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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 58 ms]
    (8) BOUNDS(1, n^1)
(9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(10) TRS for Loop Detection
    (11) DecreasingLoopProof [LOWER BOUND(ID), 1 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.

"[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, 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]
{(50,51,[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]), (50,52,[2_1|1]), (50,57,[4_1|1]), (50,62,[0_1|1]), (50,66,[0_1|1]), (50,70,[2_1|1]), (50,74,[5_1|1]), (50,79,[0_1|1]), (50,84,[0_1|1]), (50,89,[5_1|1]), (50,93,[5_1|1]), (50,98,[0_1|1]), (50,102,[0_1|1]), (50,106,[5_1|1]), (50,111,[0_1|1]), (50,116,[3_1|1]), (50,121,[3_1|1]), (50,126,[3_1|1]), (50,131,[1_1|1, 2_1|1, 4_1|1, 0_1|1, 3_1|1]), (50,137,[0_1|2]), (50,141,[2_1|2]), (50,146,[0_1|2]), (50,150,[0_1|2]), (50,154,[0_1|2]), (50,158,[0_1|2]), (50,163,[2_1|2]), (50,168,[0_1|2]), (50,173,[2_1|2]), (50,178,[0_1|2]), (50,183,[3_1|2]), (50,188,[5_1|2]), (50,193,[0_1|2]), (50,198,[4_1|2]), (50,203,[0_1|2]), (50,207,[0_1|2]), (50,211,[2_1|2]), (50,215,[5_1|2]), (50,220,[0_1|2]), (50,225,[0_1|2]), (50,230,[5_1|2]), (50,234,[5_1|2]), (50,239,[0_1|2]), (50,243,[0_1|2]), (50,247,[5_1|2]), (50,252,[0_1|2]), (50,257,[0_1|2]), (50,262,[0_1|2]), (50,267,[3_1|2]), (50,271,[3_1|2]), (50,275,[0_1|2]), (50,280,[0_1|2]), (50,285,[0_1|2]), (50,290,[0_1|2]), (50,295,[4_1|2]), (50,300,[3_1|2]), (50,305,[0_1|2]), (50,310,[0_1|2]), (50,315,[4_1|2]), (50,320,[5_1|2]), (50,325,[0_1|2]), (50,330,[3_1|2]), (50,335,[0_1|2]), (50,340,[3_1|2]), (50,345,[3_1|2]), (50,350,[0_1|2]), (50,355,[3_1|2]), (50,360,[0_1|2]), (51,51,[1_1|0, 2_1|0, 4_1|0, 5_1|0, cons_0_1|0, cons_3_1|0]), (52,53,[5_1|1]), (53,54,[0_1|1]), (54,55,[4_1|1]), (55,56,[1_1|1]), (56,51,[1_1|1]), (57,58,[5_1|1]), (58,59,[0_1|1]), (59,60,[3_1|1]), (60,61,[1_1|1]), (61,51,[1_1|1]), (62,63,[4_1|1]), (63,64,[1_1|1]), (64,65,[2_1|1]), (65,51,[3_1|1]), (65,132,[0_1|1]), (65,116,[3_1|1]), (65,121,[3_1|1]), (65,126,[3_1|1]), (66,67,[4_1|1]), (67,68,[1_1|1]), (68,69,[3_1|1]), (68,116,[3_1|1]), (68,121,[3_1|1]), (69,51,[2_1|1]), (70,71,[0_1|1]), (71,72,[4_1|1]), (72,73,[1_1|1]), (73,51,[4_1|1]), (74,75,[5_1|1]), (74,51,[encArg_1|1]), (74,131,[1_1|1, 