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


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


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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 54 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
    (7) CpxTrsMatchBoundsProof [FINISHED, 76 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(0(2(x1)))) -> 0(0(3(1(2(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(0(3(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(1(3(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(3(1(x1)))))
   0(2(1(4(x1)))) -> 0(4(1(2(3(x1)))))
   0(2(1(4(x1)))) -> 0(4(1(3(2(x1)))))
   0(2(1(4(x1)))) -> 2(0(4(1(4(x1)))))
   0(2(1(4(x1)))) -> 5(5(0(4(1(2(x1))))))
   0(2(1(5(x1)))) -> 5(0(4(1(2(x1)))))
   0(2(2(4(x1)))) -> 0(4(2(2(5(x1)))))
   0(2(2(4(x1)))) -> 0(4(2(5(2(x1)))))
   3(4(0(2(x1)))) -> 3(0(4(5(2(x1)))))
   3(4(0(2(x1)))) -> 3(5(0(4(2(x1)))))
   0(0(1(4(5(x1))))) -> 0(4(1(0(3(5(x1))))))
   0(1(0(2(4(x1))))) -> 2(0(0(4(1(1(x1))))))
   0(1(2(3(4(x1))))) -> 2(0(4(1(0(3(x1))))))
   0(1(3(3(4(x1))))) -> 0(0(3(1(3(4(x1))))))
   0(1(4(0(2(x1))))) -> 0(4(1(5(0(2(x1))))))
   0(1(4(1(5(x1))))) -> 2(5(0(4(1(1(x1))))))
   0(1(4(3(4(x1))))) -> 0(4(0(3(1(4(x1))))))
   0(1(4(3(4(x1))))) -> 3(0(4(1(5(4(x1))))))
   0(1(4(3(5(x1))))) -> 5(4(5(0(3(1(x1))))))
   0(1(5(0(2(x1))))) -> 0(0(4(1(2(5(x1))))))
   0(1(5(1(4(x1))))) -> 4(5(0(3(1(1(x1))))))
   0(2(1(4(4(x1))))) -> 0(4(1(2(4(3(x1))))))
   0(2(1(4(5(x1))))) -> 0(4(1(2(5(2(x1))))))
   0(2(1(5(4(x1))))) -> 5(0(2(0(4(1(x1))))))
   0(2(4(1(5(x1))))) -> 5(0(4(1(5(2(x1))))))
   0(2(4(3(5(x1))))) -> 0(4(5(2(5(3(x1))))))
   0(2(5(1(4(x1))))) -> 0(0(5(4(1(2(x1))))))
   3(0(1(3(2(x1))))) -> 0(3(1(0(3(2(x1))))))
   3(0(2(1(4(x1))))) -> 4(0(4(1(3(2(x1))))))
   3(0(2(1(5(x1))))) -> 5(3(2(0(4(1(x1))))))
   3(0(4(0(2(x1))))) -> 0(3(4(0(4(2(x1))))))
   3(0(4(0(2(x1))))) -> 0(4(1(2(0(3(x1))))))
   3(0(5(1(4(x1))))) -> 3(0(4(1(1(5(x1))))))
   3(0(5(1(5(x1))))) -> 0(4(1(3(5(5(x1))))))
   3(2(4(1(2(x1))))) -> 3(1(2(2(5(4(x1))))))
   3(2(4(1(5(x1))))) -> 3(1(4(5(2(5(x1))))))
   3(4(0(1(2(x1))))) -> 0(4(2(0(3(1(x1))))))
   3(4(0(1(4(x1))))) -> 0(4(1(5(3(4(x1))))))
   3(4(0(1(5(x1))))) -> 0(4(1(5(5(3(x1))))))
   3(4(0(2(4(x1))))) -> 0(3(4(0(4(2(x1))))))
   3(4(1(2(4(x1))))) -> 0(4(1(2(4(3(x1))))))
   3(4(1(3(5(x1))))) -> 4(3(0(3(1(5(x1))))))
   3(4(3(0(2(x1))))) -> 3(3(0(4(1(2(x1))))))
   3(4(5(0(2(x1))))) -> 0(3(0(4(2(5(x1))))))
   3(5(0(2(2(x1))))) -> 0(3(2(5(2(5(x1))))))
   3(5(2(1(4(x1))))) -> 3(5(1(0(4(2(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(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_3(x_1)) -> 3(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(0(2(x1)))) -> 0(0(3(1(2(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(0(3(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(1(3(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(3(1(x1)))))
   0(2(1(4(x1)))) -> 0(4(1(2(3(x1)))))
   0(2(1(4(x1)))) -> 0(4(1(3(2(x1)))))
   0(2(1(4(x1)))) -> 2(0(4(1(4(x1)))))
   0(2(1(4(x1)))) -> 5(5(0(4(1(2(x1))))))
   0(2(1(5(x1)))) -> 5(0(4(1(2(x1)))))
   0(2(2(4(x1)))) -> 0(4(2(2(5(x1)))))
   0(2(2(4(x1)))) -> 0(4(2(5(2(x1)))))
   3(4(0(2(x1)))) -> 3(0(4(5(2(x1)))))
   3(4(0(2(x1)))) -> 3(5(0(4(2(x1)))))
   0(0(1(4(5(x1))))) -> 0(4(1(0(3(5(x1))))))
   0(1(0(2(4(x1))))) -> 2(0(0(4(1(1(x1))))))
   0(1(2(3(4(x1))))) -> 2(0(4(1(0(3(x1))))))
   0(1(3(3(4(x1))))) -> 0(0(3(1(3(4(x1))))))
   0(1(4(0(2(x1))))) -> 0(4(1(5(0(2(x1))))))
   0(1(4(1(5(x1))))) -> 2(5(0(4(1(1(x1))))))
   0(1(4(3(4(x1))))) -> 0(4(0(3(1(4(x1))))))
   0(1(4(3(4(x1))))) -> 3(0(4(1(5(4(x1))))))
   0(1(4(3(5(x1))))) -> 5(4(5(0(3(1(x1))))))
   0(1(5(0(2(x1))))) -> 0(0(4(1(2(5(x1))))))
   0(1(5(1(4(x1))))) -> 4(5(0(3(1(1(x1))))))
   0(2(1(4(4(x1))))) -> 0(4(1(2(4(3(x1))))))
   0(2(1(4(5(x1))))) -> 0(4(1(2(5(2(x1))))))
   0(2(1(5(4(x1))))) -> 5(0(2(0(4(1(x1))))))
   0(2(4(1(5(x1))))) -> 5(0(4(1(5(2(x1))))))
   0(2(4(3(5(x1))))) -> 0(4(5(2(5(3(x1))))))
   0(2(5(1(4(x1))))) -> 0(0(5(4(1(2(x1))))))
   3(0(1(3(2(x1))))) -> 0(3(1(0(3(2(x1))))))
   3(0(2(1(4(x1))))) -> 4(0(4(1(3(2(x1))))))
   3(0(2(1(5(x1))))) -> 5(3(2(0(4(1(x1))))))
   3(0(4(0(2(x1))))) -> 0(3(4(0(4(2(x1))))))
   3(0(4(0(2(x1))))) -> 0(4(1(2(0(3(x1))))))
   3(0(5(1(4(x1))))) -> 3(0(4(1(1(5(x1))))))
   3(0(5(1(5(x1))))) -> 0(4(1(3(5(5(x1))))))
   3(2(4(1(2(x1))))) -> 3(1(2(2(5(4(x1))))))
   3(2(4(1(5(x1))))) -> 3(1(4(5(2(5(x1))))))
   3(4(0(1(2(x1))))) -> 0(4(2(0(3(1(x1))))))
   3(4(0(1(4(x1))))) -> 0(4(1(5(3(4(x1))))))
   3(4(0(1(5(x1))))) -> 0(4(1(5(5(3(x1))))))
   3(4(0(2(4(x1))))) -> 0(3(4(0(4(2(x1))))))
   3(4(1(2(4(x1))))) -> 0(4(1(2(4(3(x1))))))
   3(4(1(3(5(x1))))) -> 4(3(0(3(1(5(x1))))))
   3(4(3(0(2(x1))))) -> 3(3(0(4(1(2(x1))))))
   3(4(5(0(2(x1))))) -> 0(3(0(4(2(5(x1))))))
   3(5(0(2(2(x1))))) -> 0(3(2(5(2(5(x1))))))
