/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 48 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
    (7) CpxTrsMatchBoundsProof [FINISHED, 165 ms]
    (8) BOUNDS(1, n^1)
(9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(10) TRS for Loop Detection
    (11) DecreasingLoopProof [LOWER BOUND(ID), 0 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(1(x1))) -> 1(2(1(2(0(x1)))))
   0(3(1(x1))) -> 1(3(2(2(0(x1)))))
   0(3(1(x1))) -> 3(2(1(2(0(x1)))))
   0(3(1(x1))) -> 1(3(3(3(2(0(x1))))))
   0(4(1(x1))) -> 2(1(2(0(4(x1)))))
   0(0(4(5(x1)))) -> 0(0(2(5(4(x1)))))
   0(1(4(1(x1)))) -> 0(1(2(2(4(1(x1))))))
   0(1(4(5(x1)))) -> 4(0(1(2(5(4(x1))))))
   0(1(5(1(x1)))) -> 1(2(2(5(0(1(x1))))))
   0(1(5(3(x1)))) -> 0(5(3(2(1(x1)))))
   0(2(4(1(x1)))) -> 1(3(3(2(0(4(x1))))))
   0(2(4(1(x1)))) -> 4(2(1(2(0(4(x1))))))
   0(2(4(5(x1)))) -> 0(2(2(5(0(4(x1))))))
   0(3(1(5(x1)))) -> 0(1(2(5(3(x1)))))
   0(3(1(5(x1)))) -> 1(2(5(3(0(4(x1))))))
   0(3(5(1(x1)))) -> 1(2(5(3(0(x1)))))
   0(3(5(1(x1)))) -> 0(5(2(1(2(3(x1))))))
   0(3(5(5(x1)))) -> 0(3(2(5(5(x1)))))
   0(4(0(1(x1)))) -> 2(0(4(4(0(1(x1))))))
   0(4(1(5(x1)))) -> 1(2(5(0(4(x1)))))
   0(4(3(5(x1)))) -> 0(4(3(2(5(4(x1))))))
   0(4(5(1(x1)))) -> 2(5(4(4(0(1(x1))))))
   3(0(1(5(x1)))) -> 3(1(4(0(5(4(x1))))))
   3(0(3(1(x1)))) -> 1(3(3(2(0(x1)))))
   3(0(3(5(x1)))) -> 3(2(5(0(2(3(x1))))))
   3(3(0(1(x1)))) -> 0(1(3(2(2(3(x1))))))
   3(4(5(1(x1)))) -> 3(2(5(4(2(1(x1))))))
   4(1(3(5(x1)))) -> 1(2(5(3(4(4(x1))))))
   4(1(5(1(x1)))) -> 4(4(5(1(2(1(x1))))))
   4(4(1(5(x1)))) -> 4(1(2(5(4(x1)))))
   0(1(4(5(5(x1))))) -> 0(5(1(4(2(5(x1))))))
   0(2(1(4(5(x1))))) -> 0(0(1(2(5(4(x1))))))
   0(2(1(5(5(x1))))) -> 0(1(2(2(5(5(x1))))))
   0(4(2(4(1(x1))))) -> 1(3(2(0(4(4(x1))))))
   0(4(5(4(3(x1))))) -> 2(5(0(4(4(3(x1))))))
   0(5(1(5(1(x1))))) -> 0(5(1(1(2(5(x1))))))
   0(5(2(1(5(x1))))) -> 1(2(5(5(0(4(x1))))))
   0(5(2(4(1(x1))))) -> 4(5(2(1(2(0(x1))))))
   3(0(1(4(1(x1))))) -> 0(4(4(1(3(1(x1))))))
   3(0(1(4(1(x1))))) -> 4(3(2(0(1(1(x1))))))
   3(0(3(5(5(x1))))) -> 3(3(2(5(0(5(x1))))))
   3(0(5(3(1(x1))))) -> 1(0(3(3(2(5(x1))))))
   4(0(1(4(1(x1))))) -> 4(4(0(1(3(1(x1))))))
   4(0(1(5(1(x1))))) -> 0(1(2(5(4(1(x1))))))
   4(0(2(4(5(x1))))) -> 4(0(2(5(0(4(x1))))))
   4(1(1(5(1(x1))))) -> 1(1(2(5(4(1(x1))))))
   4(5(1(4(1(x1))))) -> 4(4(1(2(1(5(x1))))))
   4(5(2(3(1(x1))))) -> 4(3(1(2(2(5(x1))))))
   4(5(4(3(1(x1))))) -> 4(1(2(5(3(4(x1))))))
   4(5(5(3(1(x1))))) -> 1(3(2(5(5(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(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))
