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


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


WORST_CASE(Omega(n^1), O(n^1))
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(n^1, n^1).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 59 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
    (7) CpxTrsMatchBoundsProof [FINISHED, 98 ms]
    (8) BOUNDS(1, n^1)
(9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(10) TRS for Loop Detection
    (11) DecreasingLoopProof [LOWER BOUND(ID), 5 ms]
    (12) BEST
        (13) proven lower bound
            (14) LowerBoundPropagationProof [FINISHED, 0 ms]
            (15) BOUNDS(n^1, INF)
        (16) TRS for Loop Detection


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

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


The TRS R consists of the following rules:

   0(1(2(x1))) -> 0(0(2(1(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
   0(3(1(x1))) -> 0(1(3(4(0(x1)))))
   0(3(1(x1))) -> 0(1(3(4(4(x1)))))
   0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
   0(3(2(x1))) -> 0(2(1(3(x1))))
   0(3(2(x1))) -> 0(2(3(4(x1))))
   0(3(2(x1))) -> 0(0(2(4(3(x1)))))
   0(3(2(x1))) -> 0(2(1(4(3(x1)))))
   0(3(2(x1))) -> 0(2(4(3(3(x1)))))
   0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
   0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
   0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
   0(4(1(x1))) -> 0(1(4(4(x1))))
   0(4(1(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(3(4(x1))))
   0(4(2(x1))) -> 0(2(4(3(x1))))
   2(0(1(x1))) -> 5(0(2(1(x1))))
   2(3(1(x1))) -> 1(3(5(2(x1))))
   2(3(1(x1))) -> 0(2(1(3(5(x1)))))
   2(3(1(x1))) -> 1(4(3(5(2(x1)))))
   0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
   0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
   0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
   0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
   0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
   0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
   0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
   0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
   0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
   0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
   2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
   2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
   2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
   2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
   0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
   0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
   0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
   0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
   0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
   0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
   0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
   0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
   2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
   2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
   2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
   2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(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(1(x_1)) -> 1(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(5(x_1)) -> 5(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))


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

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


The TRS R consists of the following rules:

   0(1(2(x1))) -> 0(0(2(1(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
   0(3(1(x1))) -> 0(1(3(4(0(x1)))))
   0(3(1(x1))) -> 0(1(3(4(4(x1)))))
   0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
   0(3(2(x1))) -> 0(2(1(3(x1))))
   0(3(2(x1))) -> 0(2(3(4(x1))))
   0(3(2(x1))) -> 0(0(2(4(3(x1)))))
   0(3(2(x1))) -> 0(2(1(4(3(x1)))))
   0(3(2(x1))) -> 0(2(4(3(3(x1)))))
   0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
   0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
   0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
   0(4(1(x1))) -> 0(1(4(4(x1))))
   0(4(1(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(3(4(x1))))
   0(4(2(x1))) -> 0(2(4(3(x1))))
   2(0(1(x1))) -> 5(0(2(1(x1))))
   2(3(1(x1))) -> 1(3(5(2(x1))))
   2(3(1(x1))) -> 0(2(1(3(5(x1)))))
   2(3(1(x1))) -> 1(4(3(5(2(x1)))))
   0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
   0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
   0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
   0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
   0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
   0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
   0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
   0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
   0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
   0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
   2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
   2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
   2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
   2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
   0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
   0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
   0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
   0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
   0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
   0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
   0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
   0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
   2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
   2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
   2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
   2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(x1))))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(5(x_1)) -> 5(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(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(n^1, n^1).


The TRS R consists of the following rules:

   0(1(2(x1))) -> 0(0(2(1(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
   0(3(1(x1))) -> 0(1(3(4(0(x1)))))
   0(3(1(x1))) -> 0(1(3(4(4(x1)))))
   0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
   0(3(2(x1))) -> 0(2(1(3(x1))))
   0(3(2(x1))) -> 0(2(3(4(x1))))
   0(3(2(x1))) -> 0(0(2(4(3(x1)))))
   0(3(2(x1))) -> 0(2(1(4(3(x1)))))
   0(3(2(x1))) -> 0(2(4(3(3(x1)))))
   0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
   0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
   0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
   0(4(1(x1))) -> 0(1(4(4(x1))))
   0(4(1(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(3(4(x1))))
   0(4(2(x1))) -> 0(2(4(3(x1))))
   2(0(1(x1))) -> 5(0(2(1(x1))))
   2(3(1(x1))) -> 1(3(5(2(x1))))
   2(3(1(x1))) -> 0(2(1(3(5(x1)))))
   2(3(1(x1))) -> 1(4(3(5(2(x1)))))
   0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
   0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
   0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
   0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
   0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
   0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
   0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
   0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
   0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
   0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
   2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
   2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
   2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
   2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
   0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
   0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
   0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
   0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
   0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
   0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
   0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
   0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
   2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
   2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
   2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
   2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(x1))))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(5(x_1)) -> 5(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))

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

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

(6)
Obligation:
The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

   0(1(2(x1))) -> 0(0(2(1(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
   0(3(1(x1))) -> 0(1(3(4(0(x1)))))
   0(3(1(x1))) -> 0(1(3(4(4(x1)))))
   0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
   0(3(2(x1))) -> 0(2(1(3(x1))))
   0(3(2(x1))) -> 0(2(3(4(x1))))
   0(3(2(x1))) -> 0(0(2(4(3(x1)))))
   0(3(2(x1))) -> 0(2(1(4(3(x1)))))
   0(3(2(x1))) -> 0(2(4(3(3(x1)))))
   0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
   0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
   0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
   0(4(1(x1))) -> 0(1(4(4(x1))))
   0(4(1(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(3(4(x1))))
   0(4(2(x1))) -> 0(2(4(3(x1))))
   2(0(1(x1))) -> 5(0(2(1(x1))))
   2(3(1(x1))) -> 1(3(5(2(x1))))
   2(3(1(x1))) -> 0(2(1(3(5(x1)))))
   2(3(1(x1))) -> 1(4(3(5(2(x1)))))
   0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
   0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
   0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
   0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
   0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
   0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
   0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
   0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
   0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
   0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
   2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
   2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
   2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
   2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
   0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
   0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
   0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
   0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
   0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
   0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
   0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
   0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
   2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
   2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
   2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
   2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(x1))))))
   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(5(x_1)) -> 5(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))

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

(7) CpxTrsMatchBoundsProof (FINISHED)
A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 4. 
The certificate found is represented by the following graph.