2_1|1, 4_1|1, 5_1|1, 0_1|1, 3_1|1]), (74,137,[0_1|2]), (74,141,[2_1|2]), (74,146,[0_1|2]), (74,150,[0_1|2]), (74,154,[0_1|2]), (74,158,[0_1|2]), (74,163,[2_1|2]), (74,168,[0_1|2]), (74,173,[2_1|2]), (74,178,[0_1|2]), (74,183,[3_1|2]), (74,188,[5_1|2]), (74,193,[0_1|2]), (74,198,[4_1|2]), (74,203,[0_1|2]), (74,207,[0_1|2]), (74,211,[2_1|2]), (74,215,[5_1|2]), (74,220,[0_1|2]), (74,225,[0_1|2]), (74,230,[5_1|2]), (74,234,[5_1|2]), (74,239,[0_1|2]), (74,243,[0_1|2]), (74,247,[5_1|2]), (74,252,[0_1|2]), (74,257,[0_1|2]), (74,262,[0_1|2]), (74,267,[3_1|2]), (74,271,[3_1|2]), (74,275,[0_1|2]), (74,280,[0_1|2]), (74,285,[0_1|2]), (74,290,[0_1|2]), (74,295,[4_1|2]), (74,300,[3_1|2]), (74,305,[0_1|2]), (74,310,[0_1|2]), (74,315,[4_1|2]), (74,320,[5_1|2]), (74,325,[0_1|2]), (74,330,[3_1|2]), (74,335,[0_1|2]), (74,340,[3_1|2]), (74,345,[3_1|2]), (74,350,[0_1|2]), (74,355,[3_1|2]), (74,360,[0_1|2]), (75,76,[0_1|1]), (76,77,[4_1|1]), (77,78,[1_1|1]), (78,51,[2_1|1]), (79,80,[4_1|1]), (80,81,[1_1|1]), (81,82,[2_1|1]), (82,83,[4_1|1]), (83,51,[3_1|1]), (83,132,[0_1|1]), (83,116,[3_1|1]), (83,121,[3_1|1]), (83,126,[3_1|1]), (84,85,[4_1|1]), (85,86,[1_1|1]), (86,87,[2_1|1]), (87,88,[5_1|1]), (88,51,[2_1|1]), (89,90,[0_1|1]), (90,91,[4_1|1]), (91,92,[1_1|1]), (92,51,[2_1|1]), (93,94,[0_1|1]), (94,95,[2_1|1]), (95,96,[0_1|1]), (96,97,[4_1|1]), (97,51,[1_1|1]), (98,99,[4_1|1]), (99,100,[2_1|1]), (100,101,[2_1|1]), (101,51,[5_1|1]), (102,103,[4_1|1]), (103,104,[2_1|1]), (104,105,[5_1|1]), (105,51,[2_1|1]), (106,107,[0_1|1]), (107,108,[4_1|1]), (108,109,[1_1|1]), (109,110,[5_1|1]), (110,51,[2_1|1]), (111,112,[0_1|1]), (112,113,[5_1|1]), (113,114,[4_1|1]), (114,115,[1_1|1]), (115,51,[2_1|1]), (116,117,[1_1|1]), (117,118,[2_1|1]), (118,119,[2_1|1]), (119,120,[5_1|1]), (120,51,[4_1|1]), (121,122,[1_1|1]), (122,123,[4_1|1]), (123,124,[5_1|1]), (124,125,[2_1|1]), (125,51,[5_1|1]), (126,127,[5_1|1]), (127,128,[1_1|1]), (128,129,[0_1|1]), (129,130,[4_1|1]), (130,51,[2_1|1]), (131,51,[encArg_1|1]), (131,131,[1_1|1, 2_1|1, 4_1|1, 5_1|1, 0_1|1, 