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


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WORST_CASE(Omega(n^1), O(n^1))
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


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

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 43 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
    (7) CpxTrsMatchBoundsProof [FINISHED, 63 ms]
    (8) BOUNDS(1, n^1)
(9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(10) TRS for Loop Detection
    (11) DecreasingLoopProof [LOWER BOUND(ID), 10 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(1(3(2(x1))))
   0(1(2(x1))) -> 0(2(1(0(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(2(2(1(x1))))
   0(1(2(x1))) -> 0(2(2(1(4(x1)))))
   0(1(2(x1))) -> 5(1(0(5(2(3(x1))))))
   0(2(4(x1))) -> 0(2(1(4(3(x1)))))
   0(4(2(x1))) -> 4(0(2(3(x1))))
   0(4(2(x1))) -> 4(0(5(5(2(x1)))))
   0(0(4(2(x1)))) -> 0(0(2(2(3(4(x1))))))
   0(1(2(2(x1)))) -> 0(2(1(0(2(x1)))))
   0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
   0(1(2(4(x1)))) -> 0(1(4(2(3(x1)))))
   0(1(2(4(x1)))) -> 4(0(2(2(1(1(x1))))))
   0(1(2(4(x1)))) -> 4(0(5(5(2(1(x1))))))
   0(1(2(5(x1)))) -> 3(5(5(2(1(0(x1))))))
   0(1(4(2(x1)))) -> 0(5(2(1(4(x1)))))
   0(1(5(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(1(5(2(x1)))) -> 0(2(2(1(0(5(x1))))))
   0(1(5(2(x1)))) -> 5(5(0(2(1(3(x1))))))
   0(2(4(2(x1)))) -> 0(5(4(3(2(2(x1))))))
   0(3(1(2(x1)))) -> 0(2(1(3(2(x1)))))
   0(3(1(2(x1)))) -> 1(0(2(5(3(x1)))))
   0(3(1(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(3(1(2(x1)))) -> 3(0(2(2(1(x1)))))
   0(3(1(2(x1)))) -> 3(2(2(1(0(x1)))))
   0(3(1(2(x1)))) -> 0(3(2(3(1(3(x1))))))
   0(3(4(2(x1)))) -> 0(2(2(3(4(x1)))))
   5(0(1(2(x1)))) -> 1(3(2(5(0(x1)))))
   5(0(1(2(x1)))) -> 5(0(2(1(3(3(x1))))))
   0(1(1(2(5(x1))))) -> 5(0(2(5(1(1(x1))))))
   0(2(3(4(2(x1))))) -> 3(2(2(3(4(0(x1))))))
   0(3(1(2(5(x1))))) -> 2(3(1(3(0(5(x1))))))
   0(3(1(5(2(x1))))) -> 0(3(2(5(1(2(x1))))))
   0(3(4(1(4(x1))))) -> 0(5(3(1(4(4(x1))))))
   0(3(5(1(2(x1))))) -> 5(5(3(2(1(0(x1))))))
   0(4(0(4(2(x1))))) -> 4(4(0(0(2(2(x1))))))
   0(4(1(1(2(x1))))) -> 3(1(4(0(2(1(x1))))))
   0(4(1(2(2(x1))))) -> 4(1(0(2(2(3(x1))))))
   0(4(1(2(5(x1))))) -> 3(4(1(0(2(5(x1))))))
   0(4(2(1(2(x1))))) -> 4(1(3(2(0(2(x1))))))
   0(4(2(1(4(x1))))) -> 0(2(1(4(4(4(x1))))))
   0(4(2(5(2(x1))))) -> 5(4(3(2(2(0(x1))))))
   0(4(5(1(2(x1))))) -> 1(4(2(0(5(5(x1))))))
   0(4(5(1(2(x1))))) -> 4(0(2(5(1(1(x1))))))
   5(0(1(2(2(x1))))) -> 5(0(2(2(1(2(x1))))))
   5(0(2(4(2(x1))))) -> 0(2(2(5(1(4(x1))))))
   5(0(4(4(2(x1))))) -> 0(5(2(5(4(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(2(x_1)) -> 2(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(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(1(3(2(x1))))
   0(1(2(x1))) -> 0(2(1(0(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(2(2(1(x1))))
   0(1(2(x1))) -> 0(2(2(1(4(x1)))))
   0(1(2(x1))) -> 5(1(0(5(2(3(x1))))))
   0(2(4(x1))) -> 0(2(1(4(3(x1)))))
   0(4(2(x1))) -> 4(0(2(3(x1))))
   0(4(2(x1))) -> 4(0(5(5(2(x1)))))
   0(0(4(2(x1)))) -> 0(0(2(2(3(4(x1))))))
   0(1(2(2(x1)))) -> 0(2(1(0(2(x1)))))
   0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
   0(1(2(4(x1)))) -> 0(1(4(2(3(x1)))))
   0(1(2(4(x1)))) -> 4(0(2(2(1(1(x1))))))
   0(1(2(4(x1)))) -> 4(0(5(5(2(1(x1))))))
   0(1(2(5(x1)))) -> 3(5(5(2(1(0(x1))))))
   0(1(4(2(x1)))) -> 0(5(2(1(4(x1)))))
   0(1(5(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(1(5(2(x1)))) -> 0(2(2(1(0(5(x1))))))
   0(1(5(2(x1)))) -> 5(5(0(2(1(3(x1))))))
   0(2(4(2(x1)))) -> 0(5(4(3(2(2(x1))))))
   0(3(1(2(x1)))) -> 0(2(1(3(2(x1)))))
   0(3(1(2(x1)))) -> 1(0(2(5(3(x1)))))
   0(3(1(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(3(1(2(x1)))) -> 3(0(2(2(1(x1)))))
   0(3(1(2(x1)))) -> 3(2(2(1(0(x1)))))
   0(3(1(2(x1)))) -> 0(3(2(3(1(3(x1))))))
   0(3(4(2(x1)))) -> 0(2(2(3(4(x1)))))
   5(0(1(2(x1)))) -> 1(3(2(5(0(x1)))))
   5(0(1(2(x1)))) -> 5(0(2(1(3(3(x1))))))
   0(1(1(2(5(x1))))) -> 5(0(2(5(1(1(x1))))))
   0(2(3(4(2(x1))))) -> 3(2(2(3(4(0(x1))))))
   0(3(1(2(5(x1))))) -> 2(3(1(3(0(5(x1))))))
   0(3(1(5(2(x1))))) -> 0(3(2(5(1(2(x1))))))
   0(3(4(1(4(x1))))) -> 0(5(3(1(4(4(x1))))))
   0(3(5(1(2(x1))))) -> 5(5(3(2(1(0(x1))))))
   0(4(0(4(2(x1))))) -> 4(4(0(0(2(2(x1))))))
   0(4(1(1(2(x1))))) -> 3(1(4(0(2(1(x1))))))
   0(4(1(2(2(x1))))) -> 4(1(0(2(2(3(x1))))))
   0(4(1(2(5(x1))))) -> 3(4(1(0(2(5(x1))))))
   0(4(2(1(2(x1))))) -> 4(1(3(2(0(2(x1))))))
   0(4(2(1(4(x1))))) -> 0(2(1(4(4(4(x1))))))
   0(4(2(5(2(x1))))) -> 5(4(3(2(2(0(x1))))))