   encArg(cons_4(x_1)) -> 4(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(1(x1))) -> 1(2(1(2(0(x1)))))
   0(3(1(x1))) -> 1(3(2(2(0(x1)))))
   0(3(1(x1))) -> 3(2(1(2(0(x1)))))
   0(3(1(x1))) -> 1(3(3(3(2(0(x1))))))
   0(4(1(x1))) -> 2(1(2(0(4(x1)))))
   0(0(4(5(x1)))) -> 0(0(2(5(4(x1)))))
   0(1(4(1(x1)))) -> 0(1(2(2(4(1(x1))))))
   0(1(4(5(x1)))) -> 4(0(1(2(5(4(x1))))))
   0(1(5(1(x1)))) -> 1(2(2(5(0(1(x1))))))
   0(1(5(3(x1)))) -> 0(5(3(2(1(x1)))))
   0(2(4(1(x1)))) -> 1(3(3(2(0(4(x1))))))
   0(2(4(1(x1)))) -> 4(2(1(2(0(4(x1))))))
   0(2(4(5(x1)))) -> 0(2(2(5(0(4(x1))))))
   0(3(1(5(x1)))) -> 0(1(2(5(3(x1)))))
   0(3(1(5(x1)))) -> 1(2(5(3(0(4(x1))))))
   0(3(5(1(x1)))) -> 1(2(5(3(0(x1)))))
   0(3(5(1(x1)))) -> 0(5(2(1(2(3(x1))))))
   0(3(5(5(x1)))) -> 0(3(2(5(5(x1)))))
   0(4(0(1(x1)))) -> 2(0(4(4(0(1(x1))))))
   0(4(1(5(x1)))) -> 1(2(5(0(4(x1)))))
   0(4(3(5(x1)))) -> 0(4(3(2(5(4(x1))))))
   0(4(5(1(x1)))) -> 2(5(4(4(0(1(x1))))))
   3(0(1(5(x1)))) -> 3(1(4(0(5(4(x1))))))
   3(0(3(1(x1)))) -> 1(3(3(2(0(x1)))))
   3(0(3(5(x1)))) -> 3(2(5(0(2(3(x1))))))
   3(3(0(1(x1)))) -> 0(1(3(2(2(3(x1))))))
   3(4(5(1(x1)))) -> 3(2(5(4(2(1(x1))))))
   4(1(3(5(x1)))) -> 1(2(5(3(4(4(x1))))))
   4(1(5(1(x1)))) -> 4(4(5(1(2(1(x1))))))
   4(4(1(5(x1)))) -> 4(1(2(5(4(x1)))))
   0(1(4(5(5(x1))))) -> 0(5(1(4(2(5(x1))))))
   0(2(1(4(5(x1))))) -> 0(0(1(2(5(4(x1))))))
   0(2(1(5(5(x1))))) -> 0(1(2(2(5(5(x1))))))
   0(4(2(4(1(x1))))) -> 1(3(2(0(4(4(x1))))))
   0(4(5(4(3(x1))))) -> 2(5(0(4(4(3(x1))))))
   0(5(1(5(1(x1))))) -> 0(5(1(1(2(5(x1))))))
   0(5(2(1(5(x1))))) -> 1(2(5(5(0(4(x1))))))
   0(5(2(4(1(x1))))) -> 4(5(2(1(2(0(x1))))))
   3(0(1(4(1(x1))))) -> 0(4(4(1(3(1(x1))))))
   3(0(1(4(1(x1))))) -> 4(3(2(0(1(1(x1))))))
   3(0(3(5(5(x1))))) -> 3(3(2(5(0(5(x1))))))
   3(0(5(3(1(x1))))) -> 1(0(3(3(2(5(x1))))))
   4(0(1(4(1(x1))))) -> 4(4(0(1(3(1(x1))))))
   4(0(1(5(1(x1))))) -> 0(1(2(5(4(1(x1))))))
   4(0(2(4(5(x1))))) -> 4(0(2(5(0(4(x1))))))
   4(1(1(5(1(x1))))) -> 1(1(2(5(4(1(x1))))))
   4(5(1(4(1(x1))))) -> 4(4(1(2(1(5(x1))))))
   4(5(2(3(1(x1))))) -> 4(3(1(2(2(5(x1))))))
   4(5(4(3(1(x1))))) -> 4(1(2(5(3(4(x1))))))
   4(5(5(3(1(x1))))) -> 1(3(2(5(5(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(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))
   encArg(cons_4(x_1)) -> 4(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(1(x1))) -> 1(2(1(2(0(x1)))))
   0(3(1(x1))) -> 1(3(2(2(0(x1)))))
   0(3(1(x1))) -> 3(2(1(2(0(x1)))))