   3(5(2(1(4(x1))))) -> 3(5(1(0(4(2(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(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_3(x_1)) -> 3(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(0(2(x1)))) -> 0(0(3(1(2(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(0(3(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(1(3(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(3(1(x1)))))
   0(2(1(4(x1)))) -> 0(4(1(2(3(x1)))))
   0(2(1(4(x1)))) -> 0(4(1(3(2(x1)))))
   0(2(1(4(x1)))) -> 2(0(4(1(4(x1)))))
   0(2(1(4(x1)))) -> 5(5(0(4(1(2(x1))))))
   0(2(1(5(x1)))) -> 5(0(4(1(2(x1)))))
   0(2(2(4(x1)))) -> 0(4(2(2(5(x1)))))
   0(2(2(4(x1)))) -> 0(4(2(5(2(x1)))))
   3(4(0(2(x1)))) -> 3(0(4(5(2(x1)))))
   3(4(0(2(x1)))) -> 3(5(0(4(2(x1)))))
   0(0(1(4(5(x1))))) -> 0(4(1(0(3(5(x1))))))
   0(1(0(2(4(x1))))) -> 2(0(0(4(1(1(x1))))))
   0(1(2(3(4(x1))))) -> 2(0(4(1(0(3(x1))))))
   0(1(3(3(4(x1))))) -> 0(0(3(1(3(4(x1))))))
   0(1(4(0(2(x1))))) -> 0(4(1(5(0(2(x1))))))
   0(1(4(1(5(x1))))) -> 2(5(0(4(1(1(x1))))))
   0(1(4(3(4(x1))))) -> 0(4(0(3(1(4(x1))))))
   0(1(4(3(4(x1))))) -> 3(0(4(1(5(4(x1))))))
   0(1(4(3(5(x1))))) -> 5(4(5(0(3(1(x1))))))
   0(1(5(0(2(x1))))) -> 0(0(4(1(2(5(x1))))))
   0(1(5(1(4(x1))))) -> 4(5(0(3(1(1(x1))))))
   0(2(1(4(4(x1))))) -> 0(4(1(2(4(3(x1))))))
   0(2(1(4(5(x1))))) -> 0(4(1(2(5(2(x1))))))
   0(2(1(5(4(x1))))) -> 5(0(2(0(4(1(x1))))))
   0(2(4(1(5(x1))))) -> 5(0(4(1(5(2(x1))))))
   0(2(4(3(5(x1))))) -> 0(4(5(2(5(3(x1))))))
   0(2(5(1(4(x1))))) -> 0(0(5(4(1(2(x1))))))
   3(0(1(3(2(x1))))) -> 0(3(1(0(3(2(x1))))))
   3(0(2(1(4(x1))))) -> 4(0(4(1(3(2(x1))))))
   3(0(2(1(5(x1))))) -> 5(3(2(0(4(1(x1))))))
   3(0(4(0(2(x1))))) -> 0(3(4(0(4(2(x1))))))
   3(0(4(0(2(x1))))) -> 0(4(1(2(0(3(x1))))))
   3(0(5(1(4(x1))))) -> 3(0(4(1(1(5(x1))))))
   3(0(5(1(5(x1))))) -> 0(4(1(3(5(5(x1))))))
   3(2(4(1(2(x1))))) -> 3(1(2(2(5(4(x1))))))
   3(2(4(1(5(x1))))) -> 3(1(4(5(2(5(x1))))))
   3(4(0(1(2(x1))))) -> 0(4(2(0(3(1(x1))))))
   3(4(0(1(4(x1))))) -> 0(4(1(5(3(4(x1))))))
   3(4(0(1(5(x1))))) -> 0(4(1(5(5(3(x1))))))
   3(4(0(2(4(x1))))) -> 0(3(4(0(4(2(x1))))))
   3(4(1(2(4(x1))))) -> 0(4(1(2(4(3(x1))))))
   3(4(1(3(5(x1))))) -> 4(3(0(3(1(5(x1))))))
   3(4(3(0(2(x1))))) -> 3(3(0(4(1(2(x1))))))
   3(4(5(0(2(x1))))) -> 0(3(0(4(2(5(x1))))))
   3(5(0(2(2(x1))))) -> 0(3(2(5(2(5(x1))))))
   3(5(2(1(4(x1))))) -> 3(5(1(0(4(2(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(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_3(x_1)) -> 3(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(0(2(x1)))) -> 0(0(3(1(2(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(0(3(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(1(3(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(3(1(x1)))))
   0(2(1(4(x1)))) -> 0(4(1(2(3(x1)))))
   0(2(1(4(x1)))) -> 0(4(1(3(2(x1)))))
   0(2(1(4(x1)))) -> 2(0(4(1(4(x1)))))
   0(2(1(4(x1)))) -> 5(5(0(4(1(2(x1))))))
   0(2(1(5(x1)))) -> 5(0(4(1(2(x1)))))
   0(2(2(4(x1)))) -> 0(4(2(2(5(x1)))))
   0(2(2(4(x1)))) -> 0(4(2(5(2(x1)))))
   3(4(0(2(x1)))) -> 3(0(4(5(2(x1)))))
   3(4(0(2(x1)))) -> 3(5(0(4(2(x1)))))
   0(0(1(4(5(x1))))) -> 0(4(1(0(3(5(x1))))))
   0(1(0(2(4(x1))))) -> 2(0(0(4(1(1(x1))))))
   0(1(2(3(4(x1))))) -> 2(0(4(1(0(3(x1))))))
   0(1(3(3(4(x1))))) -> 0(0(3(1(3(4(x1))))))
   0(1(4(0(2(x1))))) -> 0(4(1(5(0(2(x1))))))
   0(1(4(1(5(x1))))) -> 2(5(0(4(1(1(x1))))))
   0(1(4(3(4(x1))))) -> 0(4(0(3(1(4(x1))))))
   0(1(4(3(4(x1))))) -> 3(0(4(1(5(4(x1))))))
   0(1(4(3(5(x1))))) -> 5(4(5(0(3(1(x1))))))
   0(1(5(0(2(x1))))) -> 0(0(4(1(2(5(x1))))))
   0(1(5(1(4(x1))))) -> 4(5(0(3(1(1(x1))))))
   0(2(1(4(4(x1))))) -> 0(4(1(2(4(3(x1))))))
   0(2(1(4(5(x1))))) -> 0(4(1(2(5(2(x1))))))
   0(2(1(5(4(x1))))) -> 5(0(2(0(4(1(x1))))))
   0(2(4(1(5(x1))))) -> 5(0(4(1(5(2(x1))))))
   0(2(4(3(5(x1))))) -> 0(4(5(2(5(3(x1))))))
   0(2(5(1(4(x1))))) -> 0(0(5(4(1(2(x1))))))
   3(0(1(3(2(x1))))) -> 0(3(1(0(3(2(x1))))))
   3(0(2(1(4(x1))))) -> 4(0(4(1(3(2(x1))))))
   3(0(2(1(5(x1))))) -> 5(3(2(0(4(1(x1))))))
   3(0(4(0(2(x1))))) -> 0(3(4(0(4(2(x1))))))
   3(0(4(0(2(x1))))) -> 0(4(1(2(0(3(x1))))))
   3(0(5(1(4(x1))))) -> 3(0(4(1(1(5(x1))))))
   3(0(5(1(5(x1))))) -> 0(4(1(3(5(5(x1))))))
   3(2(4(1(2(x1))))) -> 3(1(2(2(5(4(x1))))))
   3(2(4(1(5(x1))))) -> 3(1(4(5(2(5(x1))))))
   3(4(0(1(2(x1))))) -> 0(4(2(0(3(1(x1))))))
   3(4(0(1(4(x1))))) -> 0(4(1(5(3(4(x1))))))
   3(4(0(1(5(x1))))) -> 0(4(1(5(5(3(x1))))))
   3(4(0(2(4(x1))))) -> 0(3(4(0(4(2(x1))))))
   3(4(1(2(4(x1))))) -> 0(4(1(2(4(3(x1))))))
   3(4(1(3(5(x1))))) -> 4(3(0(3(1(5(x1))))))
   3(4(3(0(2(x1))))) -> 3(3(0(4(1(2(x1))))))
   3(4(5(0(2(x1))))) -> 0(3(0(4(2(5(x1))))))
   3(5(0(2(2(x1))))) -> 0(3(2(5(2(5(x1))))))
   3(5(2(1(4(x1))))) -> 3(5(1(0(4(2(x1))))))
   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(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_3(x_1)) -> 3(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.