   0(4(5(1(2(x1))))) -> 1(4(2(0(5(5(x1))))))
   0(4(5(1(2(x1))))) -> 4(0(2(5(1(1(x1))))))
   5(0(1(2(2(x1))))) -> 5(0(2(2(1(2(x1))))))
   5(0(2(4(2(x1))))) -> 0(2(2(5(1(4(x1))))))
   5(0(4(4(2(x1))))) -> 0(5(2(5(4(4(x1))))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(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(1(3(2(x1))))
   0(1(2(x1))) -> 0(2(1(0(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(2(2(1(x1))))
   0(1(2(x1))) -> 0(2(2(1(4(x1)))))
   0(1(2(x1))) -> 5(1(0(5(2(3(x1))))))
   0(2(4(x1))) -> 0(2(1(4(3(x1)))))
   0(4(2(x1))) -> 4(0(2(3(x1))))
   0(4(2(x1))) -> 4(0(5(5(2(x1)))))
   0(0(4(2(x1)))) -> 0(0(2(2(3(4(x1))))))
   0(1(2(2(x1)))) -> 0(2(1(0(2(x1)))))
   0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
   0(1(2(4(x1)))) -> 0(1(4(2(3(x1)))))
   0(1(2(4(x1)))) -> 4(0(2(2(1(1(x1))))))
   0(1(2(4(x1)))) -> 4(0(5(5(2(1(x1))))))
   0(1(2(5(x1)))) -> 3(5(5(2(1(0(x1))))))
   0(1(4(2(x1)))) -> 0(5(2(1(4(x1)))))
   0(1(5(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(1(5(2(x1)))) -> 0(2(2(1(0(5(x1))))))
   0(1(5(2(x1)))) -> 5(5(0(2(1(3(x1))))))
   0(2(4(2(x1)))) -> 0(5(4(3(2(2(x1))))))
   0(3(1(2(x1)))) -> 0(2(1(3(2(x1)))))
   0(3(1(2(x1)))) -> 1(0(2(5(3(x1)))))
   0(3(1(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(3(1(2(x1)))) -> 3(0(2(2(1(x1)))))
   0(3(1(2(x1)))) -> 3(2(2(1(0(x1)))))
   0(3(1(2(x1)))) -> 0(3(2(3(1(3(x1))))))
   0(3(4(2(x1)))) -> 0(2(2(3(4(x1)))))
   5(0(1(2(x1)))) -> 1(3(2(5(0(x1)))))
   5(0(1(2(x1)))) -> 5(0(2(1(3(3(x1))))))
   0(1(1(2(5(x1))))) -> 5(0(2(5(1(1(x1))))))
   0(2(3(4(2(x1))))) -> 3(2(2(3(4(0(x1))))))
   0(3(1(2(5(x1))))) -> 2(3(1(3(0(5(x1))))))
   0(3(1(5(2(x1))))) -> 0(3(2(5(1(2(x1))))))
   0(3(4(1(4(x1))))) -> 0(5(3(1(4(4(x1))))))
   0(3(5(1(2(x1))))) -> 5(5(3(2(1(0(x1))))))
   0(4(0(4(2(x1))))) -> 4(4(0(0(2(2(x1))))))
   0(4(1(1(2(x1))))) -> 3(1(4(0(2(1(x1))))))
   0(4(1(2(2(x1))))) -> 4(1(0(2(2(3(x1))))))
   0(4(1(2(5(x1))))) -> 3(4(1(0(2(5(x1))))))
   0(4(2(1(2(x1))))) -> 4(1(3(2(0(2(x1))))))
   0(4(2(1(4(x1))))) -> 0(2(1(4(4(4(x1))))))
   0(4(2(5(2(x1))))) -> 5(4(3(2(2(0(x1))))))
   0(4(5(1(2(x1))))) -> 1(4(2(0(5(5(x1))))))
   0(4(5(1(2(x1))))) -> 4(0(2(5(1(1(x1))))))
   5(0(1(2(2(x1))))) -> 5(0(2(2(1(2(x1))))))
   5(0(2(4(2(x1))))) -> 0(2(2(5(1(4(x1))))))
   5(0(4(4(2(x1))))) -> 0(5(2(5(4(4(x1))))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(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(1(3(2(x1))))
   0(1(2(x1))) -> 0(2(1(0(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(2(2(1(x1))))
   0(1(2(x1))) -> 0(2(2(1(4(x1)))))
   0(1(2(x1))) -> 5(1(0(5(2(3(x1))))))
   0(2(4(x1))) -> 0(2(1(4(3(x1)))))
   0(4(2(x1))) -> 4(0(2(3(x1))))
   0(4(2(x1))) -> 4(0(5(5(2(x1)))))
   0(0(4(2(x1)))) -> 0(0(2(2(3(4(x1))))))
   0(1(2(2(x1)))) -> 0(2(1(0(2(x1)))))
   0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
   0(1(2(4(x1)))) -> 0(1(4(2(3(x1)))))
   0(1(2(4(x1)))) -> 4(0(2(2(1(1(x1))))))
   0(1(2(4(x1)))) -> 4(0(5(5(2(1(x1))))))
   0(1(2(5(x1)))) -> 3(5(5(2(1(0(x1))))))
   0(1(4(2(x1)))) -> 0(5(2(1(4(x1)))))
   0(1(5(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(1(5(2(x1)))) -> 0(2(2(1(0(5(x1))))))
   0(1(5(2(x1)))) -> 5(5(0(2(1(3(x1))))))
   0(2(4(2(x1)))) -> 0(5(4(3(2(2(x1))))))
   0(3(1(2(x1)))) -> 0(2(1(3(2(x1)))))
   0(3(1(2(x1)))) -> 1(0(2(5(3(x1)))))
   0(3(1(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(3(1(2(x1)))) -> 3(0(2(2(1(x1)))))
   0(3(1(2(x1)))) -> 3(2(2(1(0(x1)))))
   0(3(1(2(x1)))) -> 0(3(2(3(1(3(x1))))))
   0(3(4(2(x1)))) -> 0(2(2(3(4(x1)))))
   5(0(1(2(x1)))) -> 1(3(2(5(0(x1)))))
   5(0(1(2(x1)))) -> 5(0(2(1(3(3(x1))))))
   0(1(1(2(5(x1))))) -> 5(0(2(5(1(1(x1))))))
   0(2(3(4(2(x1))))) -> 3(2(2(3(4(0(x1))))))
   0(3(1(2(5(x1))))) -> 2(3(1(3(0(5(x1))))))
   0(3(1(5(2(x1))))) -> 0(3(2(5(1(2(x1))))))
   0(3(4(1(4(x1))))) -> 0(5(3(1(4(4(x1))))))
   0(3(5(1(2(x1))))) -> 5(5(3(2(1(0(x1))))))
   0(4(0(4(2(x1))))) -> 4(4(0(0(2(2(x1))))))
   0(4(1(1(2(x1))))) -> 3(1(4(0(2(1(x1))))))
   0(4(1(2(2(x1))))) -> 4(1(0(2(2(3(x1))))))
   0(4(1(2(5(x1))))) -> 3(4(1(0(2(5(x1))))))
   0(4(2(1(2(x1))))) -> 4(1(3(2(0(2(x1))))))
   0(4(2(1(4(x1))))) -> 0(2(1(4(4(4(x1))))))
   0(4(2(5(2(x1))))) -> 5(4(3(2(2(0(x1))))))
   0(4(5(1(2(x1))))) -> 1(4(2(0(5(5(x1))))))
   0(4(5(1(2(x1))))) -> 4(0(2(5(1(1(x1))))))
   5(0(1(2(2(x1))))) -> 5(0(2(2(1(2(x1))))))
   5(0(2(4(2(x1))))) -> 0(2(2(5(1(4(x1))))))
   5(0(4(4(2(x1))))) -> 0(5(2(5(4(4(x1))))))
   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(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 3. 