"[50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 325, 326, 327, 328, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369]
{(50,51,[0_1|0, 2_1|0, encArg_1|0, encode_0_1|0, encode_1_1|0, encode_2_1|0, encode_3_1|0, encode_4_1|0, encode_5_1|0]), (50,52,[0_1|1]), (50,56,[0_1|1]), (50,60,[1_1|1]), (50,65,[0_1|1]), (50,70,[0_1|1]), (50,73,[0_1|1]), (50,76,[0_1|1]), (50,81,[0_1|1]), (50,86,[1_1|1]), (50,89,[0_1|1]), (50,93,[1_1|1]), (50,97,[5_1|1]), (50,102,[1_1|1, 3_1|1, 4_1|1, 5_1|1, 0_1|1, 2_1|1]), (50,103,[0_1|2]), (50,106,[0_1|2]), (50,109,[0_1|2]), (50,114,[0_1|2]), (50,119,[2_1|2]), (50,124,[0_1|2]), (50,128,[0_1|2]), (50,132,[1_1|2]), (50,137,[0_1|2]), (50,142,[0_1|2]), (50,145,[0_1|2]), (50,149,[0_1|2]), (50,153,[0_1|2]), (50,157,[0_1|2]), (50,162,[0_1|2]), (50,167,[2_1|2]), (50,172,[0_1|2]), (50,177,[1_1|2]), (50,182,[0_1|2]), (50,187,[0_1|2]), (50,190,[0_1|2]), (50,193,[1_1|2]), (50,197,[0_1|2]), (50,200,[2_1|2]), (50,205,[5_1|2]), (50,209,[0_1|2]), (50,214,[0_1|2]), (50,219,[0_1|2]), (50,223,[0_1|2]), (50,227,[0_1|2]), (50,232,[0_1|2]), (50,237,[0_1|2]), (50,242,[0_1|2]), (50,247,[0_1|2]), (50,252,[5_1|2]), (50,255,[2_1|2]), (50,260,[2_1|2]), (50,265,[2_1|2]), (50,269,[1_1|2]), (50,272,[0_1|2]), (50,276,[1_1|2]), (50,280,[2_1|2]), (50,284,[0_1|2]), (50,288,[5_1|2]), (50,293,[1_1|2]), (50,298,[2_1|2]), (50,303,[0_1|2]), (50,306,[1_1|3]), (50,309,[0_1|3]), (50,313,[1_1|3]), (50,317,[5_1|3]), (51,51,[1_1|0, 3_1|0, 4_1|0, 5_1|0, cons_0_1|0, cons_2_1|0]), (52,53,[1_1|1]), (53,54,[3_1|1]), (54,55,[4_1|1]), (55,51,[0_1|1]), (55,52,[0_1|1]), (55,56,[0_1|1]), (55,60,[1_1|1]), (55,65,[0_1|1]), (55,70,[0_1|1]), (55,73,[0_1|1]), (55,76,[0_1|1]), (55,81,[0_1|1]), (56,57,[1_1|1]), (57,58,[3_1|1]), (58,59,[4_1|1]), (59,51,[4_1|1]), (60,61,[3_1|1]), (61,62,[4_1|1]), (62,63,[4_1|1]), (63,64,[4_1|1]), (64,51,[0_1|1]), (64,52,[0_1|1]), (64,56,[0_1|1]), (64,60,[1_1|1]), (64,65,[0_1|1]), (64,70,[0_1|1]), (64,73,[0_1|1]), (64,76,[0_1|1]), (64,81,[0_1|1]), (65,66,[1_1|1]), (66,67,[4_1|1]), (67,68,[1_1|1]), (68,69,[3_1|1]), (69,51,[4_1|1]), (70,71,[1_1|1]), (71,72,[4_1|1]), (72,51,[4_1|1]), (73,74,[2_1|1]), (74,75,[1_1|1]), (75,51,[4_1|1]), (76,77,[1_1|1]), (77,78,[4_1|1]), (78,79,[3_1|1]), (79,80,[5_1|1]), (80,51,[4_1|1]), (81,82,[1_1|1]), (82,83,[5_1|1]), (83,84,[3_1|1]), (84,85,[4_1|1]), (85,51,[0_1|1]), (85,52,[0_1|1]), (85,56,[0_1|1]), (85,60,[1_1|1]), (85,65,[0_1|1]), (85,70,[0_1|1]), (85,73,[0_1|1]), (85,76,[0_1|1]), (85,81,[0_1|1]), (86,87,[3_1|1]), (87,88,[5_1|1]), (88,51,[2_1|1]), (88,86,[1_1|1]), (88,89,[0_1|1]), (88,93,[1_1|1]), (88,97,[5_1|1]), (89,90,[2_1|1]), (90,91,[1_1|1]), (91,92,[3_1|1]), (92,51,[5_1|1]), (93,94,[4_1|1]), (94,95,[3_1|1]), (95,96,[5_1|1]), (96,51,[2_1|1]), (96,86,[1_1|1]), (96,89,[0_1|1]), (96,93,[1_1|1]), (96,97,[5_1|1]), (97,98,[5_1|1]), (98,99,[2_1|1]), (99,100,[1_1|1]), (100,101,[3_1|1]), (101,51,[4_1|1]), (102,51,[encArg_1|1]), (102,102,[1_1|1, 3_1|1, 4_1|1, 5_1|1, 0_1|1, 2_1|1]), (102,103,[0_1|2]), (102,106,[0_1|2]), (102,109,[0_1|2]), (102,114,[0_1|2]), (102,119,[2_1|2]), (102,124,[0_1|2]), (102,128,[0_1|2]), (102,132,[1_1|2]), (102,137,[0_1|2]), (102,142,[0_1|2]), (102,145,[0_1|2]), (102,149,[0_1|2]), (102,153,[0_1|2]), (102,157,[0_1|2]), (102,162,[0_1|2]), (102,167,[2_1|2]), (102,172,[0_1|2]), (102,177,[1_1|2]), (102,182,[0_1|2]), (102,187,[0_1|2]), (102,190,[0_1|2]), (102,193,[1_1|2]), (102,197,[0_1|2]), (102,200,[2_1|2]), (102,205,[5_1|2]), (102,209,[0_1|2]), (102,214,[0_1|2]), (102,219,[0_1|2]), (102,223,[0_1|2]), (102,227,[0_1|2]), (102,232,[0_1|2]), (102,237,[0_1|2]), (102,242,[0_1|2]), (102,247,[0_1|2]), (102,252,[5_1|2]), (102,255,[2_1|2]), (102,260,[2_1|2]), (102,265,[2_1|2]), (102,269,[1_1|2]), (102,272,[0_1|2]), (102,276,[1_1|2]), (102,280,[2_1|2]), (102,284,[0_1|2]), (102,288,[5_1|2]), (102,293,[1_1|2]), (102,298,[2_1|2]), (102,303,[0_1|2]), (102,306,[1_1|3]), (102,309,[0_1|3]), (102,313,[1_1|3]), (102,317,[5_1|3]), (103,104,[0_1|2]), (104,105,[2_1|2]), (105,102,[1_1|2]), (105,119,[1_1|2]), (105,167,[1_1|2]), (105,200,[1_1|2]), (105,255,[1_1|2]), (105,260,[1_1|2]), (105,265,[1_1|2]), (105,280,[1_1|2]), (105,298,[1_1|2]), (106,107,[2_1|2]), (107,108,[1_1|2]), (108,102,[3_1|2]), (108,119,[3_1|2]), (108,167,[3_1|2]), (108,200,[3_1|2]), (108,255,[3_1|2]), (108,260,[3_1|2]), (108,265,[3_1|2]), (108,280,[3_1|2]), (108,298,[3_1|2]), (109,110,[0_1|2]), (110,111,[2_1|2]), (111,112,[1_1|2]), (112,113,[4_1|2]), (113,102,[4_1|2]), (113,119,[4_1|2]), (113,167,[4_1|2]), (113,200,[4_1|2]), (113,255,[4_1|2]), (113,260,[4_1|2]), (113,265,[4_1|2]), (113,280,[4_1|2]), (113,298,[4_1|2]), (114,115,[1_1|2]), (115,116,[4_1|2]), (116,117,[3_1|2]), (117,118,[2_1|2]), (117,252,[5_1|2]), (117,255,[2_1|2]), (117,260,[2_1|2]), (117,265,[2_1|2]), (117,320,[5_1|3]), (117,339,[2_1|3]), (117,367,[5_1|4]), (118,102,[0_1|2]), (118,119,[0_1|2, 