"[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, 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]
{(54,55,[0_1|0, 3_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]), (54,56,[2_1|1]), (54,61,[4_1|1]), (54,66,[0_1|1]), (54,70,[0_1|1]), (54,74,[2_1|1]), (54,78,[5_1|1]), (54,83,[0_1|1]), (54,88,[0_1|1]), (54,93,[5_1|1]), (54,97,[5_1|1]), (54,102,[0_1|1]), (54,106,[0_1|1]), (54,110,[5_1|1]), (54,115,[0_1|1]), (54,120,[3_1|1]), (54,125,[3_1|1]), (54,130,[3_1|1]), (54,135,[1_1|1, 2_1|1, 4_1|1, 0_1|1, 3_1|1]), (54,141,[0_1|2]), (54,145,[2_1|2]), (54,150,[0_1|2]), (54,154,[0_1|2]), (54,158,[0_1|2]), (54,162,[0_1|2]), (54,167,[2_1|2]), (54,172,[0_1|2]), (54,177,[2_1|2]), (54,182,[0_1|2]), (54,187,[3_1|2]), (54,192,[5_1|2]), (54,197,[0_1|2]), (54,202,[4_1|2]), (54,207,[0_1|2]), (54,211,[0_1|2]), (54,215,[2_1|2]), (54,219,[5_1|2]), (54,224,[0_1|2]), (54,229,[0_1|2]), (54,234,[5_1|2]), (54,238,[5_1|2]), (54,243,[0_1|2]), (54,247,[0_1|2]), (54,251,[5_1|2]), (54,256,[0_1|2]), (54,261,[0_1|2]), (54,266,[0_1|2]), (54,271,[3_1|2]), (54,275,[3_1|2]), (54,279,[0_1|2]), (54,284,[0_1|2]), (54,289,[0_1|2]), (54,294,[0_1|2]), (54,299,[4_1|2]), (54,304,[3_1|2]), (54,309,[0_1|2]), (54,314,[0_1|2]), (54,319,[4_1|2]), (54,324,[5_1|2]), (54,329,[0_1|2]), (54,334,[3_1|2]), (54,339,[0_1|2]), (54,344,[3_1|2]), (54,349,[3_1|2]), (54,354,[0_1|2]), (54,359,[3_1|2]), (54,364,[0_1|2]), (55,55,[1_1|0, 2_1|0, 4_1|0, 5_1|0, cons_0_1|0, cons_3_1|0]), (56,57,[5_1|1]), (57,58,[0_1|1]), (58,59,[4_1|1]), (59,60,[1_1|1]), (60,55,[1_1|1]), (61,62,[5_1|1]), (62,63,[0_1|1]), (63,64,[3_1|1]), (64,65,[1_1|1]), (65,55,[1_1|1]), (66,67,[4_1|1]), (67,68,[1_1|1]), (68,69,[2_1|1]), (69,55,[3_1|1]), (69,136,[0_1|1]), (69,120,[3_1|1]), (69,125,[3_1|1]), (69,130,[3_1|1]), (70,71,[4_1|1]), (71,72,[1_1|1]), (72,73,[3_1|1]), (72,120,[3_1|1]), (72,125,[3_1|1]), (73,55,[2_1|1]), (74,75,[0_1|1]), (75,76,[4_1|1]), (76,77,[1_1|1]), (77,55,[4_1|1]), (78,79,[5_1|1]), (78,55,[encArg_1|1]), (78,135,[1_1|1, 2_1|1, 4_1|1, 5_1|1, 0_1|1, 3_1|1]), (78,141,[0_1|2]), (78,145,[2_1|2]), (78,150,[0_1|2]), (78,154,[0_1|2]), (78,158,[0_1|2]), (78,162,[0_1|2]), (78,167,[2_1|2]), (78,172,[0_1|2]), (78,177,[2_1|2]), (78,182,[0_1|2]), (78,187,[3_1|2]), (78,192,[5_1|2]), (78,197,[0_1|2]), (78,202,[4_1|2]), (78,207,[0_1|2]), (78,211,[0_1|2]), (78,215,[2_1|2]), (78,219,[5_1|2]), (78,224,[0_1|2]), (78,229,[0_1|2]), (78,234,[5_1|2]), (78,238,[5_1|2]), (78,243,[0_1|2]), (78,247,[0_1|2]), (78,251,[5_1|2]), (78,256,[0_1|2]), (78,261,[0_1|2]), (78,266,[0_1|2]), (78,271,[3_1|2]), (78,275,[3_1|2]), (78,279,[0_1|2]), (78,284,[0_1|2]), (78,289,[0_1|2]), (78,294,[0_1|2]), (78,299,[4_1|2]), (78,304,[3_1|2]), (78,309,[0_1|2]), (78,314,[0_1|2]), (78,319,[4_1|2]), (78,324,[5_1|2]), (78,329,[0_1|2]), (78,334,[3_1|2]), (78,339,[0_1|2]), (78,344,[3_1|2]), (78,349,[3_1|2]), (78,354,[0_1|2]), (78,359,[3_1|2]), (78,364,[0_1|2]), (79,80,[0_1|1]), (80,81,[4_1|1]), (81,82,[1_1|1]), (82,55,[2_1|1]), (83,84,[4_1|1]), (84,85,[1_1|1]), (85,86,[2_1|1]), (86,87,[4_1|1]), (87,55,[3_1|1]), (87,136,[0_1|1]), (87,120,[3_1|1]), (87,125,[3_1|1]), (87,130,[3_1|1]), (88,89,[4_1|1]), (89,90,[1_1|1]), (90,91,[2_1|1]), (91,92,[5_1|1]), (92,55,[2_1|1]), (93,94,[0_1|1]), (94,95,[4_1|1]), (95,96,[1_1|1]), (96,55,[2_1|1]), (97,98,[0_1|1]), (98,99,[2_1|1]), (99,100,[0_1|1]), (100,101,[4_1|1]), (101,55,[1_1|1]), (102,103,[4_1|1]), (103,104,[2_1|1]), (104,105,[2_1|1]), (105,55,[5_1|1]), (106,107,[4_1|1]), (107,108,[2_1|1]), (108,109,[5_1|1]), (109,55,[2_1|1]), (110,111,[0_1|1]), (111,112,[4_1|1]), (112,113,[1_1|1]), (113,114,[5_1|1]), (114,55,[2_1|1]), (115,116,[0_1|1]), (116,117,[5_1|1]), (117,118,[4_1|1]), (118,119,[1_1|1]), (119,55,[2_1|1]), (120,121,[1_1|1]), (121,122,[2_1|1]), (122,123,[2_1|1]), (123,124,[5_1|1]), (124,55,[4_1|1]), (125,126,[1_1|1]), (126,127,[4_1|1]), (127,128,[5_1|1]), (128,129,[2_1|1]), (129,55,[5_1|1]), (130,131,[5_1|1]), (131,132,[1_1|1]), (132,133,[0_1|1]), (133,134,[4_1|1]), (134,55,[2_1|1]), (135,55,[encArg_1|1]), (135,135,[1_1|1, 2_1|1, 4_1|1, 5_1|1, 0_1|1, 