The certificate found is represented by the following graph.

"[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, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 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, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406]
{(59,60,[0_1|0, 5_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]), (59,61,[0_1|1]), (59,64,[0_1|1]), (59,67,[0_1|1]), (59,70,[0_1|1]), (59,73,[0_1|1]), (59,77,[5_1|1]), (59,82,[0_1|1]), (59,86,[1_1|1]), (59,90,[0_1|1]), (59,94,[4_1|1]), (59,99,[4_1|1]), (59,104,[0_1|1]), (59,108,[0_1|1]), (59,112,[0_1|1]), (59,117,[3_1|1]), (59,122,[4_1|1]), (59,125,[4_1|1]), (59,129,[4_1|1]), (59,134,[0_1|1]), (59,139,[3_1|1]), (59,144,[4_1|1]), (59,149,[0_1|1]), (59,153,[1_1|1]), (59,157,[1_1|1]), (59,161,[3_1|1]), (59,165,[3_1|1]), (59,169,[0_1|1]), (59,174,[0_1|1]), (59,178,[0_1|1]), (59,183,[1_1|1, 2_1|1, 3_1|1, 4_1|1, 0_1|1, 5_1|1]), (59,184,[0_1|2]), (59,188,[0_1|2]), (59,191,[0_1|2]), (59,194,[0_1|2]), (59,197,[0_1|2]), (59,200,[0_1|2]), (59,204,[5_1|2]), (59,209,[0_1|2]), (59,213,[1_1|2]), (59,217,[0_1|2]), (59,221,[4_1|2]), (59,226,[4_1|2]), (59,231,[3_1|2]), (59,236,[1_1|2]), (59,240,[0_1|2]), (59,245,[5_1|2]), (59,250,[5_1|2]), (59,255,[0_1|2]), (59,259,[0_1|2]), (59,264,[3_1|2]), (59,269,[4_1|2]), (59,272,[4_1|2]), (59,276,[4_1|2]), (59,281,[0_1|2]), (59,286,[5_1|2]), (59,291,[4_1|2]), (59,296,[3_1|2]), (59,301,[4_1|2]), (59,306,[3_1|2]), (59,311,[1_1|2]), (59,316,[4_1|2]), (59,321,[0_1|2]), (59,326,[0_1|2]), (59,330,[1_1|2]), (59,334,[3_1|2]), (59,338,[3_1|2]), (59,342,[0_1|2]), (59,347,[2_1|2]), (59,352,[0_1|2]), (59,357,[0_1|2]), (59,361,[0_1|2]), (59,366,[5_1|2]), (59,371,[1_1|2]), (59,375,[5_1|2]), (59,380,[5_1|2]), (59,385,[0_1|2]), (59,390,[0_1|2]), (59,395,[0_1|3]), (60,60,[1_1|0, 2_1|0, 3_1|0, 4_1|0, cons_0_1|0, cons_5_1|0]), (61,62,[1_1|1]), (62,63,[3_1|1]), (63,60,[2_1|1]), (64,65,[2_1|1]), (65,66,[1_1|1]), (66,60,[0_1|1]), (66,61,[0_1|1]), (66,64,[0_1|1]), (66,67,[0_1|1]), (66,70,[0_1|1]), (66,73,[0_1|1]), (66,77,[5_1|1]), (66,82,[0_1|1]), (66,86,[1_1|1]), (66,90,[0_1|1]), (66,94,[4_1|1]), (66,99,[4_1|1]), (66,104,[0_1|1]), (66,108,[0_1|1]), (66,112,[0_1|1]), (66,117,[3_1|1]), (66,122,[4_1|1]), (66,125,[4_1|1]), (66,129,[4_1|1]), (66,134,[0_1|1]), (66,139,[3_1|1]), (66,144,[4_1|1]), (66,149,[0_1|1]), (66,153,[1_1|1]), (66,157,[1_1|1]), (66,161,[3_1|1]), (66,165,[3_1|1]), (66,169,[0_1|1]), (66,174,[0_1|1]), (66,178,[0_1|1]), (66,184,[0_1|2]), (67,68,[2_1|1]), (68,69,[1_1|1]), (69,60,[3_1|1]), (70,71,[2_1|1]), (71,72,[2_1|1]), (72,60,[1_1|1]), (73,74,[2_1|1]), (74,75,[2_1|1]), (75,76,[1_1|1]), (76,60,[4_1|1]), (77,78,[1_1|1]), (78,79,[0_1|1]), (79,80,[5_1|1]), (80,81,[2_1|1]), (81,60,[3_1|1]), (82,83,[2_1|1]), (83,84,[1_1|1]), (84,85,[0_1|1]), (84,108,[0_1|1]), (84,112,[0_1|1]), (84,117,[3_1|1]), (85,60,[2_1|1]), (86,87,[3_1|1]), (87,88,[0_1|1]), (88,89,[2_1|1]), (89,60,[2_1|1]), (90,91,[1_1|1]), (91,92,[4_1|1]), (92,93,[2_1|1]), (93,60,[3_1|1]), (94,95,[0_1|1]), (95,96,[2_1|1]), (96,97,[2_1|1]), (97,98,[1_1|1]), (98,60,[1_1|1]), (99,100,[0_1|1]), (100,101,[5_1|1]), (101,102,[5_1|1]), (102,103,[2_1|1]), (103,60,[1_1|1]), (104,105,[5_1|1]), (105,106,[2_1|1]), (106,107,[1_1|1]), (107,60,[4_1|1]), (108,109,[2_1|1]), (109,110,[1_1|1]), (110,111,[4_1|1]), (111,60,[3_1|1]), (112,113,[5_1|1]), (113,114,[4_1|1]), (114,115,[3_1|1]), (115,116,[2_1|1]), (116,60,[2_1|1]), (117,118,[2_1|1]), (118,119,[2_1|1]), (119,120,[3_1|1]), (120,121,[4_1|1]), (121,60,[0_1|1]), (121,61,[0_1|1]), (121,64,[0_1|1]), (121,67,[0_1|1]), (121,70,[0_1|1]), (121,73,[0_1|1]), (121,77,[5_1|1]), (121,82,[0_1|1]), (121,86,[1_1|1]), (121,90,[0_1|1]), (121,94,[4_1|1]), (121,99,[4_1|1]), (121,104,[0_1|1]), (121,108,[0_1|1]), (121,112,[0_1|1]), (121,117,[3_1|1]), (121,122,[4_1|1]), (121,125,[4_1|1]), (121,129,[4_1|1]), (121,134,[0_1|1]), (121,139,[3_1|1]), (121,144,[4_1|1]), (121,149,[0_1|1]), (121,153,[1_1|1]), (121,157,[1_1|1]), (121,161,[3_1|1]), (121,165,[3_1|1]), (121,169,[0_1|1]), (121,174,[0_1|1]), (121,178,[0_1|1]), (121,184,[0_1|2