2_1|2]), (118,167,[0_1|2, 2_1|2]), (118,200,[0_1|2, 2_1|2]), (118,255,[0_1|2]), (118,260,[0_1|2]), (118,265,[0_1|2]), (118,280,[0_1|2]), (118,298,[0_1|2]), (118,103,[0_1|2]), (118,106,[0_1|2]), (118,109,[0_1|2]), (118,114,[0_1|2]), (118,124,[0_1|2]), (118,128,[0_1|2]), (118,132,[1_1|2]), (118,137,[0_1|2]), (118,142,[0_1|2]), (118,145,[0_1|2]), (118,149,[0_1|2]), (118,153,[0_1|2]), (118,157,[0_1|2]), (118,162,[0_1|2]), (118,172,[0_1|2]), (118,177,[1_1|2]), (118,182,[0_1|2]), (118,187,[0_1|2]), (118,190,[0_1|2]), (118,193,[1_1|2]), (118,197,[0_1|2]), (118,303,[0_1|2]), (118,205,[5_1|2]), (118,209,[0_1|2]), (118,214,[0_1|2]), (118,219,[0_1|2]), (118,223,[0_1|2]), (118,227,[0_1|2]), (118,232,[0_1|2]), (118,237,[0_1|2]), (118,242,[0_1|2]), (118,247,[0_1|2]), (118,325,[5_1|3]), (118,344,[0_1|3]), (118,348,[0_1|3]), (118,352,[1_1|3]), (118,306,[1_1|3]), (118,309,[0_1|3]), (118,313,[1_1|3]), (119,120,[3_1|2]), (120,121,[1_1|2]), (121,122,[0_1|2]), (122,123,[0_1|2]), (122,209,[0_1|2]), (122,214,[0_1|2]), (122,219,[0_1|2]), (122,223,[0_1|2]), (122,227,[0_1|2]), (122,232,[0_1|2]), (122,237,[0_1|2]), (122,242,[0_1|2]), (122,357,[0_1|3]), (122,362,[0_1|3]), (123,102,[5_1|2]), (123,119,[5_1|2]), (123,167,[5_1|2]), (123,200,[5_1|2]), (123,255,[5_1|2]), (123,260,[5_1|2]), (123,265,[5_1|2]), (123,280,[5_1|2]), (123,298,[5_1|2]), (124,125,[1_1|2]), (125,126,[3_1|2]), (126,127,[4_1|2]), (127,102,[0_1|2]), (127,132,[0_1|2, 1_1|2]), (127,177,[0_1|2, 1_1|2]), (127,193,[0_1|2, 1_1|2]), (127,269,[0_1|2]), (127,276,[0_1|2]), (127,293,[0_1|2]), (127,103,[0_1|2]), (127,106,[0_1|2]), (127,109,[0_1|2]), (127,114,[0_1|2]), (127,119,[2_1|2]), (127,124,[0_1|2]), (127,128,[0_1|2]), (127,137,[0_1|2]), (127,142,[0_1|2]), (127,145,[0_1|2]), (127,149,[0_1|2]), (127,153,[0_1|2]), (127,157,[0_1|2]), (127,162,[0_1|2]), (127,167,[2_1|2]), (127,172,[0_1|2]), (127,182,[0_1|2]), (127,187,[0_1|2]), (127,190,[0_1|2]), (127,197,[0_1|2]), (127,200,[2_1|2]), (127,303,[0_1|2]), (127,205,[5_1|2]), (127,209,[0_1|2]), (127,214,[0_1|2]), (127,219,[0_1|2]), (127,223,[0_1|2]), (127,227,[0_1|2]), (127,232,[0_1|2]), (127,237,[0_1|2]), (127,242,[0_1|2]), (127,247,[0_1|2]), (127,325,[5_1|3]), (127,306,[0_1|2, 1_1|3]), (127,313,[0_1|2, 1_1|3]), (127,309,[0_1|3]), (128,129,[1_1|2]), (129,130,[3_1|2]), (130,131,[4_1|2]), (131,102,[4_1|2]), (131,132,[4_1|2]), (131,177,[4_1|2]), (131,193,[4_1|2]), (131,269,[4_1|2]), (131,276,[4_1|2]), (131,293,[4_1|2]), (131,306,[4_1|2]), (131,313,[4_1|2]), (132,133,[3_1|2]), (133,134,[4_1|2]), (134,135,[4_1|2]), (135,136,[4_1|2]), (136,102,[0_1|2]), (136,132,[0_1|2, 1_1|2]), (136,177,[0_1|2, 1_1|2]), (136,193,[0_1|2, 1_1|2]), (136,269,[0_1|2]), (136,276,[0_1|2]), (136,293,[0_1|2]), (136,103,[0_1|2]), (136,106,[0_1|2]), (136,109,[0_1|2]), (136,114,[0_1|2]), (136,119,[2_1|2]), (136,124,[0_1|2]), (136,128,[0_1|2]), (136,137,[0_1|2]), (136,142,[0_1|2]), (136,145,[0_1|2]), (136,149,[0_1|2]), (136,153,[0_1|2]), (136,157,[0_1|2]), (136,162,[0_1|2]), (136,167,[2_1|2]), (136,172,[0_1|2]), (136,182,[0_1|2]), (136,187,[0_1|2]), (136,190,[0_1|2]), (136,197,[0_1|2]), (136,200,[2_1|2]), (136,303,[0_1|2]), (136,205,[5_1|2]), (136,209,[0_1|2]), (136,214,[0_1|2]), (136,219,[0_1|2]), (136,223,[0_1|2]), (136,227,[0_1|2]), (136,232,[0_1|2]), (136,237,[0_1|2]), (136,242,[0_1|2]), (136,247,[0_1|2]), (136,325,[5_1|3]), (136,306,[0_1|2, 1_1|3]), (136,313,[0_1|2, 1_1|3]), (136,309,[0_1|3]), (137,138,[1_1|2]), (138,139,[4_1|2]), (139,140,[1_1|2]), (140,141,[3_1|2]), (141,102,[4_1|2]), (141,132,[4_1|2]), (141,177,[4_1|2]), (141,193,[4_1|2]), (141,269,[4_1|2]), (141,276,[4_1|2]), (141,293,[4_1|2]), (141,306,[4_1|2]), (141,313,[4_1|2]), (142,143,[2_1|2]), (143,144,[3_1|2]), (144,102,[4_1|2]), (144,119,[4_1|2]), (144,167,[4_1|2]), (144,200,[4_1|2]), (144,255,[4_1|2]), (144,260,[4_1|2]), (144,265,[4_1|2]), (144,280,[4_1|2]), (144,298,[4_1|2]), (145,146,[0_1|2]), (146,147,[2_1|2]), (147,148,[4_1|2]), (148,102,[3_1|2]), (148,119,[3_1|2]), (148,167,[3_1|2]), (148,200,[3_1|2]), (148,255,[3_1|2]), (148,260,[3_1|2]), (148,265,[3_1|2]), (148,280,[3_1|2]), (148,298,[3_1|2]), (149,150,[2_1|2]), (150,151,[1_1|2]), (151,152,[4_1|2]), (152,102,[3_1|2]), (152,119,[3_1|2]), (152,167,[3_1|2]), (152,200,[3_1|2]), (152,255,[3_1|2]), (152,260,[3_1|2]), (152,265,[3_1|2]), (152,280,[3_1|2]), (152,298,[3_1|2]), (153,154,[2_1|2]), (154,155,[4_1|2]), (155,156,[3_1|2]), (156,102,[3_1|2]), (156,119,[3_1|2]), (156,167,[3_1|2]), (156,200,[3_1|2]), (156,255,[3_1|2]), (156,260,[3_1|2]), (156,265,[3_1|2]), (156,280,[3_1|2]), (156,298,[3_1|2]), (157,158,[2_1|2]), (158,159,[1_1|2]), (159,160,[3_1|2]), (160,161,[3_1|2]), (161,102,[4_1|2]), (161,119,[4_1|2]), (161,167,[4_1|2]), (161,200,[4_1|2]), (161,255,[4_1|2]), (161,260,[4_1|2]), (161,265,[4_1|2]), (161,280,[4_1|2]), (161,298,[4_1|2]), (162,163,[2_1|2]), (163,164,[3_1|2]), (164,165,[4_1|2]), (165,166,[5_1|2]), (166,102,[5_1|2]), (166,119,[5_1|2]), (166,167,[5_1|2]), (166,200,[5_1|2]), (166,255,[5_1|2]), (166,260,[5_1|2]), (166,265,[5_1|2]), (166,280,[5_1|2]), (166,298,[5_1|2]), (167,168,[4_1|2]), (168,169,[4_1|2]), (169,170,[3_1|2]), (170,171,[4_1|2]), (171,102,[0_1|2]), (171,119,[0_1|2, 