3_1|1]), (135,141,[0_1|2]), (135,145,[2_1|2]), (135,150,[0_1|2]), (135,154,[0_1|2]), (135,158,[0_1|2]), (135,162,[0_1|2]), (135,167,[2_1|2]), (135,172,[0_1|2]), (135,177,[2_1|2]), (135,182,[0_1|2]), (135,187,[3_1|2]), (135,192,[5_1|2]), (135,197,[0_1|2]), (135,202,[4_1|2]), (135,207,[0_1|2]), (135,211,[0_1|2]), (135,215,[2_1|2]), (135,219,[5_1|2]), (135,224,[0_1|2]), (135,229,[0_1|2]), (135,234,[5_1|2]), (135,238,[5_1|2]), (135,243,[0_1|2]), (135,247,[0_1|2]), (135,251,[5_1|2]), (135,256,[0_1|2]), (135,261,[0_1|2]), (135,266,[0_1|2]), (135,271,[3_1|2]), (135,275,[3_1|2]), (135,279,[0_1|2]), (135,284,[0_1|2]), (135,289,[0_1|2]), (135,294,[0_1|2]), (135,299,[4_1|2]), (135,304,[3_1|2]), (135,309,[0_1|2]), (135,314,[0_1|2]), (135,319,[4_1|2]), (135,324,[5_1|2]), (135,329,[0_1|2]), (135,334,[3_1|2]), (135,339,[0_1|2]), (135,344,[3_1|2]), (135,349,[3_1|2]), (135,354,[0_1|2]), (135,359,[3_1|2]), (135,364,[0_1|2]), (136,137,[4_1|1]), (137,138,[1_1|1]), (138,139,[2_1|1]), (139,140,[4_1|1]), (140,55,[3_1|1]), (140,136,[0_1|1]), (140,120,[3_1|1]), (140,125,[3_1|1]), (140,130,[3_1|1]), (141,142,[0_1|2]), (142,143,[3_1|2]), (143,144,[1_1|2]), (144,135,[2_1|2]), (144,145,[2_1|2]), (144,167,[2_1|2]), (144,177,[2_1|2]), (144,215,[2_1|2]), (145,146,[0_1|2]), (146,147,[0_1|2]), (147,148,[4_1|2]), (148,149,[1_1|2]), (149,135,[1_1|2]), (149,202,[1_1|2]), (149,299,[1_1|2]), (149,319,[1_1|2]), (150,151,[4_1|2]), (151,152,[1_1|2]), (152,153,[0_1|2]), (153,135,[3_1|2]), (153,202,[3_1|2]), (153,299,[3_1|2, 4_1|2]), (153,319,[3_1|2, 4_1|2]), (153,271,[3_1|2]), (153,275,[3_1|2]), (153,279,[0_1|2]), (153,284,[0_1|2]), (153,289,[0_1|2]), (153,294,[0_1|2]), (153,369,[0_1|2]), (153,304,[3_1|2]), (153,309,[0_1|2]), (153,314,[0_1|2]), (153,324,[5_1|2]), (153,329,[0_1|2]), (153,364,[0_1|2]), (153,334,[3_1|2]), (153,339,[0_1|2]), (153,344,[3_1|2]), (153,349,[3_1|2]), (153,354,[0_1|2]), (153,359,[3_1|2]), (154,155,[4_1|2]), (155,156,[1_1|2]), (156,157,[1_1|2]), (157,135,[3_1|2]), (157,202,[3_1|2]), (157,299,[3_1|2, 4_1|2]), (157,319,[3_1|2, 4_1|2]), (157,271,[3_1|2]), (157,275,[3_1|2]), (157,279,[0_1|2]), (157,284,[0_1|2]), (157,289,[0_1|2]), (157,294,[0_1|2]), (157,369,[0_1|2]), (157,304,[3_1|2]), (157,309,[0_1|2]), (157,314,[0_1|2]), (157,324,[5_1|2]), (157,329,[0_1|2]), (157,364,[0_1|2]), (157,334,[3_1|2]), (157,339,[0_1|2]), (157,344,[3_1|2]), (157,349,[3_1|2]), (157,354,[0_1|2]), (157,359,[3_1|2]), (158,159,[4_1|2]), (159,160,[1_1|2]), (160,161,[3_1|2]), (161,135,[1_1|2]), (161,202,[1_1|2]), (161,299,[1_1|2]), (161,319,[1_1|2]), (162,163,[0_1|2]), (163,164,[3_1|2]), (164,165,[1_1|2]), (165,166,[3_1|2]), (165,271,[3_1|2]), (165,275,[3_1|2]), (165,279,[0_1|2]), (165,284,[0_1|2]), (165,289,[0_1|2]), (165,294,[0_1|2]), (165,369,[0_1|2]), (165,299,[4_1|2]), (165,304,[3_1|2]), (165,309,[0_1|2]), (165,374,[0_1|3]), (166,135,[4_1|2]), (166,202,[4_1|2]), (166,299,[4_1|2]), (166,319,[4_1|2]), (167,168,[0_1|2]), (168,169,[4_1|2]), (169,170,[1_1|2]), (170,171,[0_1|2]), (171,135,[3_1|2]), (171,202,[3_1|2]), (171,299,[3_1|2, 4_1|2]), (171,319,[3_1|2, 4_1|2]), (171,271,[3_1|2]), (171,275,[3_1|2]), (171,279,[0_1|2]), (171,284,[0_1|2]), (171,289,[0_1|2]), (171,294,[0_1|2]), (171,369,[0_1|2]), (171,304,[3_1|2]), (171,309,[0_1|2]), (171,314,[0_1|2]), (171,324,[5_1|2]), (171,329,[0_1|2]), (171,364,[0_1|2]), (171,334,[3_1|2]), (171,339,[0_1|2]), (171,344,[3_1|2]), (171,349,[3_1|2]), (171,354,[0_1|2]), (171,359,[3_1|2]), (172,173,[4_1|2]), (173,174,[1_1|2]), (174,175,[5_1|2]), (175,176,[0_1|2]), (175,207,[0_1|2]), (175,211,[0_1|2]), (175,215,[2_1|2]), (175,219,[5_1|2]), (175,224,[0_1|2]), (175,229,[0_1|2]), (175,234,[5_1|2]), (175,238,[5_1|2]), (175,243,[0_1|2]), (175,247,[0_1|2]), (175,251,[5_1|2]), (175,256,[0_1|2]), (175,261,[0_1|2]), (176,135,[2_1|2]), (176,145,[2_1|2]), (176,167,[2_1|2]), (176,177,[2_1|2]), (176,215,[2_1|2]), (177,178,[5_1|2]), (178,179,[0_1|2]), (179,180,[4_1|2]), (180,181,[1_1|2]), (181,135,[1_1|2]), (181,192,[1_1|2]), (181,219,[1_1|2]), (181,234,[1_1|2]), (181,238,[1_1|2]), (181,251,[1_1|2]), (181,324,[1_1|2]), (182,183,[4_1|2]), (183,184,[0_1|2]), (184,185,[3_1|2]), (185,186,[1_1|2]), (186,135,[4_1|2]), (186,202,[4_1|2]), (186,299,[4_1|2]), (186,319,[4_1|2]), (187,188,[0_1|2]), (188,189,[4_1|2]), (189,190,[1_1|2]), (190,191,[5_1|2]), (191,135,