]), (122,123,[0_1|1]), (122,117,[3_1|1]), (123,124,[2_1|1]), (124,60,[3_1|1]), (125,126,[0_1|1]), (126,127,[5_1|1]), (127,128,[5_1|1]), (128,60,[2_1|1]), (129,130,[1_1|1]), (130,131,[3_1|1]), (131,132,[2_1|1]), (132,133,[0_1|1]), (132,108,[0_1|1]), (132,112,[0_1|1]), (132,117,[3_1|1]), (133,60,[2_1|1]), (134,135,[2_1|1]), (135,136,[1_1|1]), (136,137,[4_1|1]), (137,138,[4_1|1]), (138,60,[4_1|1]), (139,140,[1_1|1]), (140,141,[4_1|1]), (141,142,[0_1|1]), (142,143,[2_1|1]), (143,60,[1_1|1]), (144,145,[1_1|1]), (145,146,[0_1|1]), (146,147,[2_1|1]), (147,148,[2_1|1]), (148,60,[3_1|1]), (149,150,[2_1|1]), (150,151,[1_1|1]), (151,152,[3_1|1]), (152,60,[2_1|1]), (153,154,[0_1|1]), (154,155,[2_1|1]), (155,156,[5_1|1]), (156,60,[3_1|1]), (157,158,[5_1|1]), (158,159,[0_1|1]), (158,117,[3_1|1]), (159,160,[2_1|1]), (160,60,[3_1|1]), (161,162,[0_1|1]), (162,163,[2_1|1]), (163,164,[2_1|1]), (164,60,[1_1|1]), (165,166,[2_1|1]), (166,167,[2_1|1]), (167,168,[1_1|1]), (168,60,[0_1|1]), (168,61,[0_1|1]), (168,64,[0_1|1]), (168,67,[0_1|1]), (168,70,[0_1|1]), (168,73,[0_1|1]), (168,77,[5_1|1]), (168,82,[0_1|1]), (168,86,[1_1|1]), (168,90,[0_1|1]), (168,94,[4_1|1]), (168,99,[4_1|1]), (168,104,[0_1|1]), (168,108,[0_1|1]), (168,112,[0_1|1]), (168,117,[3_1|1]), (168,122,[4_1|1]), (168,125,[4_1|1]), (168,129,[4_1|1]), (168,134,[0_1|1]), (168,139,[3_1|1]), (168,144,[4_1|1]), (168,149,[0_1|1]), (168,153,[1_1|1]), (168,157,[1_1|1]), (168,161,[3_1|1]), (168,165,[3_1|1]), (168,169,[0_1|1]), (168,174,[0_1|1]), (168,178,[0_1|1]), (168,184,[0_1|2]), (169,170,[3_1|1]), (170,171,[2_1|1]), (171,172,[3_1|1]), (172,173,[1_1|1]), (173,60,[3_1|1]), (174,175,[2_1|1]), (175,176,[2_1|1]), (176,177,[3_1|1]), (177,60,[4_1|1]), (178,179,[5_1|1]), (179,180,[3_1|1]), (180,181,[1_1|1]), (181,182,[4_1|1]), (182,60,[4_1|1]), (183,60,[encArg_1|1]), (183,183,[1_1|1, 2_1|1, 3_1|1, 4_1|1, 0_1|1, 5_1|1]), (183,188,[0_1|2]), (183,191,[0_1|2]), (183,194,[0_1|2]), (183,197,[0_1|2]), (183,200,[0_1|2]), (183,204,[5_1|2]), (183,209,[0_1|2]), (183,213,[1_1|2]), (183,217,[0_1|2]), (183,221,[4_1|2]), (183,226,[4_1|2]), (183,231,[3_1|2]), (183,184,[0_1|2]), (183,236,[1_1|2]), (183,240,[0_1|2]), (183,245,[5_1|2]), (183,250,[5_1|2]), (183,255,[0_1|2]), (183,259,[0_1|2]), (183,264,[3_1|2]), (183,269,[4_1|2]), (183,272,[4_1|2]), (183,276,[4_1|2]), (183,281,[0_1|2]), (183,286,[5_1|2]), (183,291,[4_1|2]), (183,296,[3_1|2]), (183,301,[4_1|2]), (183,306,[3_1|2]), (183,311,[1_1|2]), (183,316,[4_1|2]), (183,321,[0_1|2]), (183,326,[0_1|2]), (183,330,[1_1|2]), (183,334,[3_1|2]), (183,338,[3_1|2]), (183,342,[0_1|2]), (183,347,[2_1|2]), (183,352,[0_1|2]), (183,357,[0_1|2]), (183,361,[0_1|2]), (183,366,[5_1|2]), (183,371,[1_1|2]), (183,375,[5_1|2]), (183,380,[5_1|2]), (183,385,[0_1|2]), (183,390,[0_1|2]), (183,395,[0_1|3]), (184,185,[5_1|2]), (185,186,[2_1|2]), (186,187,[1_1|2]), (187,93,[4_1|2]), (187,183,[4_1|2]), (187,347,[4_1|2]), (187,313,[4_1|2]), (188,189,[1_1|2]), (189,190,[3_1|2]), (190,183,[2_1|2]), (190,347,[2_1|2]), (191,192,[2_1|2]), (192,193,[1_1|2]), (193,183,[0_1|2]), (193,347,[0_1|2, 2_1|2]), (193,188,[0_1|2]), (193,191,[0_1|2]), (193,194,[0_1|2]), (193,197,[0_1|2]), (193,200,[0_1|2]), (193,204,[5_1|2]), (193,209,[0_1|2]), (193,213,[1_1|2]), (193,217,[0_1|2]), (193,221,[4_1|2]), (193,226,[4_1|2]), (193,231,[3_1|2]), (193,184,[0_1|2]), (193,236,[1_1|2]), (193,240,[0_1|2]), (193,245,[5_1|2]), (193,250,[5_1|2]), (193,255,[0_1|2]), (193,259,[0_1|2]), (193,264,[3_1|2]), (193,269,[4_1|2]), (193,272,[4_1|2]), (193,276,[4_1|2]), (193,281,[0_1|2]), (193,286,[5_1|2]), (193,291,[4_1|2]), (193,296,[3_1|2]), (193,301,[4_1|2]), (193,306,[3_1|2]), (193,311,[1_1|2]), (193,316,[4_1|2]), (193,321,[0_1|2]), (193,326,[0_1|2]), (193,330,[1_1|2]), (193,334,[3_1|2]), (193,338,[3_1|2]), (193,342,[0_1|2]), (193,352,[0_1|2]), (193,357,[0_1|2]), (193,361,[0_1|2]), (193,366,[5_1|2]), (193,399,[0_1|3]), (194,195,[2_1|2]), (195,196,[1_1|2]), (196,183,[3_1|2]), (196,347,[3_1|2]), (197,198,[2_1|2]), (198,199,[2_1|2]), (199,183,[1_1|2]), (199,347,[1_1|2]), (200,201,[2_1|2]), (201,202,[2_