2_1|2]), (171,167,[0_1|2, 2_1|2]), (171,200,[0_1|2, 2_1|2]), (171,255,[0_1|2]), (171,260,[0_1|2]), (171,265,[0_1|2]), (171,280,[0_1|2]), (171,298,[0_1|2]), (171,103,[0_1|2]), (171,106,[0_1|2]), (171,109,[0_1|2]), (171,114,[0_1|2]), (171,124,[0_1|2]), (171,128,[0_1|2]), (171,132,[1_1|2]), (171,137,[0_1|2]), (171,142,[0_1|2]), (171,145,[0_1|2]), (171,149,[0_1|2]), (171,153,[0_1|2]), (171,157,[0_1|2]), (171,162,[0_1|2]), (171,172,[0_1|2]), (171,177,[1_1|2]), (171,182,[0_1|2]), (171,187,[0_1|2]), (171,190,[0_1|2]), (171,193,[1_1|2]), (171,197,[0_1|2]), (171,303,[0_1|2]), (171,205,[5_1|2]), (171,209,[0_1|2]), (171,214,[0_1|2]), (171,219,[0_1|2]), (171,223,[0_1|2]), (171,227,[0_1|2]), (171,232,[0_1|2]), (171,237,[0_1|2]), (171,242,[0_1|2]), (171,247,[0_1|2]), (171,325,[5_1|3]), (171,344,[0_1|3]), (171,348,[0_1|3]), (171,352,[1_1|3]), (171,306,[1_1|3]), (171,309,[0_1|3]), (171,313,[1_1|3]), (172,173,[0_1|2]), (173,174,[3_1|2]), (174,175,[4_1|2]), (175,176,[2_1|2]), (176,102,[1_1|2]), (176,132,[1_1|2]), (176,177,[1_1|2]), (176,193,[1_1|2]), (176,269,[1_1|2]), (176,276,[1_1|2]), (176,293,[1_1|2]), (176,261,[1_1|2]), (176,306,[1_1|2]), (176,313,[1_1|2]), (177,178,[3_1|2]), (178,179,[4_1|2]), (179,180,[0_1|2]), (180,181,[2_1|2]), (180,293,[1_1|2]), (180,298,[2_1|2]), (181,102,[2_1|2]), (181,119,[2_1|2]), (181,167,[2_1|2]), (181,200,[2_1|2]), (181,255,[2_1|2]), (181,260,[2_1|2]), (181,265,[2_1|2]), (181,280,[2_1|2]), (181,298,[2_1|2]), (181,252,[5_1|2]), (181,269,[1_1|2]), (181,272,[0_1|2]), (181,276,[1_1|2]), (181,284,[0_1|2]), (181,288,[5_1|2]), (181,293,[1_1|2]), (181,336,[5_1|3]), (181,306,[1_1|3]), (181,309,[0_1|3]), (181,313,[1_1|3]), (182,183,[2_1|2]), (183,184,[5_1|2]), (184,185,[1_1|2]), (185,186,[3_1|2]), (186,102,[3_1|2]), (186,132,[3_1|2]), (186,177,[3_1|2]), (186,193,[3_1|2]), (186,269,[3_1|2]), (186,276,[3_1|2]), (186,293,[3_1|2]), (186,306,[3_1|2]), (186,313,[3_1|2]), (187,188,[1_1|2]), (188,189,[4_1|2]), (189,102,[4_1|2]), (189,132,[4_1|2]), (189,177,[4_1|2]), (189,193,[4_1|2]), (189,269,[4_1|2]), (189,276,[4_1|2]), (189,293,[4_1|2]), (189,306,[4_1|2]), (189,313,[4_1|2]), (190,191,[2_1|2]), (191,192,[1_1|2]), (192,102,[4_1|2]), (192,132,[4_1|2]), (192,177,[4_1|2]), (192,193,[4_1|2]), (192,269,[4_1|2]), (192,276,[4_1|2]), (192,293,[4_1|2]), (192,306,[4_1|2]), (192,313,[4_1|2]), (193,194,[4_1|2]), (194,195,[0_1|2]), (195,196,[2_1|2]), (195,280,[2_1|2]), (195,284,[0_1|2]), (195,288,[5_1|2]), (196,102,[5_1|2]), (196,119,[5_1|2]), (196,167,[5_1|2]), (196,200,[5_1|2]), (196,255,[5_1|2]), (196,260,[5_1|2]), (196,265,[5_1|2]), (196,280,[5_1|2]), (196,298,[5_1|2]), (197,198,[2_1|2]), (198,199,[4_1|2]), (199,102,[3_1|2]), (199,119,[3_1|2]), (199,167,[3_1|2]), (199,200,[3_1|2]), (199,255,[3_1|2]), (199,260,[3_1|2]), (199,265,[3_1|2]), (199,280,[3_1|2]), (199,298,[3_1|2]), (200,201,[3_1|2]), (201,202,[4_1|2]), (202,203,[4_1|2]), (203,204,[0_1|2]), (203,247,[0_1|2]), (204,102,[0_1|2]), (204,119,[0_1|2, 2_1|2]), (204,167,[0_1|2, 2_1|2]), (204,200,[0_1|2, 2_1|2]), (204,255,[0_1|2]), (204,260,[0_1|2]), (204,265,[0_1|2]), (204,280,[0_1|2]), (204,298,[0_1|2]), (204,103,[0_1|2]), (204,106,[0_1|2]), (204,109,[0_1|2]), (204,114,[0_1|2]), (204,124,[0_1|2]), (204,128,[0_1|2]), (204,132,[1_1|2]), (204,137,[0_1|2]), (204,142,[0_1|2]), (204,145,[0_1|2]), (204,149,[0_1|2]), (204,153,[0_1|2]), (204,157,[0_1|2]), (204,162,[0_1|2]), (204,172,[0_1|2]), (204,177,[1_1|2]), (204,182,[0_1|2]), (204,187,[0_1|2]), (204,190,[0_1|2]), (204,193,[1_1|2]), (204,197,[0_1|2]), (204,303,[0_1|2]), (204,205,[5_1|2]), (204,209,[0_1|2]), (204,214,[0_1|2]), (204,219,[0_1|2]), (204,223,[0_1|2]), (204,227,[0_1|2]), (204,232,[0_1|2]), (204,237,[0_1|2]), (204,242,[0_1|2]), (204,247,[0_1|2]), (204,325,[5_1|3]), (204,344,[0_1|3]), (204,348,[0_1|3]), (204,352,[1_1|3]), (204,306,[1_1|3]), (204,309,[0_1|3]), (204,313,[1_1|3]), (205,206,[0_1|2]), (206,207,[0_1|2]), (207,208,[2_1|2]), (208,102,[1_1|2]), (208,132,[1_1|2]), (208,177,[1_1|2]), (208,193,[1_1|2]), (208,269,[1_1|2]), (208,276,[1_1|2]), (208,293,[1_1|2]), (208,115,[1_1|2]), (208,125,[1_1|2]), (208,129,[1_1|2]), (208,138,[1_1|2]), (208,188,[1_1|2]), (208,210,[1_1|2]), (208,215,[1_1|2]), (208,228,[1_1|2]), (208,257,[1_1|2]), (208,267,[1_1|2]), (208,306,[1_1|2]), (208,313,[1_1|2]), (209,210,[1_1|2]), (210,211,[4_1|2]), (211,212,[3_1|2]), (212,213,[5_1|2]), (213,102,[4_1|2]), (213,132,[4_1|2]), (213,177,[4_1|2]), (213,193,[4_1|2]), (213,269,[4_1|2]), (213,276,[4_1|2]), (213,293,[4_1|2]), (213,306,[4_1|2]), (213,313,[4_1|2]), (214,215,[1_1|2]), (215,216,[5_1|2]), (216,217,[3_1|2]), (217,218,[4_1|2]), (218,102,[0_1|2]), (218,132,[0_1|2, 