[4_1|2]), (191,202,[4_1|2]), (191,299,[4_1|2]), (191,319,[4_1|2]), (192,193,[4_1|2]), (193,194,[5_1|2]), (194,195,[0_1|2]), (195,196,[3_1|2]), (196,135,[1_1|2]), (196,192,[1_1|2]), (196,219,[1_1|2]), (196,234,[1_1|2]), (196,238,[1_1|2]), (196,251,[1_1|2]), (196,324,[1_1|2]), (196,276,[1_1|2]), (196,360,[1_1|2]), (197,198,[0_1|2]), (198,199,[4_1|2]), (199,200,[1_1|2]), (200,201,[2_1|2]), (201,135,[5_1|2]), (201,145,[5_1|2]), (201,167,[5_1|2]), (201,177,[5_1|2]), (201,215,[5_1|2]), (201,240,[5_1|2]), (202,203,[5_1|2]), (203,204,[0_1|2]), (204,205,[3_1|2]), (205,206,[1_1|2]), (206,135,[1_1|2]), (206,202,[1_1|2]), (206,299,[1_1|2]), (206,319,[1_1|2]), (207,208,[4_1|2]), (208,209,[1_1|2]), (209,210,[2_1|2]), (210,135,[3_1|2]), (210,202,[3_1|2]), (210,299,[3_1|2, 4_1|2]), (210,319,[3_1|2, 4_1|2]), (210,271,[3_1|2]), (210,275,[3_1|2]), (210,279,[0_1|2]), (210,284,[0_1|2]), (210,289,[0_1|2]), (210,294,[0_1|2]), (210,369,[0_1|2]), (210,304,[3_1|2]), (210,309,[0_1|2]), (210,314,[0_1|2]), (210,324,[5_1|2]), (210,329,[0_1|2]), (210,364,[0_1|2]), (210,334,[3_1|2]), (210,339,[0_1|2]), (210,344,[3_1|2]), (210,349,[3_1|2]), (210,354,[0_1|2]), (210,359,[3_1|2]), (211,212,[4_1|2]), (212,213,[1_1|2]), (213,214,[3_1|2]), (213,344,[3_1|2]), (213,349,[3_1|2]), (214,135,[2_1|2]), (214,202,[2_1|2]), (214,299,[2_1|2]), (214,319,[2_1|2]), (215,216,[0_1|2]), (216,217,[4_1|2]), (217,218,[1_1|2]), (218,135,[4_1|2]), (218,202,[4_1|2]), (218,299,[4_1|2]), (218,319,[4_1|2]), (219,220,[5_1|2]), (220,221,[0_1|2]), (221,222,[4_1|2]), (222,223,[1_1|2]), (223,135,[2_1|2]), (223,202,[2_1|2]), (223,299,[2_1|2]), (223,319,[2_1|2]), (224,225,[4_1|2]), (225,226,[1_1|2]), (226,227,[2_1|2]), (227,228,[4_1|2]), (228,135,[3_1|2]), (228,202,[3_1|2]), (228,299,[3_1|2, 4_1|2]), (228,319,[3_1|2, 4_1|2]), (228,271,[3_1|2]), (228,275,[3_1|2]), (228,279,[0_1|2]), (228,284,[0_1|2]), (228,289,[0_1|2]), (228,294,[0_1|2]), (228,369,[0_1|2]), (228,304,[3_1|2]), (228,309,[0_1|2]), (228,314,[0_1|2]), (228,324,[5_1|2]), (228,329,[0_1|2]), (228,364,[0_1|2]), (228,334,[3_1|2]), (228,339,[0_1|2]), (228,344,[3_1|2]), (228,349,[3_1|2]), (228,354,[0_1|2]), (228,359,[3_1|2]), (229,230,[4_1|2]), (230,231,[1_1|2]), (231,232,[2_1|2]), (232,233,[5_1|2]), (233,135,[2_1|2]), (233,192,[2_1|2]), (233,219,[2_1|2]), (233,234,[2_1|2]), (233,238,[2_1|2]), (233,251,[2_1|2]), (233,324,[2_1|2]), (233,203,[2_1|2]), (234,235,[0_1|2]), (235,236,[4_1|2]), (236,237,[1_1|2]), (237,135,[2_1|2]), (237,192,[2_1|2]), (237,219,[2_1|2]), (237,234,[2_1|2]), (237,238,[2_1|2]), (237,251,[2_1|2]), (237,324,[2_1|2]), (238,239,[0_1|2]), (239,240,[2_1|2]), (240,241,[0_1|2]), (241,242,[4_1|2]), (242,135,[1_1|2]), (242,202,[1_1|2]), (242,299,[1_1|2]), (242,319,[1_1|2]), (242,193,[1_1|2]), (243,244,[4_1|2]), (244,245,[2_1|2]), (245,246,[2_1|2]), (246,135,[5_1|2]), (246,202,[5_1|2]), (246,299,[5_1|2]), (246,319,[5_1|2]), (247,248,[4_1|2]), (248,249,[2_1|2]), (249,250,[5_1|2]), (250,135,[2_1|2]), (250,202,[2_1|2]), (250,299,[2_1|2]), (250,319,[2_1|2]), (251,252,[0_1|2]), (252,253,[4_1|2]), (253,254,[1_1|2]), (254,255,[5_1|2]), (255,135,[2_1|2]), (255,192,[2_1|2]), (255,219,[2_1|2]), (255,234,[2_1|2]), (255,238,[2_1|2]), (255,251,[2_1|2]), (255,324,[2_1|2]), (256,257,[4_1|2]), (257,258,[5_1|2]), (258,259,[2_1|2]), (259,260,[5_1|2]), (260,135,[3_1|2]), (260,192,[3_1|2]), (260,219,[3_1|2]), (260,234,[3_1|2]), (260,238,[3_1|2]), (260,251,[3_1|2]), (260,324,[3_1|2, 5_1|2]), (260,276,[3_1|2]), (260,360,[3_1|2]), (260,271,[3_1|2]), (260,275,[3_1|2]), (260,279,[0_1|2]), (260,284,[0_1|2]), (260,289,[0_1|2]), (260,294,[0_1|2]), (260,369,[0_1|2]), (260,299,[4_1|2]), (260,304,[3_1|2]), (260,309,[0_1|2]), (260,314,[0_1|2]), (260,319,[4_1|2]), (260,329,[0_1|2]), (260,364,[0_1|2]), (260,334,[3_1|2]), (260,339,[0_1|2]), (260,344,[3_1|2]), (260,349,[3_1|2]), (260,354,[0_1|2]), (260,359,[3_1|2]), (261,262,[0_1|2]), (262,263,[5_1|2]), (263,264,[4_1|2]), (264,265,[1_1|2]), (265,135,[2_1|2]), (265,202,[2_1|2]), (265,299,[2_1|2]), (265,319,[2_1|2]), (266,267,[4_1|2]), (267,268,[1_1|2]), (268,269,[0_1|2]), (269,270,[3_1|2]), (269,354,[0_1|2]), (269,359,[3_1|2]), (270,135,[5_1|2]), (270,192,[5_1|2]), (270,219,[5_1|2]), (270,