1|2]), (202,203,[1_1|2]), (203,183,[4_1|2]), (203,347,[4_1|2]), (204,205,[1_1|2]), (205,206,[0_1|2]), (206,207,[5_1|2]), (207,208,[2_1|2]), (208,183,[3_1|2]), (208,347,[3_1|2]), (209,210,[2_1|2]), (210,211,[1_1|2]), (211,212,[0_1|2]), (211,255,[0_1|2]), (211,259,[0_1|2]), (211,264,[3_1|2]), (211,403,[0_1|3]), (212,183,[2_1|2]), (212,347,[2_1|2]), (213,214,[3_1|2]), (214,215,[0_1|2]), (215,216,[2_1|2]), (216,183,[2_1|2]), (216,347,[2_1|2]), (217,218,[1_1|2]), (218,219,[4_1|2]), (219,220,[2_1|2]), (220,183,[3_1|2]), (220,221,[3_1|2]), (220,226,[3_1|2]), (220,269,[3_1|2]), (220,272,[3_1|2]), (220,276,[3_1|2]), (220,291,[3_1|2]), (220,301,[3_1|2]), (220,316,[3_1|2]), (221,222,[0_1|2]), (222,223,[2_1|2]), (223,224,[2_1|2]), (224,225,[1_1|2]), (225,183,[1_1|2]), (225,221,[1_1|2]), (225,226,[1_1|2]), (225,269,[1_1|2]), (225,272,[1_1|2]), (225,276,[1_1|2]), (225,291,[1_1|2]), (225,301,[1_1|2]), (225,316,[1_1|2]), (226,227,[0_1|2]), (227,228,[5_1|2]), (228,229,[5_1|2]), (229,230,[2_1|2]), (230,183,[1_1|2]), (230,221,[1_1|2]), (230,226,[1_1|2]), (230,269,[1_1|2]), (230,272,[1_1|2]), (230,276,[1_1|2]), (230,291,[1_1|2]), (230,301,[1_1|2]), (230,316,[1_1|2]), (231,232,[5_1|2]), (232,233,[5_1|2]), (233,234,[2_1|2]), (234,235,[1_1|2]), (235,183,[0_1|2]), (235,204,[0_1|2, 5_1|2]), (235,245,[0_1|2, 5_1|2]), (235,250,[0_1|2, 5_1|2]), (235,286,[0_1|2, 5_1|2]), (235,366,[0_1|2, 5_1|2]), (235,375,[0_1|2]), (235,380,[0_1|2]), (235,188,[0_1|2]), (235,191,[0_1|2]), (235,194,[0_1|2]), (235,197,[0_1|2]), (235,200,[0_1|2]), (235,209,[0_1|2]), (235,213,[1_1|2]), (235,217,[0_1|2]), (235,221,[4_1|2]), (235,226,[4_1|2]), (235,231,[3_1|2]), (235,184,[0_1|2]), (235,236,[1_1|2]), (235,240,[0_1|2]), (235,255,[0_1|2]), (235,259,[0_1|2]), (235,264,[3_1|2]), (235,269,[4_1|2]), (235,272,[4_1|2]), (235,276,[4_1|2]), (235,281,[0_1|2]), (235,291,[4_1|2]), (235,296,[3_1|2]), (235,301,[4_1|2]), (235,306,[3_1|2]), (235,311,[1_1|2]), (235,316,[4_1|2]), (235,321,[0_1|2]), (235,326,[0_1|2]), (235,330,[1_1|2]), (235,334,[3_1|2]), (235,338,[3_1|2]), (235,342,[0_1|2]), (235,347,[2_1|2]), (235,352,[0_1|2]), (235,357,[0_1|2]), (235,361,[0_1|2]), (235,399,[0_1|3]), (236,237,[5_1|2]), (237,238,[0_1|2]), (237,264,[3_1|2]), (238,239,[2_1|2]), (239,183,[3_1|2]), (239,347,[3_1|2]), (240,241,[2_1|2]), (241,242,[2_1|2]), (242,243,[1_1|2]), (243,244,[0_1|2]), (244,183,[5_1|2]), (244,347,[5_1|2]), (244,371,[1_1|2]), (244,375,[5_1|2]), (244,380,[5_1|2]), (244,385,[0_1|2]), (244,390,[0_1|2]), (245,246,[5_1|2]), (246,247,[0_1|2]), (247,248,[2_1|2]), (248,249,[1_1|2]), (249,183,[3_1|2]), (249,347,[3_1|2]), (250,251,[0_1|2]), (251,252,[2_1|2]), (252,253,[5_1|2]), (253,254,[1_1|2]), (254,183,[1_1|2]), (254,204,[1_1|2]), (254,245,[1_1|2]), (254,250,[1_1|2]), (254,286,[1_1|2]), (254,366,[1_1|2]), (254,375,[1_1|2]), (254,380,[1_1|2]), (255,256,[2_1|2]), (256,257,[1_1|2]), (257,258,[4_1|2]), (258,183,[3_1|2]), (258,221,[3_1|2]), (258,226,[3_1|2]), (258,269,[3_1|2]), (258,272,[3_1|2]), (258,276,[3_1|2]), (258,291,[3_1|2]), (258,301,[3_1|2]), (258,316,[3_1|2]), (259,260,[5_1|2]), (260,261,[4_1|2]), (261,262,[3_1|2]), (262,263,[2_1|2]), (263,183,[2_1|2]), (263,347,[2_1|2]), (264,265,[2_1|2]), (265,266,[2_1|2]), (266,267,[3_1|2]), (267,268,[4_1|2]), (268,183,[0_1|2]), (268,347,[0_1|2, 2_1|2]), (268,188,[0_1|2]), (268,191,[0_1|2]), (268,194,[0_1|2]), (268,197,[0_1|2]), (268,200,[0_1|2]), (268,204,[5_1|2]), (268,209,[0_1|2]), (268,213,[1_1|2]), (268,217,[0_1|2]), (268,221,[4_1|2]), (268,226,[4_1|2]), (268,231,[3_1|2]), (268,184,[0_1|2]), (268,236,[1_1|2]), (268,240,[0_1|2]), (268,245,[5_1|2]), (268,250,[5_1|2]), (268,255,[0_1|2]), (268,259,[0_1|2]), (268,264,[3_1|2]), (268,269,[4_1|2]), (268,272,[4_1|2]), (268,276,[4_1|2]), (268,281,[0_1|2]), (268,286,[5_1|2]), (268,291,[4_1|2]), (268,296,[3_1|2]), (268,301,[4_1|2]), (268,306,[3_1|2]), (268,311,[1_1|2]), (268,316,[4_1|2]), (268,321,[0_1|2]), (268,326,[0_1|2]), (268,330,[1_1|2]), (268,334,[3_1|2]), (268,338,[3_1|2]), (268,342,[0_1|2]), (268,352,[0_1|2]), (268,357,[0_1|2]), (268,361,[0_1|2]), (268,366,[5_1|2]), (268,399