1_1|2]), (218,177,[0_1|2, 1_1|2]), (218,193,[0_1|2, 1_1|2]), (218,269,[0_1|2]), (218,276,[0_1|2]), (218,293,[0_1|2]), (218,103,[0_1|2]), (218,106,[0_1|2]), (218,109,[0_1|2]), (218,114,[0_1|2]), (218,119,[2_1|2]), (218,124,[0_1|2]), (218,128,[0_1|2]), (218,137,[0_1|2]), (218,142,[0_1|2]), (218,145,[0_1|2]), (218,149,[0_1|2]), (218,153,[0_1|2]), (218,157,[0_1|2]), (218,162,[0_1|2]), (218,167,[2_1|2]), (218,172,[0_1|2]), (218,182,[0_1|2]), (218,187,[0_1|2]), (218,190,[0_1|2]), (218,197,[0_1|2]), (218,200,[2_1|2]), (218,303,[0_1|2]), (218,205,[5_1|2]), (218,209,[0_1|2]), (218,214,[0_1|2]), (218,219,[0_1|2]), (218,223,[0_1|2]), (218,227,[0_1|2]), (218,232,[0_1|2]), (218,237,[0_1|2]), (218,242,[0_1|2]), (218,247,[0_1|2]), (218,325,[5_1|3]), (218,306,[0_1|2, 1_1|3]), (218,313,[0_1|2, 1_1|3]), (218,309,[0_1|3]), (219,220,[2_1|2]), (220,221,[4_1|2]), (221,222,[5_1|2]), (222,102,[3_1|2]), (222,119,[3_1|2]), (222,167,[3_1|2]), (222,200,[3_1|2]), (222,255,[3_1|2]), (222,260,[3_1|2]), (222,265,[3_1|2]), (222,280,[3_1|2]), (222,298,[3_1|2]), (223,224,[2_1|2]), (224,225,[5_1|2]), (225,226,[3_1|2]), (226,102,[3_1|2]), (226,119,[3_1|2]), (226,167,[3_1|2]), (226,200,[3_1|2]), (226,255,[3_1|2]), (226,260,[3_1|2]), (226,265,[3_1|2]), (226,280,[3_1|2]), (226,298,[3_1|2]), (227,228,[1_1|2]), (228,229,[3_1|2]), (229,230,[4_1|2]), (230,231,[2_1|2]), (230,280,[2_1|2]), (230,284,[0_1|2]), (230,288,[5_1|2]), (231,102,[5_1|2]), (231,132,[5_1|2]), (231,177,[5_1|2]), (231,193,[5_1|2]), (231,269,[5_1|2]), (231,276,[5_1|2]), (231,293,[5_1|2]), (231,261,[5_1|2]), (231,306,[5_1|2]), (231,313,[5_1|2]), (232,233,[2_1|2]), (233,234,[4_1|2]), (234,235,[1_1|2]), (235,236,[1_1|2]), (236,102,[5_1|2]), (236,119,[5_1|2]), (236,167,[5_1|2]), (236,200,[5_1|2]), (236,255,[5_1|2]), (236,260,[5_1|2]), (236,265,[5_1|2]), (236,280,[5_1|2]), (236,298,[5_1|2]), (237,238,[2_1|2]), (238,239,[5_1|2]), (239,240,[2_1|2]), (240,241,[1_1|2]), (241,102,[2_1|2]), (241,119,[2_1|2]), (241,167,[2_1|2]), (241,200,[2_1|2]), (241,255,[2_1|2]), (241,260,[2_1|2]), (241,265,[2_1|2]), (241,280,[2_1|2]), (241,298,[2_1|2]), (241,252,[5_1|2]), (241,269,[1_1|2]), (241,272,[0_1|2]), (241,276,[1_1|2]), (241,284,[0_1|2]), (241,288,[5_1|2]), (241,293,[1_1|2]), (241,336,[5_1|3]), (241,306,[1_1|3]), (241,309,[0_1|3]), (241,313,[1_1|3]), (242,243,[2_1|2]), (243,244,[5_1|2]), (244,245,[1_1|2]), (245,246,[3_1|2]), (246,102,[5_1|2]), (246,119,[5_1|2]), (246,167,[5_1|2]), (246,200,[5_1|2]), (246,255,[5_1|2]), (246,260,[5_1|2]), (246,265,[5_1|2]), (246,280,[5_1|2]), (246,298,[5_1|2]), (247,248,[0_1|2]), (248,249,[1_1|2]), (249,250,[3_1|2]), (250,251,[5_1|2]), (251,102,[2_1|2]), (251,132,[2_1|2]), (251,177,[2_1|2]), (251,193,[2_1|2]), (251,269,[2_1|2, 1_1|2]), (251,276,[2_1|2, 1_1|2]), (251,293,[2_1|2, 1_1|2]), (251,261,[2_1|2]), (251,252,[5_1|2]), (251,255,[2_1|2]), (251,260,[2_1|2]), (251,265,[2_1|2]), (251,272,[0_1|2]), (251,280,[2_1|2]), (251,284,[0_1|2]), (251,288,[5_1|2]), (251,298,[2_1|2]), (251,336,[5_1|3]), (251,306,[2_1|2]), (251,313,[2_1|2]), (252,253,[0_1|2]), (253,254,[2_1|2]), (254,102,[1_1|2]), (254,132,[1_1|2]), (254,177,[1_1|2]), (254,193,[1_1|2]), (254,269,[1_1|2]), (254,276,[1_1|2]), (254,293,[1_1|2]), (254,115,[1_1|2]), (254,125,[1_1|2]), (254,129,[1_1|2]), (254,138,[1_1|2]), (254,188,[1_1|2]), (254,210,[1_1|2]), (254,215,[1_1|2]), (254,228,[1_1|2]), (254,306,[1_1|2]), (254,313,[1_1|2]), (255,256,[0_1|2]), (256,257,[1_1|2]), (257,258,[3_1|2]), (258,259,[5_1|2]), (259,102,[2_1|2]), (259,132,[2_1|2]), (259,177,[2_1|2]), (259,193,[2_1|2]), (259,269,[2_1|2, 1_1|2]), (259,276,[2_1|2, 1_1|2]), (259,293,[2_1|2, 1_1|2]), (259,252,[5_1|2]), (259,255,[2_1|2]), (259,260,[2_1|2]), (259,265,[2_1|2]), (259,272,[0_1|2]), (259,280,[2_1|2]), (259,284,[0_1|2]), (259,288,[5_1|2]), (259,298,[2_1|2]), (259,336,[5_1|3]), (259,306,[2_1|2]), (259,313,[2_1|2]), (260,261,[1_1|2]), (261,262,[0_1|2]), (262,263,[1_1|2]), (263,264,[3_1|2]), (264,102,[4_1|2]), (264,132,[4_1|2]), (264,177,[4_1|2]), (264,193,[4_1|2]), (264,269,[4_1|2]), (264,276,[4_1|2]), (264,293,[4_1|2]), (264,306,[4_1|2]), (264,313,[4_1|2]), (265,266,[0_1|2]), (266,267,[1_1|2]), (267,268,[4_1|2]), (268,102,[5_1|2]), (268,132,[5_1|2]), (268,177,[5_1|2]), (268,193,[5_1|2]), (268,269,[5_1|2]), (268,276,[5_1|2]), (268,293,[5_1|2]), (268,306,[5_1|2]), (268,313,[5_1|2]), (269,270,[3_1|2]), (270,271,[5_1|2]), (271,102,[2_1|2]), (271,132,[2_1|2]), (271,177,[2_1|2]), (271,193,[2_1|2]), (271,269,[2_1|2, 