   0(3(1(x1))) -> 1(3(3(3(2(0(x1))))))
   0(4(1(x1))) -> 2(1(2(0(4(x1)))))
   0(0(4(5(x1)))) -> 0(0(2(5(4(x1)))))
   0(1(4(1(x1)))) -> 0(1(2(2(4(1(x1))))))
   0(1(4(5(x1)))) -> 4(0(1(2(5(4(x1))))))
   0(1(5(1(x1)))) -> 1(2(2(5(0(1(x1))))))
   0(1(5(3(x1)))) -> 0(5(3(2(1(x1)))))
   0(2(4(1(x1)))) -> 1(3(3(2(0(4(x1))))))
   0(2(4(1(x1)))) -> 4(2(1(2(0(4(x1))))))
   0(2(4(5(x1)))) -> 0(2(2(5(0(4(x1))))))
   0(3(1(5(x1)))) -> 0(1(2(5(3(x1)))))
   0(3(1(5(x1)))) -> 1(2(5(3(0(4(x1))))))
   0(3(5(1(x1)))) -> 1(2(5(3(0(x1)))))
   0(3(5(1(x1)))) -> 0(5(2(1(2(3(x1))))))
   0(3(5(5(x1)))) -> 0(3(2(5(5(x1)))))
   0(4(0(1(x1)))) -> 2(0(4(4(0(1(x1))))))
   0(4(1(5(x1)))) -> 1(2(5(0(4(x1)))))
   0(4(3(5(x1)))) -> 0(4(3(2(5(4(x1))))))
   0(4(5(1(x1)))) -> 2(5(4(4(0(1(x1))))))
   3(0(1(5(x1)))) -> 3(1(4(0(5(4(x1))))))
   3(0(3(1(x1)))) -> 1(3(3(2(0(x1)))))
   3(0(3(5(x1)))) -> 3(2(5(0(2(3(x1))))))
   3(3(0(1(x1)))) -> 0(1(3(2(2(3(x1))))))
   3(4(5(1(x1)))) -> 3(2(5(4(2(1(x1))))))
   4(1(3(5(x1)))) -> 1(2(5(3(4(4(x1))))))
   4(1(5(1(x1)))) -> 4(4(5(1(2(1(x1))))))
   4(4(1(5(x1)))) -> 4(1(2(5(4(x1)))))
   0(1(4(5(5(x1))))) -> 0(5(1(4(2(5(x1))))))
   0(2(1(4(5(x1))))) -> 0(0(1(2(5(4(x1))))))
   0(2(1(5(5(x1))))) -> 0(1(2(2(5(5(x1))))))
   0(4(2(4(1(x1))))) -> 1(3(2(0(4(4(x1))))))
   0(4(5(4(3(x1))))) -> 2(5(0(4(4(3(x1))))))
   0(5(1(5(1(x1))))) -> 0(5(1(1(2(5(x1))))))
   0(5(2(1(5(x1))))) -> 1(2(5(5(0(4(x1))))))
   0(5(2(4(1(x1))))) -> 4(5(2(1(2(0(x1))))))
   3(0(1(4(1(x1))))) -> 0(4(4(1(3(1(x1))))))
   3(0(1(4(1(x1))))) -> 4(3(2(0(1(1(x1))))))
   3(0(3(5(5(x1))))) -> 3(3(2(5(0(5(x1))))))
   3(0(5(3(1(x1))))) -> 1(0(3(3(2(5(x1))))))
   4(0(1(4(1(x1))))) -> 4(4(0(1(3(1(x1))))))
   4(0(1(5(1(x1))))) -> 0(1(2(5(4(1(x1))))))
   4(0(2(4(5(x1))))) -> 4(0(2(5(0(4(x1))))))
   4(1(1(5(1(x1))))) -> 1(1(2(5(4(1(x1))))))
   4(5(1(4(1(x1))))) -> 4(4(1(2(1(5(x1))))))
   4(5(2(3(1(x1))))) -> 4(3(1(2(2(5(x1))))))
   4(5(4(3(1(x1))))) -> 4(1(2(5(3(4(x1))))))
   4(5(5(3(1(x1))))) -> 1(3(2(5(5(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(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))
   encArg(cons_4(x_1)) -> 4(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(1(x1))) -> 1(2(1(2(0(x1)))))
   0(3(1(x1))) -> 1(3(2(2(0(x1)))))
   0(3(1(x1))) -> 3(2(1(2(0(x1)))))
   0(3(1(x1))) -> 1(3(3(3(2(0(x1))))))
   0(4(1(x1))) -> 2(1(2(0(4(x1)))))
   0(0(4(5(x1)))) -> 0(0(2(5(4(x1)))))
   0(1(4(1(x1)))) -> 0(1(2(2(4(1(x1))))))
   0(1(4(5(x1)))) -> 4(0(1(2(5(4(x1))))))
   0(1(5(1(x1)))) -> 1(2(2(5(0(1(x1))))))