,[0_1|3]), (269,270,[0_1|2]), (269,264,[3_1|2]), (270,271,[2_1|2]), (271,183,[3_1|2]), (271,347,[3_1|2]), (272,273,[0_1|2]), (273,274,[5_1|2]), (274,275,[5_1|2]), (275,183,[2_1|2]), (275,347,[2_1|2]), (276,277,[1_1|2]), (277,278,[3_1|2]), (278,279,[2_1|2]), (279,280,[0_1|2]), (279,255,[0_1|2]), (279,259,[0_1|2]), (279,264,[3_1|2]), (279,403,[0_1|3]), (280,183,[2_1|2]), (280,347,[2_1|2]), (281,282,[2_1|2]), (282,283,[1_1|2]), (283,284,[4_1|2]), (284,285,[4_1|2]), (285,183,[4_1|2]), (285,221,[4_1|2]), (285,226,[4_1|2]), (285,269,[4_1|2]), (285,272,[4_1|2]), (285,276,[4_1|2]), (285,291,[4_1|2]), (285,301,[4_1|2]), (285,316,[4_1|2]), (285,312,[4_1|2]), (286,287,[4_1|2]), (287,288,[3_1|2]), (288,289,[2_1|2]), (289,290,[2_1|2]), (290,183,[0_1|2]), (290,347,[0_1|2, 2_1|2]), (290,188,[0_1|2]), (290,191,[0_1|2]), (290,194,[0_1|2]), (290,197,[0_1|2]), (290,200,[0_1|2]), (290,204,[5_1|2]), (290,209,[0_1|2]), (290,213,[1_1|2]), (290,217,[0_1|2]), (290,221,[4_1|2]), (290,226,[4_1|2]), (290,231,[3_1|2]), (290,184,[0_1|2]), (290,236,[1_1|2]), (290,240,[0_1|2]), (290,245,[5_1|2]), (290,250,[5_1|2]), (290,255,[0_1|2]), (290,259,[0_1|2]), (290,264,[3_1|2]), (290,269,[4_1|2]), (290,272,[4_1|2]), (290,276,[4_1|2]), (290,281,[0_1|2]), (290,286,[5_1|2]), (290,291,[4_1|2]), (290,296,[3_1|2]), (290,301,[4_1|2]), (290,306,[3_1|2]), (290,311,[1_1|2]), (290,316,[4_1|2]), (290,321,[0_1|2]), (290,326,[0_1|2]), (290,330,[1_1|2]), (290,334,[3_1|2]), (290,338,[3_1|2]), (290,342,[0_1|2]), (290,352,[0_1|2]), (290,357,[0_1|2]), (290,361,[0_1|2]), (290,366,[5_1|2]), (290,399,[0_1|3]), (291,292,[4_1|2]), (292,293,[0_1|2]), (293,294,[0_1|2]), (294,295,[2_1|2]), (295,183,[2_1|2]), (295,347,[2_1|2]), (296,297,[1_1|2]), (297,298,[4_1|2]), (298,299,[0_1|2]), (299,300,[2_1|2]), (300,183,[1_1|2]), (300,347,[1_1|2]), (301,302,[1_1|2]), (302,303,[0_1|2]), (303,304,[2_1|2]), (304,305,[2_1|2]), (305,183,[3_1|2]), (305,347,[3_1|2]), (306,307,[4_1|2]), (307,308,[1_1|2]), (308,309,[0_1|2]), (309,310,[2_1|2]), (310,183,[5_1|2]), (310,204,[5_1|2]), (310,245,[5_1|2]), (310,250,[5_1|2]), (310,286,[5_1|2]), (310,366,[5_1|2]), (310,375,[5_1|2]), (310,380,[5_1|2]), (310,371,[1_1|2]), (310,385,[0_1|2]), (310,390,[0_1|2]), (311,312,[4_1|2]), (312,313,[2_1|2]), (313,314,[0_1|2]), (314,315,[5_1|2]), (315,183,[5_1|2]), (315,347,[5_1|2]), (315,371,[1_1|2]), (315,375,[5_1|2]), (315,380,[5_1|2]), (315,385,[0_1|2]), (315,390,[0_1|2]), (316,317,[0_1|2]), (317,318,[2_1|2]), (318,319,[5_1|2]), (319,320,[1_1|2]), (320,183,[1_1|2]), (320,347,[1_1|2]), (321,322,[0_1|2]), (322,323,[2_1|2]), (323,324,[2_1|2]), (324,325,[3_1|2]), (325,183,[4_1|2]), (325,347,[4_1|2]), (326,327,[2_1|2]), (327,328,[1_1|2]), (328,329,[3_1|2]), (329,183,[2_1|2]), (329,347,[2_1|2]), (330,331,[0_1|2]), (331,332,[2_1|2]), (332,333,[5_1|2]), (333,183,[3_1|2]), (333,347,[3_1|2]), (334,335,[0_1|2]), (335,336,[2_1|2]), (336,337,[2_1|2]), (337,183,[1_1|2]), (337,347,[1_1|2]), (338,339,[2_1|2]), (339,340,[2_1|2]), (340,341,[1_1|2]), (341,183,[0_1|2]), (341,347,[0_1|2, 2_1|2]), (341,188,[0_1|2]), (341,191,[0_1|2]), (341,194,[0_1|2]), (341,197,[0_1|2]), (341,200,[0_1|2]), (341,204,[5_1|2]), (341,209,[0_1|2]), (341,213,[1_1|2]), (341,217,[0_1|2]), (341,221,[4_1|2]), (341,226,[4_1|2]), (341,231,[3_1|2]), (341,184,[0_1|2]), (341,236,[1_1|2]), (341,240,[0_1|2]), (341,245,[5_1|2]), (341,250,[5_1|2]), (341,255,[0_1|2]), (341,259,[0_1|2]), (341,264,[3_1|2]), (341,269,[4_1|2]), (341,272,[4_1|2]), (341,276,[4_1|2]), (341,281,[0_1|2]), (341,286,[5_1|2]), (341,291,[4_1|2]), (341,296,[3_1|2]), (341,301,[4_1|2]), (341,306,[3_1|2]), (341,311,[1_1|2]), (341,316,[4_1|2]), (341,321,[0_1|2]), (341,326,[0_1|2]), (341,330,[1_1|2]), (341,334,[3_1|2]), (341,338,[3_1|2]), (341,342,[0_1|2]), (341,352,[0_1|2]), (341,357,[0_1|2]), (341,361,[0_1|2]), (341,366,[5_1|2]), (341,399,[0_1|3]), (342,343,[3_1|2]), (343,344,[2_1|2]), (344,345,[3_1|2]), (345,346,[1_1|2]), (346,183,[3_1|2]), (346,347,[3_1|2]), (347,348,[3_1|2]), (348,349,[1_1|2]), (349,350,[3_1|2]), (350,351,[0_1|2]), (351,183,[5_1|2]), (351,204,[5_1|2]), (351,245,[