1_1|2]), (271,276,[2_1|2, 1_1|2]), (271,293,[2_1|2, 1_1|2]), (271,252,[5_1|2]), (271,255,[2_1|2]), (271,260,[2_1|2]), (271,265,[2_1|2]), (271,272,[0_1|2]), (271,280,[2_1|2]), (271,284,[0_1|2]), (271,288,[5_1|2]), (271,298,[2_1|2]), (271,336,[5_1|3]), (271,306,[2_1|2]), (271,313,[2_1|2]), (272,273,[2_1|2]), (273,274,[1_1|2]), (274,275,[3_1|2]), (275,102,[5_1|2]), (275,132,[5_1|2]), (275,177,[5_1|2]), (275,193,[5_1|2]), (275,269,[5_1|2]), (275,276,[5_1|2]), (275,293,[5_1|2]), (275,306,[5_1|2]), (275,313,[5_1|2]), (276,277,[4_1|2]), (277,278,[3_1|2]), (278,279,[5_1|2]), (279,102,[2_1|2]), (279,132,[2_1|2]), (279,177,[2_1|2]), (279,193,[2_1|2]), (279,269,[2_1|2, 1_1|2]), (279,276,[2_1|2, 1_1|2]), (279,293,[2_1|2, 1_1|2]), (279,252,[5_1|2]), (279,255,[2_1|2]), (279,260,[2_1|2]), (279,265,[2_1|2]), (279,272,[0_1|2]), (279,280,[2_1|2]), (279,284,[0_1|2]), (279,288,[5_1|2]), (279,298,[2_1|2]), (279,336,[5_1|3]), (279,306,[2_1|2]), (279,313,[2_1|2]), (280,281,[5_1|2]), (281,282,[2_1|2]), (282,283,[3_1|2]), (283,102,[3_1|2]), (283,119,[3_1|2]), (283,167,[3_1|2]), (283,200,[3_1|2]), (283,255,[3_1|2]), (283,260,[3_1|2]), (283,265,[3_1|2]), (283,280,[3_1|2]), (283,298,[3_1|2]), (284,285,[2_1|2]), (285,286,[5_1|2]), (286,287,[2_1|2]), (287,102,[4_1|2]), (287,119,[4_1|2]), (287,167,[4_1|2]), (287,200,[4_1|2]), (287,255,[4_1|2]), (287,260,[4_1|2]), (287,265,[4_1|2]), (287,280,[4_1|2]), (287,298,[4_1|2]), (288,289,[5_1|2]), (289,290,[2_1|2]), (290,291,[1_1|2]), (291,292,[3_1|2]), (292,102,[4_1|2]), (292,132,[4_1|2]), (292,177,[4_1|2]), (292,193,[4_1|2]), (292,269,[4_1|2]), (292,276,[4_1|2]), (292,293,[4_1|2]), (292,306,[4_1|2]), (292,313,[4_1|2]), (293,294,[3_1|2]), (294,295,[0_1|2]), (295,296,[2_1|2]), (296,297,[5_1|2]), (297,102,[2_1|2]), (297,132,[2_1|2]), (297,177,[2_1|2]), (297,193,[2_1|2]), (297,269,[2_1|2, 1_1|2]), (297,276,[2_1|2, 1_1|2]), (297,293,[2_1|2, 1_1|2]), (297,252,[5_1|2]), (297,255,[2_1|2]), (297,260,[2_1|2]), (297,265,[2_1|2]), (297,272,[0_1|2]), (297,280,[2_1|2]), (297,284,[0_1|2]), (297,288,[5_1|2]), (297,298,[2_1|2]), (297,336,[5_1|3]), (297,306,[2_1|2]), (297,313,[2_1|2]), (298,299,[0_1|2]), (299,300,[2_1|2]), (300,301,[1_1|2]), (301,302,[5_1|2]), (302,102,[1_1|2]), (302,132,[1_1|2]), (302,177,[1_1|2]), (302,193,[1_1|2]), (302,269,[1_1|2]), (302,276,[1_1|2]), (302,293,[1_1|2]), (302,306,[1_1|2]), (302,313,[1_1|2]), (303,304,[2_1|2]), (304,305,[1_1|2]), (305,119,[4_1|2]), (305,167,[4_1|2]), (305,200,[4_1|2]), (305,255,[4_1|2]), (305,260,[4_1|2]), (305,265,[4_1|2]), (305,280,[4_1|2]), (305,298,[4_1|2]), (306,307,[3_1|3]), (307,308,[5_1|3]), (308,121,[2_1|3]), (309,310,[2_1|3]), (310,311,[1_1|3]), (311,312,[3_1|3]), (312,121,[5_1|3]), (313,314,[4_1|3]), (314,315,[3_1|3]), (315,316,[5_1|3]), (316,121,[2_1|3]), (317,318,[0_1|3]), (318,319,[2_1|3]), (319,257,[1_1|3]), (319,267,[1_1|3]), (320,321,[0_1|3]), (321,322,[2_1|3]), (322,132,[1_1|3]), (322,177,[1_1|3]), (322,193,[1_1|3]), (322,269,[1_1|3]), (322,276,[1_1|3]), (322,293,[1_1|3]), (322,306,[1_1|3]), (322,313,[1_1|3]), (322,261,[1_1|3]), (322,115,[1_1|3]), (322,125,[1_1|3]), (322,129,[1_1|3]), (322,138,[1_1|3]), (322,188,[1_1|3]), (322,210,[1_1|3]), (322,215,[1_1|3]), (322,228,[1_1|3]), (322,257,[1_1|3]), (322,267,[1_1|3]), (322,345,[1_1|3]), (322,349,[1_1|3]), (325,326,[0_1|3]), (326,327,[0_1|3]), (327,328,[2_1|3]), (328,257,[1_1|3]), (328,267,[1_1|3]), (336,337,[0_1|3]), (337,338,[2_1|3]), (338,115,[1_1|3]), (338,125,[1_1|3]), (338,129,[1_1|3]), (338,138,[1_1|3]), (338,188,[1_1|3]), (338,210,[1_1|3]), (338,215,[1_1|3]), (338,228,[1_1|3]), (338,257,[1_1|3]), (338,267,[1_1|3]), (338,263,[1_1|3]), (339,340,[0_1|3]), (340,341,[1_1|3]), (341,342,[3_1|3]), (342,343,[5_1|3]), (343,121,[2_1|3]), (344,345,[1_1|3]), (345,346,[3_1|3]), (346,347,[4_1|3]), (347,121,[0_1|3]), (348,349,[1_1|3]), (349,350,[3_1|3]), (350,351,[4_1|3]), (351,121,[4_1|3]), (352,353,[3_1|3]), (353,354,[4_1|3]), (354,355,[4_1|3]), (355,356,[4_1|3]), (356,121,[0_1|3]), (357,358,[1_1|3]), (358,359,[4_1|3]), (359,360,[3_1|3]), (360,361,[5_1|3]), (361,121,[4_1|3]), (362,363,[1_1|3]), (363,364,[5_1|3]), (364,365,[3_1|3]), (365,366,[4_1|3]), (366,121,[0_1|3]), (367,368,[0_1|4]), (368,369,[2_1|4]), (369,341,[1_1|4])}"
----------------------------------------