3_1|1]), (131,137,[0_1|2]), (131,141,[2_1|2]), (131,146,[0_1|2]), (131,150,[0_1|2]), (131,154,[0_1|2]), (131,158,[0_1|2]), (131,163,[2_1|2]), (131,168,[0_1|2]), (131,173,[2_1|2]), (131,178,[0_1|2]), (131,183,[3_1|2]), (131,188,[5_1|2]), (131,193,[0_1|2]), (131,198,[4_1|2]), (131,203,[0_1|2]), (131,207,[0_1|2]), (131,211,[2_1|2]), (131,215,[5_1|2]), (131,220,[0_1|2]), (131,225,[0_1|2]), (131,230,[5_1|2]), (131,234,[5_1|2]), (131,239,[0_1|2]), (131,243,[0_1|2]), (131,247,[5_1|2]), (131,252,[0_1|2]), (131,257,[0_1|2]), (131,262,[0_1|2]), (131,267,[3_1|2]), (131,271,[3_1|2]), (131,275,[0_1|2]), (131,280,[0_1|2]), (131,285,[0_1|2]), (131,290,[0_1|2]), (131,295,[4_1|2]), (131,300,[3_1|2]), (131,305,[0_1|2]), (131,310,[0_1|2]), (131,315,[4_1|2]), (131,320,[5_1|2]), (131,325,[0_1|2]), (131,330,[3_1|2]), (131,335,[0_1|2]), (131,340,[3_1|2]), (131,345,[3_1|2]), (131,350,[0_1|2]), (131,355,[3_1|2]), (131,360,[0_1|2]), (132,133,[4_1|1]), (133,134,[1_1|1]), (134,135,[2_1|1]), (135,136,[4_1|1]), (136,51,[3_1|1]), (136,132,[0_1|1]), (136,116,[3_1|1]), (136,121,[3_1|1]), (136,126,[3_1|1]), (137,138,[0_1|2]), (138,139,[3_1|2]), (139,140,[1_1|2]), (140,131,[2_1|2]), (140,141,[2_1|2]), (140,163,[2_1|2]), (140,173,[2_1|2]), (140,211,[2_1|2]), (141,142,[0_1|2]), (142,143,[0_1|2]), (143,144,[4_1|2]), (144,145,[1_1|2]), (145,131,[1_1|2]), (145,198,[1_1|2]), (145,295,[1_1|2]), (145,315,[1_1|2]), (146,147,[4_1|2]), (147,148,[1_1|2]), (148,149,[0_1|2]), (149,131,[3_1|2]), (149,198,[3_1|2]), (149,295,[3_1|2, 4_1|2]), (149,315,[3_1|2, 4_1|2]), (149,267,[3_1|2]), (149,271,[3_1|2]), (149,275,[0_1|2]), (149,280,[0_1|2]), (149,285,[0_1|2]), (149,290,[0_1|2]), (149,365,[0_1|2]), (149,300,[3_1|2]), (149,305,[0_1|2]), (149,310,[0_1|2]), (149,320,[5_1|2]), (149,325,[0_1|2]), (149,360,[0_1|2]), (149,330,[3_1|2]), (149,335,[0_1|2]), (149,340,[3_1|2]), (149,345,[3_1|2]), (149,350,[0_1|2]), (149,355,[3_1|2]), (150,151,[4_1|2]), (151,152,[1_1|2]), (152,153,[1_1|2]), (153,131,[3_1|2]), (153,198,[3_1|2]), (153,295,[3_1|2, 4_1|2]), (153,315,[3_1|2, 4_1|2]), (153,267,[3_1|2]), (153,271,[3_1|2]), (153,275,[0_1|2]), (153,280,[0_1|2]), (153,285,[0_1|2]), (153,290,[0_1|2]), (153,365,[0_1|2]), (153,300,[3_1|2]), (153,305,[0_1|2]), (153,310,[0_1|2]), (153,320,[5_1|2]), (153,325,[0_1|2]), (153,360,[0_1|2]), (153,330,[3_1|2]), (153,335,[0_1|2]), (153,340,[3_1|2]), (153,345,[3_1|2]), (153,350,[0_1|2]), (153,355,[3_1|2]), (154,155,[4_1|2]), (155,156,[1_1|2]), (156,157