234,[5_1|2]), (270,238,[5_1|2]), (270,251,[5_1|2]), (270,324,[5_1|2]), (270,203,[5_1|2]), (271,272,[0_1|2]), (272,273,[4_1|2]), (273,274,[5_1|2]), (274,135,[2_1|2]), (274,145,[2_1|2]), (274,167,[2_1|2]), (274,177,[2_1|2]), (274,215,[2_1|2]), (275,276,[5_1|2]), (276,277,[0_1|2]), (277,278,[4_1|2]), (278,135,[2_1|2]), (278,145,[2_1|2]), (278,167,[2_1|2]), (278,177,[2_1|2]), (278,215,[2_1|2]), (279,280,[3_1|2]), (280,281,[4_1|2]), (281,282,[0_1|2]), (282,283,[4_1|2]), (283,135,[2_1|2]), (283,202,[2_1|2]), (283,299,[2_1|2]), (283,319,[2_1|2]), (284,285,[4_1|2]), (285,286,[2_1|2]), (286,287,[0_1|2]), (287,288,[3_1|2]), (288,135,[1_1|2]), (288,145,[1_1|2]), (288,167,[1_1|2]), (288,177,[1_1|2]), (288,215,[1_1|2]), (289,290,[4_1|2]), (290,291,[1_1|2]), (291,292,[5_1|2]), (292,293,[3_1|2]), (292,271,[3_1|2]), (292,275,[3_1|2]), (292,279,[0_1|2]), (292,284,[0_1|2]), (292,289,[0_1|2]), (292,294,[0_1|2]), (292,369,[0_1|2]), (292,299,[4_1|2]), (292,304,[3_1|2]), (292,309,[0_1|2]), (292,374,[0_1|3]), (293,135,[4_1|2]), (293,202,[4_1|2]), (293,299,[4_1|2]), (293,319,[4_1|2]), (294,295,[4_1|2]), (295,296,[1_1|2]), (296,297,[5_1|2]), (297,298,[5_1|2]), (298,135,[3_1|2]), (298,192,[3_1|2]), (298,219,[3_1|2]), (298,234,[3_1|2]), (298,238,[3_1|2]), (298,251,[3_1|2]), (298,324,[3_1|2, 5_1|2]), (298,271,[3_1|2]), (298,275,[3_1|2]), (298,279,[0_1|2]), (298,284,[0_1|2]), (298,289,[0_1|2]), (298,294,[0_1|2]), (298,369,[0_1|2]), (298,299,[4_1|2]), (298,304,[3_1|2]), (298,309,[0_1|2]), (298,314,[0_1|2]), (298,319,[4_1|2]), (298,329,[0_1|2]), (298,364,[0_1|2]), (298,334,[3_1|2]), (298,339,[0_1|2]), (298,344,[3_1|2]), (298,349,[3_1|2]), (298,354,[0_1|2]), (298,359,[3_1|2]), (299,300,[3_1|2]), (300,301,[0_1|2]), (301,302,[3_1|2]), (302,303,[1_1|2]), (303,135,[5_1|2]), (303,192,[5_1|2]), (303,219,[5_1|2]), (303,234,[5_1|2]), (303,238,[5_1|2]), (303,251,[5_1|2]), (303,324,[5_1|2]), (303,276,[5_1|2]), (303,360,[5_1|2]), (304,305,[3_1|2]), (305,306,[0_1|2]), (306,307,[4_1|2]), (307,308,[1_1|2]), (308,135,[2_1|2]), (308,145,[2_1|2]), (308,167,[2_1|2]), (308,177,[2_1|2]), (308,215,[2_1|2]), (309,310,[3_1|2]), (310,311,[0_1|2]), (311,312,[4_1|2]), (312,313,[2_1|2]), (313,135,[5_1|2]), (313,145,[5_1|2]), (313,167,[5_1|2]), (313,177,[5_1|2]), (313,215,[5_1|2]), (313,240,[5_1|2]), (314,315,[3_1|2]), (315,316,[1_1|2]), (316,317,[0_1|2]), (317,318,[3_1|2]), (317,344,[3_1|2]), (317,349,[3_1|2]), (318,135,[2_1|2]), (318,145,[2_1|2]), (318,167,[2_1|2]), (318,177,[2_1|2]), (318,215,[2_1|2]), (319,320,[0_1|2]), (320,321,[4_1|2]), (321,322,[1_1|2]), (322,323,[3_1|2]), (322,344,[3_1|2]), (322,349,[3_1|2]), (323,135,[2_1|2]), (323,202,[2_1|2]), (323,299,[2_1|2]), (323,319,[2_1|2]), (324,325,[3_1|2]), (325,326,[2_1|2]), (326,327,[0_1|2]), (327,328,[4_1|2]), (328,135,[1_1|2]), (328,192,[1_1|2]), (328,219,[1_1|2]), (328,234,[1_1|2]), (328,238,[1_1|2]), (328,251,[1_1|2]), (328,324,[1_1|2]), (329,330,[4_1|2]), (330,331,[1_1|2]), (331,332,[2_1|2]), (332,333,[0_1|2]), (333,135,[3_1|2]), (333,145,[3_1|2]), (333,167,[3_1|2]), (333,177,[3_1|2]), (333,215,[3_1|2]), (333,271,[3_1|2]), (333,275,[3_1|2]), (333,279,[0_1|2]), (333,284,[0_1|2]), (333,289,[0_1|2]), (333,294,[0_1|2]), (333,369,[0_1|2]), (333,299,[4_1|2]), (333,304,[3_1|2]), (333,309,[0_1|2]), (333,314,[0_1|2]), (333,319,[4_1|2]), (333,324,[5_1|2]), (333,329,[0_1|2]), (333,364,[0_1|2]), (333,334,[3_1|2]), (333,339,[0_1|2]), (333,344,[3_1|2]), (333,349,[3_1|2]), (333,354,[0_1|2]), (333,359,[3_1|2]), (334,335,[0_1|2]), (335,336,[4_1|2]), (336,337,[1_1|2]), (337,338,[1_1|2]), (338,135,[5_1|2]), (338,202,[5_1|2]), (338,299,[5_1|2]), (338,319,[5_1|2]), (339,340,[4_1|2]), (340,341,[1_1|2]), (341,342,[3_1|2]), (342,343,[5_1|2]), (343,135,[5_1|2]), (343,192,[5_1|2]), (343,219,[5_1|2]), (343,234,[5_1|2]), (343,238,[5_1|2]), (343,251,[5_1|2]), (343,324,[5_1|2]), (344,345,[1_1|2]), (345,346,[2_1|2]), (346,347,[2_1|2]), (347,348,[5_1|2]), (348,135,[4_1|2]), (348,145,[4_1|2]), (348,167,[4_1|2]), (348,177,[4_1|2]), (348,215,[4_1|2]), (349,350,[1_1|2]), (350,351,[4_1|2]), (351,352,[5_1|2]), (352,353,[2_1|2]), (353,135,[5_1|2]), (353,192,[5_1|2]), (353,219,[5_1|2]), (353,234,[5_1|2]), (353,238,[5_1|2]), (353,251,