5_1|2]), (351,250,[5_1|2]), (351,286,[5_1|2]), (351,366,[5_1|2]), (351,375,[5_1|2]), (351,380,[5_1|2]), (351,371,[1_1|2]), (351,385,[0_1|2]), (351,390,[0_1|2]), (352,353,[3_1|2]), (353,354,[2_1|2]), (354,355,[5_1|2]), (355,356,[1_1|2]), (356,183,[2_1|2]), (356,347,[2_1|2]), (357,358,[2_1|2]), (358,359,[2_1|2]), (359,360,[3_1|2]), (360,183,[4_1|2]), (360,347,[4_1|2]), (361,362,[5_1|2]), (362,363,[3_1|2]), (363,364,[1_1|2]), (364,365,[4_1|2]), (365,183,[4_1|2]), (365,221,[4_1|2]), (365,226,[4_1|2]), (365,269,[4_1|2]), (365,272,[4_1|2]), (365,276,[4_1|2]), (365,291,[4_1|2]), (365,301,[4_1|2]), (365,316,[4_1|2]), (365,312,[4_1|2]), (366,367,[5_1|2]), (367,368,[3_1|2]), (368,369,[2_1|2]), (369,370,[1_1|2]), (370,183,[0_1|2]), (370,347,[0_1|2, 2_1|2]), (370,188,[0_1|2]), (370,191,[0_1|2]), (370,194,[0_1|2]), (370,197,[0_1|2]), (370,200,[0_1|2]), (370,204,[5_1|2]), (370,209,[0_1|2]), (370,213,[1_1|2]), (370,217,[0_1|2]), (370,221,[4_1|2]), (370,226,[4_1|2]), (370,231,[3_1|2]), (370,184,[0_1|2]), (370,236,[1_1|2]), (370,240,[0_1|2]), (370,245,[5_1|2]), (370,250,[5_1|2]), (370,255,[0_1|2]), (370,259,[0_1|2]), (370,264,[3_1|2]), (370,269,[4_1|2]), (370,272,[4_1|2]), (370,276,[4_1|2]), (370,281,[0_1|2]), (370,286,[5_1|2]), (370,291,[4_1|2]), (370,296,[3_1|2]), (370,301,[4_1|2]), (370,306,[3_1|2]), (370,311,[1_1|2]), (370,316,[4_1|2]), (370,321,[0_1|2]), (370,326,[0_1|2]), (370,330,[1_1|2]), (370,334,[3_1|2]), (370,338,[3_1|2]), (370,342,[0_1|2]), (370,352,[0_1|2]), (370,357,[0_1|2]), (370,361,[0_1|2]), (370,366,[5_1|2]), (370,399,[0_1|3]), (371,372,[3_1|2]), (372,373,[2_1|2]), (373,374,[5_1|2]), (373,371,[1_1|2]), (373,375,[5_1|2]), (373,380,[5_1|2]), (373,385,[0_1|2]), (373,390,[0_1|2]), (374,183,[0_1|2]), (374,347,[0_1|2, 2_1|2]), (374,188,[0_1|2]), (374,191,[0_1|2]), (374,194,[0_1|2]), (374,197,[0_1|2]), (374,200,[0_1|2]), (374,204,[5_1|2]), (374,209,[0_1|2]), (374,213,[1_1|2]), (374,217,[0_1|2]), (374,221,[4_1|2]), (374,226,[4_1|2]), (374,231,[3_1|2]), (374,184,[0_1|2]), (374,236,[1_1|2]), (374,240,[0_1|2]), (374,245,[5_1|2]), (374,250,[5_1|2]), (374,255,[0_1|2]), (374,259,[0_1|2]), (374,264,[3_1|2]), (374,269,[4_1|2]), (374,272,[4_1|2]), (374,276,[4_1|2]), (374,281,[0_1|2]), (374,286,[5_1|2]), (374,291,[4_1|2]), (374,296,[3_1|2]), (374,301,[4_1|2]), (374,306,[3_1|2]), (374,311,[1_1|2]), (374,316,[4_1|2]), (374,321,[0_1|2]), (374,326,[0_1|2]), (374,330,[1_1|2]), (374,334,[3_1|2]), (374,338,[3_1|2]), (374,342,[0_1|2]), (374,352,[0_1|2]), (374,357,[0_1|2]), (374,361,[0_1|2]), (374,366,[5_1|2]), (374,399,[0_1|3]), (375,376,[0_1|2]), (376,377,[2_1|2]), (377,378,[1_1|2]), (378,379,[3_1|2]), (379,183,[3_1|2]), (379,347,[3_1|2]), (380,381,[0_1|2]), (381,382,[2_1|2]), (382,383,[2_1|2]), (383,384,[1_1|2]), (384,183,[2_1|2]), (384,347,[2_1|2]), (385,386,[2_1|2]), (386,387,[2_1|2]), (387,388,[5_1|2]), (388,389,[1_1|2]), (389,183,[4_1|2]), (389,347,[4_1|2]), (390,391,[5_1|2]), (391,392,[2_1|2]), (392,393,[5_1|2]), (393,394,[4_1|2]), (394,183,[4_1|2]), (394,347,[4_1|2]), (395,396,[5_1|3]), (396,397,[2_1|3]), (397,398,[1_1|3]), (398,220,[4_1|3]), (399,400,[5_1|3]), (400,401,[2_1|3]), (401,402,[1_1|3]), (402,313,[4_1|3]), (402,220,[4_1|3]), (403,404,[2_1|3]), (404,405,[1_1|3]), (405,406,[4_1|3]), (406,221,[3_1|3]), (406,226,[3_1|3]), (406,269,[3_1|3]), (406,272,[3_1|3]), (406,276,[3_1|3]), (406,291,[3_1|3]), (406,301,[3_1|3]), (406,316,[3_1|3])}"
----------------------------------------

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

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(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
----------------------------------------

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

The rewrite sequence

0(1(2(x1))) ->^+ 0(2(1(0(x1))))

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

The pumping substitution is [x1 / 1(2(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(1(3(2(x1))))
   0(1(2(x1))) -> 0(2(1(0(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(2(2(1(x1))))
   0(1(2(x1))) -> 0(2(2(1(4(x1)))))
   0(1(2(x1))) -> 5(1(0(5(2(3(x1))))))