,[3_1|2]), (157,131,[1_1|2]), (157,198,[1_1|2]), (157,295,[1_1|2]), (157,315,[1_1|2]), (158,159,[0_1|2]), (159,160,[3_1|2]), (160,161,[1_1|2]), (161,162,[3_1|2]), (161,267,[3_1|2]), (161,271,[3_1|2]), (161,275,[0_1|2]), (161,280,[0_1|2]), (161,285,[0_1|2]), (161,290,[0_1|2]), (161,365,[0_1|2]), (161,295,[4_1|2]), (161,300,[3_1|2]), (161,305,[0_1|2]), (161,370,[0_1|3]), (162,131,[4_1|2]), (162,198,[4_1|2]), (162,295,[4_1|2]), (162,315,[4_1|2]), (163,164,[0_1|2]), (164,165,[4_1|2]), (165,166,[1_1|2]), (166,167,[0_1|2]), (167,131,[3_1|2]), (167,198,[3_1|2]), (167,295,[3_1|2, 4_1|2]), (167,315,[3_1|2, 4_1|2]), (167,267,[3_1|2]), (167,271,[3_1|2]), (167,275,[0_1|2]), (167,280,[0_1|2]), (167,285,[0_1|2]), (167,290,[0_1|2]), (167,365,[0_1|2]), (167,300,[3_1|2]), (167,305,[0_1|2]), (167,310,[0_1|2]), (167,320,[5_1|2]), (167,325,[0_1|2]), (167,360,[0_1|2]), (167,330,[3_1|2]), (167,335,[0_1|2]), (167,340,[3_1|2]), (167,345,[3_1|2]), (167,350,[0_1|2]), (167,355,[3_1|2]), (168,169,[4_1|2]), (169,170,[1_1|2]), (170,171,[5_1|2]), (171,172,[0_1|2]), (171,203,[0_1|2]), (171,207,[0_1|2]), (171,211,[2_1|2]), (171,215,[5_1|2]), (171,220,[0_1|2]), (171,225,[0_1|2]), (171,230,[5_1|2]), (171,234,[5_1|2]), (171,239,[0_1|2]), (171,243,[0_1|2]), (171,247,[5_1|2]), (171,252,[0_1|2]), (171,257,[0_1|2]), (172,131,[2_1|2]), (172,141,[2_1|2]), (172,163,[2_1|2]), (172,173,[2_1|2]), (172,211,[2_1|2]), (173,174,[5_1|2]), (174,175,[0_1|2]), (175,176,[4_1|2]), (176,177,[1_1|2]), (177,131,[1_1|2]), (177,188,[1_1|2]), (177,215,[1_1|2]), (177,230,[1_1|2]), (177,234,[1_1|2]), (177,247,[1_1|2]), (177,320,[1_1|2]), (178,179,[4_1|2]), (179,180,[0_1|2]), (180,181,[3_1|2]), (181,182,[1_1|2]), (182,131,[4_1|2]), (182,198,[4_1|2]), (182,295,[4_1|2]), (182,315,[4_1|2]), (183,184,[0_1|2]), (184,185,[4_1|2]), (185,186,[1_1|2]), (186,187,[5_1|2]), (187,131,[4_1|2]), (187,198,[4_1|2]), (187,295,[4_1|2]), (187,315,[4_1|2]), (188,189,[4_1|2]), (189,190,[5_1|2]), (190,191,[0_1|2]), (191,192,[3_1|2]), (192,131,[1_1|2]), (192,188,[1_1|2]), (192,215,[1_1|2]), (192,230,[1_1|2]), (192,234,[1_1|2]), (192,247,[1_1|2]), (192,320,[1_1|2]), (192,272,[1_1|2]), (192,356,[1_1|2]), (193,194,[0_1|2]), (194,195,[4_1|2]), (195,196,[1_1|2]), (196,197,[2_1|2]), (197,131,[5_1|2]), (197,141,[5_1|2]), (197,163,[5_1|2]), (197,173,[5_1|2]), (197,211,[5_1|2]), (197,236,[5_1|2]), (198,199,[5_1|2]), (199,200,[0_1|2]), (200,201,[3_1|2]), (201,202,[1_1|2]), (202,131,[1_1|2]), (202,198,[1_1|2]), (202,295,[1_1|2]), (202,315,[1_1|2]), (203,204,[4_1|2]), (204,205,[1_1|2]), (205,206,[2_1|2]), (206,131,[3_1|2]), (206,198,[3_1|2]), (206,295,[3_1|2, 