[5_1|2]), (353,324,[5_1|2]), (354,355,[3_1|2]), (355,356,[2_1|2]), (356,357,[5_1|2]), (357,358,[2_1|2]), (358,135,[5_1|2]), (358,145,[5_1|2]), (358,167,[5_1|2]), (358,177,[5_1|2]), (358,215,[5_1|2]), (359,360,[5_1|2]), (360,361,[1_1|2]), (361,362,[0_1|2]), (362,363,[4_1|2]), (363,135,[2_1|2]), (363,202,[2_1|2]), (363,299,[2_1|2]), (363,319,[2_1|2]), (364,365,[3_1|2]), (365,366,[4_1|2]), (366,367,[0_1|2]), (367,368,[4_1|2]), (368,145,[2_1|2]), (368,167,[2_1|2]), (368,177,[2_1|2]), (368,215,[2_1|2]), (369,370,[4_1|2]), (370,371,[1_1|2]), (371,372,[2_1|2]), (372,373,[4_1|2]), (373,135,[3_1|2]), (373,202,[3_1|2]), (373,299,[3_1|2, 4_1|2]), (373,319,[3_1|2, 4_1|2]), (373,271,[3_1|2]), (373,275,[3_1|2]), (373,279,[0_1|2]), (373,284,[0_1|2]), (373,289,[0_1|2]), (373,294,[0_1|2]), (373,369,[0_1|2]), (373,304,[3_1|2]), (373,309,[0_1|2]), (373,314,[0_1|2]), (373,324,[5_1|2]), (373,329,[0_1|2]), (373,364,[0_1|2]), (373,334,[3_1|2]), (373,339,[0_1|2]), (373,344,[3_1|2]), (373,349,[3_1|2]), (373,354,[0_1|2]), (373,359,[3_1|2]), (374,375,[3_1|3]), (375,376,[0_1|3]), (376,377,[4_1|3]), (377,378,[2_1|3]), (378,240,[5_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(0(2(x1)))) -> 0(0(3(1(2(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(0(3(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(1(3(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(3(1(x1)))))
   0(2(1(4(x1)))) -> 0(4(1(2(3(x1)))))
   0(2(1(4(x1)))) -> 0(4(1(3(2(x1)))))
   0(2(1(4(x1)))) -> 2(0(4(1(4(x1)))))
   0(2(1(4(x1)))) -> 5(5(0(4(1(2(x1))))))
   0(2(1(5(x1)))) -> 5(0(4(1(2(x1)))))
   0(2(2(4(x1)))) -> 0(4(2(2(5(x1)))))
   0(2(2(4(x1)))) -> 0(4(2(5(2(x1)))))
   3(4(0(2(x1)))) -> 3(0(4(5(2(x1)))))
   3(4(0(2(x1)))) -> 3(5(0(4(2(x1)))))
   0(0(1(4(5(x1))))) -> 0(4(1(0(3(5(x1))))))
   0(1(0(2(4(x1))))) -> 2(0(0(4(1(1(x1))))))
   0(1(2(3(4(x1))))) -> 2(0(4(1(0(3(x1))))))
   0(1(3(3(4(x1))))) -> 0(0(3(1(3(4(x1))))))
   0(1(4(0(2(x1))))) -> 0(4(1(5(0(2(x1))))))
   0(1(4(1(5(x1))))) -> 2(5(0(4(1(1(x1))))))
   0(1(4(3(4(x1))))) -> 0(4(0(3(1(4(x1))))))
   0(1(4(3(4(x1))))) -> 3(0(4(1(5(4(x1))))))
   0(1(4(3(5(x1))))) -> 5(4(5(0(3(1(x1))))))
   0(1(5(0(2(x1))))) -> 0(0(4(1(2(5(x1))))))
   0(1(5(1(4(x1))))) -> 4(5(0(3(1(1(x1))))))
   0(2(1(4(4(x1))))) -> 0(4(1(2(4(3(x1))))))
   0(2(1(4(5(x1))))) -> 0(4(1(2(5(2(x1))))))
   0(2(1(5(4(x1))))) -> 5(0(2(0(4(1(x1))))))
   0(2(4(1(5(x1))))) -> 5(0(4(1(5(2(x1))))))
   0(2(4(3(5(x1))))) -> 0(4(5(2(5(3(x1))))))
   0(2(5(1(4(x1))))) -> 0(0(5(4(1(2(x1))))))
   3(0(1(3(2(x1))))) -> 0(3(1(0(3(2(x1))))))
   3(0(2(1(4(x1))))) -> 4(0(4(1(3(2(x1))))))
   3(0(2(1(5(x1))))) -> 5(3(2(0(4(1(x1))))))
   3(0(4(0(2(x1))))) -> 0(3(4(0(4(2(x1))))))
   3(0(4(0(2(x1))))) -> 0(4(1(2(0(3(x1))))))
   3(0(5(1(4(x1))))) -> 3(0(4(1(1(5(x1))))))
   3(0(5(1(5(x1))))) -> 0(4(1(3(5(5(x1))))))
   3(2(4(1(2(x1))))) -> 3(1(2(2(5(4(x1))))))
   3(2(4(1(5(x1))))) -> 3(1(4(5(2(5(x1))))))
   3(4(0(1(2(x1))))) -> 0(4(2(0(3(1(x1))))))
   3(4(0(1(4(x1))))) -> 0(4(1(5(3(4(x1))))))
   3(4(0(1(5(x1))))) -> 0(4(1(5(5(3(x1))))))
   3(4(0(2(4(x1))))) -> 0(3(4(0(4(2(x1))))))
   3(4(1(2(4(x1))))) -> 0(4(1(2(4(3(x1))))))
   3(4(1(3(5(x1))))) -> 4(3(0(3(1(5(x1))))))
   3(4(3(0(2(x1))))) -> 3(3(0(4(1(2(x1))))))
   3(4(5(0(2(x1))))) -> 0(3(0(4(2(5(x1))))))
   3(5(0(2(2(x1))))) -> 0(3(2(5(2(5(x1))))))
   3(5(2(1(4(x1))))) -> 3(5(1(0(4(2(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(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_3(x_1)) -> 3(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

3(4(1(2(4(x1))))) ->^+ 0(4(1(2(4(3(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 / 4(1(2(4(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(0(2(x1)))) -> 0(0(3(1(2(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(0(3(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(1(3(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(3(1(x1)))))
   0(2(1(4(x1)))) -> 0(4(1(2(3(x1)))))
   0(2(1(4(x1)))) -> 0(4(1(3(2(x1)))))
   0(2(1(4(x1)))) -> 2(0(4(1(4(x1)))))
   0(2(1(4(x1)))) -> 5(5(0(4(1(2(x1))))))
   0(2(1(5(x1)))) -> 5(0(4(1(2(x1)))))
   0(2(2(4(x1)))) -> 0(4(2(2(5(x1)))))
   0(2(2(4(x1)))) -> 0(4(2(5(2(x1)))))
