z0))))))
   0'(0(0(0(1(0(1(0(0(z0))))))))) -> c4(0'(1(1(0(0(0(1(1(1(z0))))))))), 1'(1(1(1(0(1(0(0(z0)))))))), 1'(1(1(0(1(0(0(z0))))))), 1'(1(0(1(0(0(z0)))))))
   0'(0(0(0(1(0(1(0(0(0(z0)))))))))) -> c4(0'(1(1(0(0(0(0(1(1(1(z0)))))))))), 1'(1(1(1(0(1(0(0(0(z0))))))))), 1'(1(1(0(1(0(0(0(z0)))))))), 1'(1(0(1(0(0(0(z0))))))))
   ENCODE_0(cons_0(cons_0(z0))) -> c6(0'(0(0(encArg(z0)))))
   ENCODE_0(cons_0(cons_1(z0))) -> c6(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_1(cons_0(z0))) -> c6(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_1(cons_1(z0))) -> c6(0'(1(1(encArg(z0)))))
S tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(1(1(1(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(1(0(1(0(z0)))))))) -> c4(0'(1(1(0(0(1(1(1(z0)))))))), 1'(1(1(1(0(1(0(z0))))))), 1'(1(1(0(1(0(z0)))))), 1'(1(0(1(0(z0))))))
   0'(0(0(0(1(0(1(0(0(z0))))))))) -> c4(0'(1(1(0(0(0(1(1(1(z0))))))))), 1'(1(1(1(0(1(0(0(z0)))))))), 1'(1(1(0(1(0(0(z0))))))), 1'(1(0(1(0(0(z0)))))))
   0'(0(0(0(1(0(1(0(0(0(z0)))))))))) -> c4(0'(1(1(0(0(0(0(1(1(1(z0)))))))))), 1'(1(1(1(0(1(0(0(0(z0))))))))), 1'(1(1(0(1(0(0(0(z0)))))))), 1'(1(0(1(0(0(0(z0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1, 1_1

Defined Pair Symbols:   1'_1, 0'_1, ENCODE_1_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c5_4, c4_1, c6_1, c_2, c1_2, c4_4


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

(69) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_1(cons_0(z0)) -> c6(1'(0(encArg(z0)))) by 
   ENCODE_1(cons_0(cons_0(z0))) -> c6(1'(0(0(encArg(z0)))))
   ENCODE_1(cons_0(cons_1(z0))) -> c6(1'(0(1(encArg(z0)))))

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

(70)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
   ENCODE_1(cons_1(z0)) -> c6(1'(1(encArg(z0))))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))
   ENCARG(cons_0(cons_1(cons_0(z0)))) -> c(0'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0))))
   ENCARG(cons_0(cons_1(cons_1(z0)))) -> c(0'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0))))
   ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))
   ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0))))
   ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0))))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(1(1(1(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(1(0(1(0(z0)))))))) -> c4(0'(1(1(0(0(1(1(1(z0)))))))), 1'(1(1(1(0(1(0(z0))))))), 1'(1(1(0(1(0(z0)))))), 1'(1(0(1(0(z0))))))
   0'(0(0(0(1(0(1(0(0(z0))))))))) -> c4(0'(1(1(0(0(0(1(1(1(z0))))))))), 1'(1(1(1(0(1(0(0(z0)))))))), 1'(1(1(0(1(0(0(z0))))))), 1'(1(0(1(0(0(z0)))))))
   0'(0(0(0(1(0(1(0(0(0(z0)))))))))) -> c4(0'(1(1(0(0(0(0(1(1(1(z0)))))))))), 1'(1(1(1(0(1(0(0(0(z0))))))))), 1'(1(1(0(1(0(0(0(z0)))))))), 1'(1(0(1(0(0(0(z0))))))))
   ENCODE_0(cons_0(cons_0(z0))) -> c6(0'(0(0(encArg(z0)))))
   ENCODE_0(cons_0(cons_1(z0))) -> c6(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_1(cons_0(z0))) -> c6(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_1(cons_1(z0))) -> c6(0'(1(1(encArg(z0)))))
   ENCODE_1(cons_0(cons_0(z0))) -> c6(1'(0(0(encArg(z0)))))
   ENCODE_1(cons_0(cons_1(z0))) -> c6(1'(0(1(encArg(z0)))))
S tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(1(1(1(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(1(0(1(0(z0)))))))) -> c4(0'(1(1(0(0(1(1(1(z0)))))))), 1'(1(1(1(0(1(0(z0))))))), 1'(1(1(0(1(0(z0)))))), 1'(1(0(1(0(z0))))))
   0'(0(0(0(1(0(1(0(0(z0))))))))) -> c4(0'(1(1(0(0(0(1(1(1(z0))))))))), 1'(1(1(1(0(1(0(0(z0)))))))), 1'(1(1(0(1(0(0(z0))))))), 1'(1(0(1(0(0(z0)))))))
   0'(0(0(0(1(0(1(0(0(0(z0)))))))))) -> c4(0'(1(1(0(0(0(0(1(1(1(z0)))))))))), 1'(1(1(1(0(1(0(0(0(z0))))))))), 1'(1(1(0(1(0(0(0(z0)))))))), 1'(1(0(1(0(0(0(z0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1, 1_1