4_1|2]), (206,315,[3_1|2, 4_1|2]), (206,267,[3_1|2]), (206,271,[3_1|2]), (206,275,[0_1|2]), (206,280,[0_1|2]), (206,285,[0_1|2]), (206,290,[0_1|2]), (206,365,[0_1|2]), (206,300,[3_1|2]), (206,305,[0_1|2]), (206,310,[0_1|2]), (206,320,[5_1|2]), (206,325,[0_1|2]), (206,360,[0_1|2]), (206,330,[3_1|2]), (206,335,[0_1|2]), (206,340,[3_1|2]), (206,345,[3_1|2]), (206,350,[0_1|2]), (206,355,[3_1|2]), (207,208,[4_1|2]), (208,209,[1_1|2]), (209,210,[3_1|2]), (209,340,[3_1|2]), (209,345,[3_1|2]), (210,131,[2_1|2]), (210,198,[2_1|2]), (210,295,[2_1|2]), (210,315,[2_1|2]), (211,212,[0_1|2]), (212,213,[4_1|2]), (213,214,[1_1|2]), (214,131,[4_1|2]), (214,198,[4_1|2]), (214,295,[4_1|2]), (214,315,[4_1|2]), (215,216,[5_1|2]), (216,217,[0_1|2]), (217,218,[4_1|2]), (218,219,[1_1|2]), (219,131,[2_1|2]), (219,198,[2_1|2]), (219,295,[2_1|2]), (219,315,[2_1|2]), (220,221,[4_1|2]), (221,222,[1_1|2]), (222,223,[2_1|2]), (223,224,[4_1|2]), (224,131,[3_1|2]), (224,198,[3_1|2]), (224,295,[3_1|2, 4_1|2]), (224,315,[3_1|2, 4_1|2]), (224,267,[3_1|2]), (224,271,[3_1|2]), (224,275,[0_1|2]), (224,280,[0_1|2]), (224,285,[0_1|2]), (224,290,[0_1|2]), (224,365,[0_1|2]), (224,300,[3_1|2]), (224,305,[0_1|2]), (224,310,[0_1|2]), (224,320,[5_1|2]), (224,325,[0_1|2]), (224,360,[0_1|2]), (224,330,[3_1|2]), (224,335,[0_1|2]), (224,340,[3_1|2]), (224,345,[3_1|2]), (224,350,[0_1|2]), (224,355,[3_1|2]), (225,226,[4_1|2]), (226,227,[1_1|2]), (227,228,[2_1|2]), (228,229,[5_1|2]), (229,131,[2_1|2]), (229,188,[2_1|2]), (229,215,[2_1|2]), (229,230,[2_1|2]), (229,234,[2_1|2]), (229,247,[2_1|2]), (229,320,[2_1|2]), (229,199,[2_1|2]), (230,231,[0_1|2]), (231,232,[4_1|2]), (232,233,[1_1|2]), (233,131,[2_1|2]), (233,188,[2_1|2]), (233,215,[2_1|2]), (233,230,[2_1|2]), (233,234,[2_1|2]), (233,247,[2_1|2]), (233,320,[2_1|2]), (234,235,[0_1|2]), (235,236,[2_1|2]), (236,237,[0_1|2]), (237,238,[4_1|2]), (238,131,[1_1|2]), (238,198,[1_1|2]), (238,295,[1_1|2]), (238