(8)
BOUNDS(1, n^1)

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

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

(10)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

   0(1(2(x1))) -> 0(0(2(1(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
   0(3(1(x1))) -> 0(1(3(4(0(x1)))))
   0(3(1(x1))) -> 0(1(3(4(4(x1)))))
   0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
   0(3(2(x1))) -> 0(2(1(3(x1))))
   0(3(2(x1))) -> 0(2(3(4(x1))))
   0(3(2(x1))) -> 0(0(2(4(3(x1)))))
   0(3(2(x1))) -> 0(2(1(4(3(x1)))))
   0(3(2(x1))) -> 0(2(4(3(3(x1)))))
   0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
   0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
   0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
   0(4(1(x1))) -> 0(1(4(4(x1))))
   0(4(1(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(3(4(x1))))
   0(4(2(x1))) -> 0(2(4(3(x1))))
   2(0(1(x1))) -> 5(0(2(1(x1))))
   2(3(1(x1))) -> 1(3(5(2(x1))))
   2(3(1(x1))) -> 0(2(1(3(5(x1)))))
   2(3(1(x1))) -> 1(4(3(5(2(x1)))))
   0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
   0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
   0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
   0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
   0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
   0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
   0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
   0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
   0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
   0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
   2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
   2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
   2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
   2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
   0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
   0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
   0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
   0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
   0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
   0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
   0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
   0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
   2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
   2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
   2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
   2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(x1))))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(5(x_1)) -> 5(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))