   3(4(0(2(x1)))) -> 3(0(4(5(2(x1)))))
   3(4(0(2(x1)))) -> 3(5(0(4(2(x1)))))
   0(0(1(4(5(x1))))) -> 0(4(1(0(3(5(x1))))))
   0(1(0(2(4(x1))))) -> 2(0(0(4(1(1(x1))))))
   0(1(2(3(4(x1))))) -> 2(0(4(1(0(3(x1))))))
   0(1(3(3(4(x1))))) -> 0(0(3(1(3(4(x1))))))
   0(1(4(0(2(x1))))) -> 0(4(1(5(0(2(x1))))))
   0(1(4(1(5(x1))))) -> 2(5(0(4(1(1(x1))))))
   0(1(4(3(4(x1))))) -> 0(4(0(3(1(4(x1))))))
   0(1(4(3(4(x1))))) -> 3(0(4(1(5(4(x1))))))
   0(1(4(3(5(x1))))) -> 5(4(5(0(3(1(x1))))))
   0(1(5(0(2(x1))))) -> 0(0(4(1(2(5(x1))))))
   0(1(5(1(4(x1))))) -> 4(5(0(3(1(1(x1))))))
   0(2(1(4(4(x1))))) -> 0(4(1(2(4(3(x1))))))
   0(2(1(4(5(x1))))) -> 0(4(1(2(5(2(x1))))))
   0(2(1(5(4(x1))))) -> 5(0(2(0(4(1(x1))))))
   0(2(4(1(5(x1))))) -> 5(0(4(1(5(2(x1))))))
   0(2(4(3(5(x1))))) -> 0(4(5(2(5(3(x1))))))
   0(2(5(1(4(x1))))) -> 0(0(5(4(1(2(x1))))))
   3(0(1(3(2(x1))))) -> 0(3(1(0(3(2(x1))))))
   3(0(2(1(4(x1))))) -> 4(0(4(1(3(2(x1))))))
   3(0(2(1(5(x1))))) -> 5(3(2(0(4(1(x1))))))
   3(0(4(0(2(x1))))) -> 0(3(4(0(4(2(x1))))))
   3(0(4(0(2(x1))))) -> 0(4(1(2(0(3(x1))))))
   3(0(5(1(4(x1))))) -> 3(0(4(1(1(5(x1))))))
   3(0(5(1(5(x1))))) -> 0(4(1(3(5(5(x1))))))
   3(2(4(1(2(x1))))) -> 3(1(2(2(5(4(x1))))))
   3(2(4(1(5(x1))))) -> 3(1(4(5(2(5(x1))))))
   3(4(0(1(2(x1))))) -> 0(4(2(0(3(1(x1))))))
   3(4(0(1(4(x1))))) -> 0(4(1(5(3(4(x1))))))
   3(4(0(1(5(x1))))) -> 0(4(1(5(5(3(x1))))))
   3(4(0(2(4(x1))))) -> 0(3(4(0(4(2(x1))))))
   3(4(1(2(4(x1))))) -> 0(4(1(2(4(3(x1))))))
   3(4(1(3(5(x1))))) -> 4(3(0(3(1(5(x1))))))
   3(4(3(0(2(x1))))) -> 3(3(0(4(1(2(x1))))))
   3(4(5(0(2(x1))))) -> 0(3(0(4(2(5(x1))))))
   3(5(0(2(2(x1))))) -> 0(3(2(5(2(5(x1))))))
   3(5(2(1(4(x1))))) -> 3(5(1(0(4(2(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(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_3(x_1)) -> 3(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(0(2(x1)))) -> 0(0(3(1(2(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(0(3(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(1(3(x1)))))
   0(1(3(4(x1)))) -> 0(4(1(3(1(x1)))))
   0(2(1(4(x1)))) -> 0(4(1(2(3(x1)))))
   0(2(1(4(x1)))) -> 0(4(1(3(2(x1)))))
   0(2(1(4(x1)))) -> 2(0(4(1(4(x1)))))
   0(2(1(4(x1)))) -> 5(5(0(4(1(2(x1))))))
   0(2(1(5(x1)))) -> 5(0(4(1(2(x1)))))
   0(2(2(4(x1)))) -> 0(4(2(2(5(x1)))))
   0(2(2(4(x1)))) -> 0(4(2(5(2(x1)))))
   3(4(0(2(x1)))) -> 3(0(4(5(2(x1)))))
   3(4(0(2(x1)))) -> 3(5(0(4(2(x1)))))
   0(0(1(4(5(x1))))) -> 0(4(1(0(3(5(x1))))))
   0(1(0(2(4(x1))))) -> 2(0(0(4(1(1(x1))))))
   0(1(2(3(4(x1))))) -> 2(0(4(1(0(3(x1))))))
   0(1(3(3(4(x1))))) -> 0(0(3(1(3(4(x1))))))
   0(1(4(0(2(x1))))) -> 0(4(1(5(0(2(x1))))))
   0(1(4(1(5(x1))))) -> 2(5(0(4(1(1(x1))))))
   0(1(4(3(4(x1))))) -> 0(4(0(3(1(4(x1))))))
   0(1(4(3(4(x1))))) -> 3(0(4(1(5(4(x1))))))
   0(1(4(3(5(x1))))) -> 5(4(5(0(3(1(x1))))))
   0(1(5(0(2(x1))))) -> 0(0(4(1(2(5(x1))))))
   0(1(5(1(4(x1))))) -> 4(5(0(3(1(1(x1))))))
   0(2(1(4(4(x1))))) -> 0(4(1(2(4(3(x1))))))
   0(2(1(4(5(x1))))) -> 0(4(1(2(5(2(x1))))))
   0(2(1(5(4(x1))))) -> 5(0(2(0(4(1(x1))))))
   0(2(4(1(5(x1))))) -> 5(0(4(1(5(2(x1))))))
   0(2(4(3(5(x1))))) -> 0(4(5(2(5(3(x1))))))
   0(2(5(1(4(x1))))) -> 0(0(5(4(1(2(x1))))))
   3(0(1(3(2(x1))))) -> 0(3(1(0(3(2(x1))))))
   3(0(2(1(4(x1))))) -> 4(0(4(1(3(2(x1))))))
   3(0(2(1(5(x1))))) -> 5(3(2(0(4(1(x1))))))
   3(0(4(0(2(x1))))) -> 0(3(4(0(4(2(x1))))))
   3(0(4(0(2(x1))))) -> 0(4(1(2(0(3(x1))))))
   3(0(5(1(4(x1))))) -> 3(0(4(1(1(5(x1))))))
   3(0(5(1(5(x1))))) -> 0(4(1(3(5(5(x1))))))
   3(2(4(1(2(x1))))) -> 3(1(2(2(5(4(x1))))))
   3(2(4(1(5(x1))))) -> 3(1(4(5(2(5(x1))))))
   3(4(0(1(2(x1))))) -> 0(4(2(0(3(1(x1))))))
   3(4(0(1(4(x1))))) -> 0(4(1(5(3(4(x1))))))
   3(4(0(1(5(x1))))) -> 0(4(1(5(5(3(x1))))))
   3(4(0(2(4(x1))))) -> 0(3(4(0(4(2(x1))))))
   3(4(1(2(4(x1))))) -> 0(4(1(2(4(3(x1))))))
   3(4(1(3(5(x1))))) -> 4(3(0(3(1(5(x1))))))
   3(4(3(0(2(x1))))) -> 3(3(0(4(1(2(x1))))))
   3(4(5(0(2(x1))))) -> 0(3(0(4(2(5(x1))))))
   3(5(0(2(2(x1))))) -> 0(3(2(5(2(5(x1))))))
   3(5(2(1(4(x1))))) -> 3(5(1(0(4(2(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(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_3(x_1)) -> 3(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