,315,[1_1|2]), (238,189,[1_1|2]), (239,240,[4_1|2]), (240,241,[2_1|2]), (241,242,[2_1|2]), (242,131,[5_1|2]), (242,198,[5_1|2]), (242,295,[5_1|2]), (242,315,[5_1|2]), (243,244,[4_1|2]), (244,245,[2_1|2]), (245,246,[5_1|2]), (246,131,[2_1|2]), (246,198,[2_1|2]), (246,295,[2_1|2]), (246,315,[2_1|2]), (247,248,[0_1|2]), (248,249,[4_1|2]), (249,250,[1_1|2]), (250,251,[5_1|2]), (251,131,[2_1|2]), (251,188,[2_1|2]), (251,215,[2_1|2]), (251,230,[2_1|2]), (251,234,[2_1|2]), (251,247,[2_1|2]), (251,320,[2_1|2]), (252,253,[4_1|2]), (253,254,[5_1|2]), (254,255,[2_1|2]), (255,256,[5_1|2]), (256,131,[3_1|2]), (256,188,[3_1|2]), (256,215,[3_1|2]), (256,230,[3_1|2]), (256,234,[3_1|2]), (256,247,[3_1|2]), (256,320,[3_1|2, 5_1|2]), (256,272,[3_1|2]), (256,356,[3_1|2]), (256,267,[3_1|2]), (256,271,[3_1|2]), (256,275,[0_1|2]), (256,280,[0_1|2]), (256,285,[0_1|2]), (256,290,[0_1|2]), (256,365,[0_1|2]), (256,295,[4_1|2]), (256,300,[3_1|2]), (256,305,[0_1|2]), (256,310,[0_1|2]), (256,315,[4_1|2]), (256,325,[0_1|2]), (256,360,[0_1|2]), (256,330,[3_1|2]), (256,335,[0_1|2]), (256,340,[3_1|2]), (256,345,[3_1|2]), (256,350,[0_1|2]), (256,355,[3_1|2]), (257,258,[0_1|2]), (258,259,[5_1|2]), (259,260,[4_1|2]), (260,261,[1_1|2]), (261,131,[2_1|2]), (261,198,[2_1|2]), (261,295,[2_1|2]), (261,315,[2_1|2]), (262,263,[4_1|2]), (263,264,[1_1|2]), (264,265,[0_1|2]), (265,266,[3_1|2]), (265,350,[0_1|2]), (265,355,[3_1|2]), (266,131,[5_1|2]), (266,188,[5_1|2]), (266,215,[5_1|2]), (266,230,[5_1|2]), (266,234,[5_1|2]), (266,247,[5_1|2]), (266,320,[5_1|2]), (266,199,[5_1|2]), (267,268,[0_1|2]), (268,269,[4_1|2]), (269,270,[5_1|2]), (270,131,[2_1|2]), (270,141,[2_1|2]), (270,163,[2_1|2]), (270,173,[2_1|2]), (270,211,[2_1|2]), (271,272,[5_1|2]), (272,273,[0_1|2]), (273,274,[4_1|2]), (274,131,[2_1|2]), (274,141,[2_1|2]), (274,163,[2_1|2]), (274,173,[2_1|2]), (274,211,[2_1|2]), (275,276,[3_1|2]), (276,277,[4_1|2]), (277,278,[0_1|2]), (278,279,[4_1|2]), (279,131,[2_1|2]), (279,198,[2_1|2]), (279,295,[2_1|2]), (279,315,[2_1|2]), (280,281,[4_1|2]), (281,282,[2_1|2]), (282,283,[0_1|2]), (283,284,[3_1|2]), (284,131,[1_1|2]), (284,141,[1_1|2]), (284,163,[1_1|2]), (284,173,[1_1|2]), (284,211,[1_1|2]), (285,286,[4_1|2]), (286,287,[1_1|2]), (287,288,[5_1|2]), (288,289,[3_1|2]), (288,267