   0(2(4(x1))) -> 0(2(1(4(3(x1)))))
   0(4(2(x1))) -> 4(0(2(3(x1))))
   0(4(2(x1))) -> 4(0(5(5(2(x1)))))
   0(0(4(2(x1)))) -> 0(0(2(2(3(4(x1))))))
   0(1(2(2(x1)))) -> 0(2(1(0(2(x1)))))
   0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
   0(1(2(4(x1)))) -> 0(1(4(2(3(x1)))))
   0(1(2(4(x1)))) -> 4(0(2(2(1(1(x1))))))
   0(1(2(4(x1)))) -> 4(0(5(5(2(1(x1))))))
   0(1(2(5(x1)))) -> 3(5(5(2(1(0(x1))))))
   0(1(4(2(x1)))) -> 0(5(2(1(4(x1)))))
   0(1(5(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(1(5(2(x1)))) -> 0(2(2(1(0(5(x1))))))
   0(1(5(2(x1)))) -> 5(5(0(2(1(3(x1))))))
   0(2(4(2(x1)))) -> 0(5(4(3(2(2(x1))))))
   0(3(1(2(x1)))) -> 0(2(1(3(2(x1)))))
   0(3(1(2(x1)))) -> 1(0(2(5(3(x1)))))
   0(3(1(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(3(1(2(x1)))) -> 3(0(2(2(1(x1)))))
   0(3(1(2(x1)))) -> 3(2(2(1(0(x1)))))
   0(3(1(2(x1)))) -> 0(3(2(3(1(3(x1))))))
   0(3(4(2(x1)))) -> 0(2(2(3(4(x1)))))
   5(0(1(2(x1)))) -> 1(3(2(5(0(x1)))))
   5(0(1(2(x1)))) -> 5(0(2(1(3(3(x1))))))
   0(1(1(2(5(x1))))) -> 5(0(2(5(1(1(x1))))))
   0(2(3(4(2(x1))))) -> 3(2(2(3(4(0(x1))))))
   0(3(1(2(5(x1))))) -> 2(3(1(3(0(5(x1))))))
   0(3(1(5(2(x1))))) -> 0(3(2(5(1(2(x1))))))
   0(3(4(1(4(x1))))) -> 0(5(3(1(4(4(x1))))))
   0(3(5(1(2(x1))))) -> 5(5(3(2(1(0(x1))))))
   0(4(0(4(2(x1))))) -> 4(4(0(0(2(2(x1))))))
   0(4(1(1(2(x1))))) -> 3(1(4(0(2(1(x1))))))
   0(4(1(2(2(x1))))) -> 4(1(0(2(2(3(x1))))))
   0(4(1(2(5(x1))))) -> 3(4(1(0(2(5(x1))))))
   0(4(2(1(2(x1))))) -> 4(1(3(2(0(2(x1))))))
   0(4(2(1(4(x1))))) -> 0(2(1(4(4(4(x1))))))
   0(4(2(5(2(x1))))) -> 5(4(3(2(2(0(x1))))))
   0(4(5(1(2(x1))))) -> 1(4(2(0(5(5(x1))))))
   0(4(5(1(2(x1))))) -> 4(0(2(5(1(1(x1))))))
   5(0(1(2(2(x1))))) -> 5(0(2(2(1(2(x1))))))
   5(0(2(4(2(x1))))) -> 0(2(2(5(1(4(x1))))))
   5(0(4(4(2(x1))))) -> 0(5(2(5(4(4(x1))))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(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(1(3(2(x1))))
   0(1(2(x1))) -> 0(2(1(0(x1))))
   0(1(2(x1))) -> 0(2(1(3(x1))))
   0(1(2(x1))) -> 0(2(2(1(x1))))
   0(1(2(x1))) -> 0(2(2(1(4(x1)))))
   0(1(2(x1))) -> 5(1(0(5(2(3(x1))))))
   0(2(4(x1))) -> 0(2(1(4(3(x1)))))
   0(4(2(x1))) -> 4(0(2(3(x1))))
   0(4(2(x1))) -> 4(0(5(5(2(x1)))))
   0(0(4(2(x1)))) -> 0(0(2(2(3(4(x1))))))
   0(1(2(2(x1)))) -> 0(2(1(0(2(x1)))))
   0(1(2(2(x1)))) -> 1(3(0(2(2(x1)))))
   0(1(2(4(x1)))) -> 0(1(4(2(3(x1)))))
   0(1(2(4(x1)))) -> 4(0(2(2(1(1(x1))))))
   0(1(2(4(x1)))) -> 4(0(5(5(2(1(x1))))))
   0(1(2(5(x1)))) -> 3(5(5(2(1(0(x1))))))
   0(1(4(2(x1)))) -> 0(5(2(1(4(x1)))))
   0(1(5(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(1(5(2(x1)))) -> 0(2(2(1(0(5(x1))))))
   0(1(5(2(x1)))) -> 5(5(0(2(1(3(x1))))))
   0(2(4(2(x1)))) -> 0(5(4(3(2(2(x1))))))
   0(3(1(2(x1)))) -> 0(2(1(3(2(x1)))))
   0(3(1(2(x1)))) -> 1(0(2(5(3(x1)))))
   0(3(1(2(x1)))) -> 1(5(0(2(3(x1)))))
   0(3(1(2(x1)))) -> 3(0(2(2(1(x1)))))
   0(3(1(2(x1)))) -> 3(2(2(1(0(x1)))))
   0(3(1(2(x1)))) -> 0(3(2(3(1(3(x1))))))
   0(3(4(2(x1)))) -> 0(2(2(3(4(x1)))))
   5(0(1(2(x1)))) -> 1(3(2(5(0(x1)))))
   5(0(1(2(x1)))) -> 5(0(2(1(3(3(x1))))))
   0(1(1(2(5(x1))))) -> 5(0(2(5(1(1(x1))))))
   0(2(3(4(2(x1))))) -> 3(2(2(3(4(0(x1))))))
   0(3(1(2(5(x1))))) -> 2(3(1(3(0(5(x1))))))
   0(3(1(5(2(x1))))) -> 0(3(2(5(1(2(x1))))))
   0(3(4(1(4(x1))))) -> 0(5(3(1(4(4(x1))))))
   0(3(5(1(2(x1))))) -> 5(5(3(2(1(0(x1))))))
   0(4(0(4(2(x1))))) -> 4(4(0(0(2(2(x1))))))
   0(4(1(1(2(x1))))) -> 3(1(4(0(2(1(x1))))))
   0(4(1(2(2(x1))))) -> 4(1(0(2(2(3(x1))))))
   0(4(1(2(5(x1))))) -> 3(4(1(0(2(5(x1))))))
   0(4(2(1(2(x1))))) -> 4(1(3(2(0(2(x1))))))
   0(4(2(1(4(x1))))) -> 0(2(1(4(4(4(x1))))))
   0(4(2(5(2(x1))))) -> 5(4(3(2(2(0(x1))))))
   0(4(5(1(2(x1))))) -> 1(4(2(0(5(5(x1))))))
   0(4(5(1(2(x1))))) -> 4(0(2(5(1(1(x1))))))
   5(0(1(2(2(x1))))) -> 5(0(2(2(1(2(x1))))))
   5(0(2(4(2(x1))))) -> 0(2(2(5(1(4(x1))))))
   5(0(4(4(2(x1))))) -> 0(5(2(5(4(4(x1))))))

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

   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(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