Rewrite Strategy: INNERMOST
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(11) DecreasingLoopProof (LOWER BOUND(ID))
The following loop(s) give(s) rise to the lower bound Omega(n^1):

The rewrite sequence

0(3(1(x1))) ->^+ 1(3(4(4(4(0(x1))))))

gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0,0,0,0].

The pumping substitution is [x1 / 3(1(x1))].

The result substitution is [ ].




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

(12)
Complex Obligation (BEST)

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

(13)
Obligation:
Proved the lower bound n^1 for the following obligation:

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


The TRS R consists of the following rules:

   0(1(2(x1))) -> 0(0(2(1(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
   0(3(1(x1))) -> 0(1(3(4(0(x1)))))
   0(3(1(x1))) -> 0(1(3(4(4(x1)))))
   0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
   0(3(2(x1))) -> 0(2(1(3(x1))))
   0(3(2(x1))) -> 0(2(3(4(x1))))
   0(3(2(x1))) -> 0(0(2(4(3(x1)))))
   0(3(2(x1))) -> 0(2(1(4(3(x1)))))
   0(3(2(x1))) -> 0(2(4(3(3(x1)))))
   0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
   0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
   0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
   0(4(1(x1))) -> 0(1(4(4(x1))))
   0(4(1(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(3(4(x1))))
   0(4(2(x1))) -> 0(2(4(3(x1))))
   2(0(1(x1))) -> 5(0(2(1(x1))))
   2(3(1(x1))) -> 1(3(5(2(x1))))
   2(3(1(x1))) -> 0(2(1(3(5(x1)))))
   2(3(1(x1))) -> 1(4(3(5(2(x1)))))
   0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
   0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
   0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
   0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
   0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
   0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
   0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
   0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
   0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
   0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
   2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
   2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
   2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
   2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
   0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
   0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
   0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
   0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
   0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
   0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
   0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
   0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
   2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
   2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
   2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
   2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(x1))))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(5(x_1)) -> 5(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))

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

(14) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
----------------------------------------

(15)
BOUNDS(n^1, INF)

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

(16)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

   0(1(2(x1))) -> 0(0(2(1(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(0(2(1(4(4(x1))))))
   0(3(1(x1))) -> 0(1(3(4(0(x1)))))
   0(3(1(x1))) -> 0(1(3(4(4(x1)))))
   0(3(1(x1))) -> 1(3(4(4(4(0(x1))))))
   0(3(2(x1))) -> 0(2(1(3(x1))))
   0(3(2(x1))) -> 0(2(3(4(x1))))
   0(3(2(x1))) -> 0(0(2(4(3(x1)))))
   0(3(2(x1))) -> 0(2(1(4(3(x1)))))
   0(3(2(x1))) -> 0(2(4(3(3(x1)))))
   0(3(2(x1))) -> 0(2(1(3(3(4(x1))))))
   0(3(2(x1))) -> 0(2(3(4(5(5(x1))))))
   0(3(2(x1))) -> 2(4(4(3(4(0(x1))))))
   0(4(1(x1))) -> 0(1(4(4(x1))))
   0(4(1(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(1(4(x1))))
   0(4(2(x1))) -> 0(2(3(4(x1))))
   0(4(2(x1))) -> 0(2(4(3(x1))))
   2(0(1(x1))) -> 5(0(2(1(x1))))
   2(3(1(x1))) -> 1(3(5(2(x1))))
   2(3(1(x1))) -> 0(2(1(3(5(x1)))))
   2(3(1(x1))) -> 1(4(3(5(2(x1)))))
   0(2(0(1(x1)))) -> 5(0(0(2(1(x1)))))
   0(3(1(1(x1)))) -> 0(1(4(1(3(4(x1))))))
   0(3(2(1(x1)))) -> 0(0(3(4(2(1(x1))))))
   0(3(2(2(x1)))) -> 1(3(4(0(2(2(x1))))))
   0(4(1(2(x1)))) -> 1(4(0(2(5(x1)))))
   0(4(3(2(x1)))) -> 2(3(4(4(0(0(x1))))))
   0(5(3(1(x1)))) -> 0(1(4(3(5(4(x1))))))
   0(5(3(1(x1)))) -> 0(1(5(3(4(0(x1))))))
   0(5(3(2(x1)))) -> 0(2(4(5(3(x1)))))
   0(5(3(2(x1)))) -> 0(2(5(3(3(x1)))))
   2(0(3(1(x1)))) -> 2(0(1(3(5(2(x1))))))
   2(0(4(1(x1)))) -> 2(0(1(4(5(x1)))))
   2(5(3(2(x1)))) -> 2(5(2(3(3(x1)))))
   2(5(4(2(x1)))) -> 0(2(5(2(4(x1)))))
   0(0(3(2(1(x1))))) -> 0(0(1(3(5(2(x1))))))
   0(1(0(3(2(x1))))) -> 0(1(4(3(2(0(x1))))))
   0(1(0(3(2(x1))))) -> 2(3(1(0(0(5(x1))))))
   0(3(2(5(1(x1))))) -> 0(2(5(1(3(3(x1))))))
   0(5(1(1(2(x1))))) -> 0(2(4(1(1(5(x1))))))
   0(5(1(2(2(x1))))) -> 0(2(5(2(1(2(x1))))))
   0(5(3(2(1(x1))))) -> 0(1(3(4(2(5(x1))))))
   0(5(5(3(2(x1))))) -> 0(2(5(1(3(5(x1))))))
   2(0(3(1(1(x1))))) -> 2(1(0(1(3(4(x1))))))
   2(2(0(3(1(x1))))) -> 1(3(0(2(5(2(x1))))))
   2(2(0(5(1(x1))))) -> 2(0(2(1(5(1(x1))))))
   2(5(5(4(1(x1))))) -> 5(5(2(1(3(4(x1))))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(5(x_1)) -> 5(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_2(x_1)) -> 2(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))

Rewrite Strategy: INNERMOST