,[3_1|2]), (288,271,[3_1|2]), (288,275,[0_1|2]), (288,280,[0_1|2]), (288,285,[0_1|2]), (288,290,[0_1|2]), (288,365,[0_1|2]), (288,295,[4_1|2]), (288,300,[3_1|2]), (288,305,[0_1|2]), (288,370,[0_1|3]), (289,131,[4_1|2]), (289,198,[4_1|2]), (289,295,[4_1|2]), (289,315,[4_1|2]), (290,291,[4_1|2]), (291,292,[1_1|2]), (292,293,[5_1|2]), (293,294,[5_1|2]), (294,131,[3_1|2]), (294,188,[3_1|2]), (294,215,[3_1|2]), (294,230,[3_1|2]), (294,234,[3_1|2]), (294,247,[3_1|2]), (294,320,[3_1|2, 5_1|2]), (294,267,[3_1|2]), (294,271,[3_1|2]), (294,275,[0_1|2]), (294,280,[0_1|2]), (294,285,[0_1|2]), (294,290,[0_1|2]), (294,365,[0_1|2]), (294,295,[4_1|2]), (294,300,[3_1|2]), (294,305,[0_1|2]), (294,310,[0_1|2]), (294,315,[4_1|2]), (294,325,[0_1|2]), (294,360,[0_1|2]), (294,330,[3_1|2]), (294,335,[0_1|2]), (294,340,[3_1|2]), (294,345,[3_1|2]), (294,350,[0_1|2]), (294,355,[3_1|2]), (295,296,[3_1|2]), (296,297,[0_1|2]), (297,298,[3_1|2]), (298,299,[1_1|2]), (299,131,[5_1|2]), (299,188,[5_1|2]), (299,215,[5_1|2]), (299,230,[5_1|2]), (299,234,[5_1|2]), (299,247,[5_1|2]), (299,320,[5_1|2]), (299,272,[5_1|2]), (299,356,[5_1|2]), (300,301,[3_1|2]), (301,302,[0_1|2]), (302,303,[4_1|2]), (303,304,[1_1|2]), (304,131,[2_1|2]), (304,141,[2_1|2]), (304,163,[2_1|2]), (304,173,[2_1|2]), (304,211,[2_1|2]), (305,306,[3_1|2]), (306,307,[0_1|2]), (307,308,[4_1|2]), (308,309,[2_1|2]), (309,131,[5_1|2]), (309,141,[5_1|2]), (309,163,[5_1|2]), (309,173,[5_1|2]), (309,211,[5_1|2]), (309,236,[5_1|2]), (310,311,[3_1|2]), (311,312,[1_1|2]), (312,313,[0_1|2]), (313,314,[3_1|2]), (313,340,[3_1|2]), (313,345,[3_1|2]), (314,131,[2_1|2]), (314,141,[2_1|2]), (314,163,[2_1|2]), (314,173,[2_1|2]), (314,211,[2_1|2]), (315,316,[0_1|2]), (316,317,[4_1|2]), (317,318,[1_1|2]), (318,319,[3_1|2]), (318,340,[3_1|2]), (318,345,[3_1|2]), (319,131,[2_1|2]), (319,198,[2_1|2]), (319,295,[2_1|2]), (319,315,[2_1|2]), (320,321,[3_1|2]), (321,322,[2_1|2]), (322,323,[0_1|2]), (323,324,[4_1|2]), (324,131,[1_1|2]), (324,188,[1_1|2]), (324,215,[1_1|2]), (324,230,[1_1|2]), (324,234,[1_1|2]), (324,247,[1_1|2]), (324,320,[1_1|2]), (325,326,[4_1|2]), (326,327,[1_1|2]), (327,328,[2_1|2]), (328,329,[0_1|2]), (329,131,[3_1|2]), (329,141,[3_1|2]), (329,163,[3_1|2]), (329,173,[3_1|2]), (329,211,[3_1|2]), (329,267,[