Defined Pair Symbols:   1'_1, 0'_1, ENCODE_1_1, ENCARG_1, ENCODE_0_1

Compound Symbols:   c5_4, c4_1, c6_1, c_2, c1_2, c4_4


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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace ENCODE_1(cons_1(z0)) -> c6(1'(1(encArg(z0)))) by 
   ENCODE_1(cons_1(cons_0(z0))) -> c6(1'(1(0(encArg(z0)))))
   ENCODE_1(cons_1(cons_1(z0))) -> c6(1'(1(1(encArg(z0)))))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   encArg(cons_0(z0)) -> 0(encArg(z0))
   encArg(cons_1(z0)) -> 1(encArg(z0))
   0(0(0(0(z0)))) -> 0(1(1(1(z0))))
   1(1(0(1(z0)))) -> 0(0(0(0(z0))))
Tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
   ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))
   ENCARG(cons_0(cons_1(cons_0(z0)))) -> c(0'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0))))
   ENCARG(cons_0(cons_1(cons_1(z0)))) -> c(0'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0))))
   ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0))))
   ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0))))
   ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0))))
   ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0))))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(1(1(1(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(1(0(1(0(z0)))))))) -> c4(0'(1(1(0(0(1(1(1(z0)))))))), 1'(1(1(1(0(1(0(z0))))))), 1'(1(1(0(1(0(z0)))))), 1'(1(0(1(0(z0))))))
   0'(0(0(0(1(0(1(0(0(z0))))))))) -> c4(0'(1(1(0(0(0(1(1(1(z0))))))))), 1'(1(1(1(0(1(0(0(z0)))))))), 1'(1(1(0(1(0(0(z0))))))), 1'(1(0(1(0(0(z0)))))))
   0'(0(0(0(1(0(1(0(0(0(z0)))))))))) -> c4(0'(1(1(0(0(0(0(1(1(1(z0)))))))))), 1'(1(1(1(0(1(0(0(0(z0))))))))), 1'(1(1(0(1(0(0(0(z0)))))))), 1'(1(0(1(0(0(0(z0))))))))
   ENCODE_0(cons_0(cons_0(z0))) -> c6(0'(0(0(encArg(z0)))))
   ENCODE_0(cons_0(cons_1(z0))) -> c6(0'(0(1(encArg(z0)))))
   ENCODE_0(cons_1(cons_0(z0))) -> c6(0'(1(0(encArg(z0)))))
   ENCODE_0(cons_1(cons_1(z0))) -> c6(0'(1(1(encArg(z0)))))
   ENCODE_1(cons_0(cons_0(z0))) -> c6(1'(0(0(encArg(z0)))))
   ENCODE_1(cons_0(cons_1(z0))) -> c6(1'(0(1(encArg(z0)))))
   ENCODE_1(cons_1(cons_0(z0))) -> c6(1'(1(0(encArg(z0)))))
   ENCODE_1(cons_1(cons_1(z0))) -> c6(1'(1(1(encArg(z0)))))
S tuples:
   1'(1(0(1(z0)))) -> c5(0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0))
   0'(0(0(0(x0)))) -> c4(1'(1(x0)))
   0'(0(0(0(1(0(1(z0))))))) -> c4(0'(1(1(0(1(1(1(z0))))))), 1'(1(1(1(0(1(z0)))))), 1'(1(1(0(1(z0))))), 1'(1(0(1(z0)))))
   0'(0(0(0(1(0(1(0(z0)))))))) -> c4(0'(1(1(0(0(1(1(1(z0)))))))), 1'(1(1(1(0(1(0(z0))))))), 1'(1(1(0(1(0(z0)))))), 1'(1(0(1(0(z0))))))
   0'(0(0(0(1(0(1(0(0(z0))))))))) -> c4(0'(1(1(0(0(0(1(1(1(z0))))))))), 1'(1(1(1(0(1(0(0(z0)))))))), 1'(1(1(0(1(0(0(z0))))))), 1'(1(0(1(0(0(z0)))))))
   0'(0(0(0(1(0(1(0(0(0(z0)))))))))) -> c4(0'(1(1(0(0(0(0(1(1(1(z0)))))))))), 1'(1(1(1(0(1(0(0(0(z0))))))))), 1'(1(1(0(1(0(0(0(z0)))))))), 1'(1(0(1(0(0(0(z0))))))))
K tuples:none
Defined Rule Symbols:   encArg_1, 0_1, 1_1

Defined Pair Symbols:   1'_1, 0'_1, ENCARG_1, ENCODE_0_1, ENCODE_1_1

Compound Symbols:   c5_4, c4_1, c_2, c1_2, c4_4, c6_1