3_1|2]), (329,271,[3_1|2]), (329,275,[0_1|2]), (329,280,[0_1|2]), (329,285,[0_1|2]), (329,290,[0_1|2]), (329,365,[0_1|2]), (329,295,[4_1|2]), (329,300,[3_1|2]), (329,305,[0_1|2]), (329,310,[0_1|2]), (329,315,[4_1|2]), (329,320,[5_1|2]), (329,325,[0_1|2]), (329,360,[0_1|2]), (329,330,[3_1|2]), (329,335,[0_1|2]), (329,340,[3_1|2]), (329,345,[3_1|2]), (329,350,[0_1|2]), (329,355,[3_1|2]), (330,331,[0_1|2]), (331,332,[4_1|2]), (332,333,[1_1|2]), (333,334,[1_1|2]), (334,131,[5_1|2]), (334,198,[5_1|2]), (334,295,[5_1|2]), (334,315,[5_1|2]), (335,336,[4_1|2]), (336,337,[1_1|2]), (337,338,[3_1|2]), (338,339,[5_1|2]), (339,131,[5_1|2]), (339,188,[5_1|2]), (339,215,[5_1|2]), (339,230,[5_1|2]), (339,234,[5_1|2]), (339,247,[5_1|2]), (339,320,[5_1|2]), (340,341,[1_1|2]), (341,342,[2_1|2]), (342,343,[2_1|2]), (343,344,[5_1|2]), (344,131,[4_1|2]), (344,141,[4_1|2]), (344,163,[4_1|2]), (344,173,[4_1|2]), (344,211,[4_1|2]), (345,346,[1_1|2]), (346,347,[4_1|2]), (347,348,[5_1|2]), (348,349,[2_1|2]), (349,131,[5_1|2]), (349,188,[5_1|2]), (349,215,[5_1|2]), (349,230,[5_1|2]), (349,234,[5_1|2]), (349,247,[5_1|2]), (349,320,[5_1|2]), (350,351,[3_1|2]), (351,352,[2_1|2]), (352,353,[5_1|2]), (353,354,[2_1|2]), (354,131,[5_1|2]), (354,141,[5_1|2]), (354,163,[5_1|2]), (354,173,[5_1|2]), (354,211,[5_1|2]), (355,356,[5_1|2]), (356,357,[1_1|2]), (357,358,[0_1|2]), (358,359,[4_1|2]), (359,131,[2_1|2]), (359,198,[2_1|2]), (359,295,[2_1|2]), (359,315,[2_1|2]), (360,361,[3_1|2]), (361,362,[4_1|2]), (362,363,[0_1|2]), (363,364,[4_1|2]), (364,141,[2_1|2]), (364,163,[2_1|2]), (364,173,[2_1|2]), (364,211,[2_1|2]), (365,366,[4_1|2]), (366,367,[1_1|2]), (367,368,[2_1|2]), (368,369,[4_1|2]), (369,131,[3_1|2]), (369,198,[3_1|2]), (369,295,[3_1|2, 4_1|2]), (369,315,[3_1|2, 4_1|2]), (369,267,[3_1|2]), (369,271,[3_1|2]), (369,275,[0_1|2]), (369,280,[0_1|2]), (369,285,[0_1|2]), (369,290,[0_1|2]), (369,365,[0_1|2]), (369,300,[3_1|2]), (369,305,[0_1|2]), (369,310,[0_1|2]), (369,320,[5_1|2]), (369,325,[0_1|2]), (369,360,[0_1|2]), (369,330,[3_1|2]), (369,335,[0_1|2]), (369,340,[3_1|2]), (369,345,[3_1|2]), (369,350,[0_1|2]), (369,355,[3_1|2]), (370,371,[3_1|3]), (371,372,[0_1|3]), (372,373,[4_1|3]), (373,374,[2_1|3]), (374,236,[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