   0(1(5(3(x1)))) -> 0(5(3(2(1(x1)))))
   0(2(4(1(x1)))) -> 1(3(3(2(0(4(x1))))))
   0(2(4(1(x1)))) -> 4(2(1(2(0(4(x1))))))
   0(2(4(5(x1)))) -> 0(2(2(5(0(4(x1))))))
   0(3(1(5(x1)))) -> 0(1(2(5(3(x1)))))
   0(3(1(5(x1)))) -> 1(2(5(3(0(4(x1))))))
   0(3(5(1(x1)))) -> 1(2(5(3(0(x1)))))
   0(3(5(1(x1)))) -> 0(5(2(1(2(3(x1))))))
   0(3(5(5(x1)))) -> 0(3(2(5(5(x1)))))
   0(4(0(1(x1)))) -> 2(0(4(4(0(1(x1))))))
   0(4(1(5(x1)))) -> 1(2(5(0(4(x1)))))
   0(4(3(5(x1)))) -> 0(4(3(2(5(4(x1))))))
   0(4(5(1(x1)))) -> 2(5(4(4(0(1(x1))))))
   3(0(1(5(x1)))) -> 3(1(4(0(5(4(x1))))))
   3(0(3(1(x1)))) -> 1(3(3(2(0(x1)))))
   3(0(3(5(x1)))) -> 3(2(5(0(2(3(x1))))))
   3(3(0(1(x1)))) -> 0(1(3(2(2(3(x1))))))
   3(4(5(1(x1)))) -> 3(2(5(4(2(1(x1))))))
   4(1(3(5(x1)))) -> 1(2(5(3(4(4(x1))))))
   4(1(5(1(x1)))) -> 4(4(5(1(2(1(x1))))))
   4(4(1(5(x1)))) -> 4(1(2(5(4(x1)))))
   0(1(4(5(5(x1))))) -> 0(5(1(4(2(5(x1))))))
   0(2(1(4(5(x1))))) -> 0(0(1(2(5(4(x1))))))
   0(2(1(5(5(x1))))) -> 0(1(2(2(5(5(x1))))))
   0(4(2(4(1(x1))))) -> 1(3(2(0(4(4(x1))))))
   0(4(5(4(3(x1))))) -> 2(5(0(4(4(3(x1))))))
   0(5(1(5(1(x1))))) -> 0(5(1(1(2(5(x1))))))
   0(5(2(1(5(x1))))) -> 1(2(5(5(0(4(x1))))))
   0(5(2(4(1(x1))))) -> 4(5(2(1(2(0(x1))))))
   3(0(1(4(1(x1))))) -> 0(4(4(1(3(1(x1))))))
   3(0(1(4(1(x1))))) -> 4(3(2(0(1(1(x1))))))
   3(0(3(5(5(x1))))) -> 3(3(2(5(0(5(x1))))))
   3(0(5(3(1(x1))))) -> 1(0(3(3(2(5(x1))))))
   4(0(1(4(1(x1))))) -> 4(4(0(1(3(1(x1))))))
   4(0(1(5(1(x1))))) -> 0(1(2(5(4(1(x1))))))
   4(0(2(4(5(x1))))) -> 4(0(2(5(0(4(x1))))))
   4(1(1(5(1(x1))))) -> 1(1(2(5(4(1(x1))))))
   4(5(1(4(1(x1))))) -> 4(4(1(2(1(5(x1))))))
   4(5(2(3(1(x1))))) -> 4(3(1(2(2(5(x1))))))
   4(5(4(3(1(x1))))) -> 4(1(2(5(3(4(x1))))))
   4(5(5(3(1(x1))))) -> 1(3(2(5(5(4(x1))))))
   encArg(1(x_1)) -> 1(encArg(x_1))
   encArg(2(x_1)) -> 2(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))
   encArg(cons_4(x_1)) -> 4(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.

"[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, 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, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437]
{(69,70,[0_1|0, 3_1|0, 4_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]), (69,71,[1_1|1]), (69,75,[1_1|1]), (69,80,[0_1|1]), (69,85,[0_1|1]), (69,90,[1_1|1]), (69,95,[4_1|1]), (69,100,[1_1|1]), (69,105,[1_1|1, 2_1|1, 5_1|1, 0_1|1, 3_1|1, 4_1|1]), (69,119,[1_1|2]), (69,123,[0_1|2]), (69,128,[4_1|2]), (69,133,[0_1|2]), (69,138,[1_1|2]), (69,143,[0_1|2]), (69,147,[1_1|2]), (69,151,[3_1|2]), (69,155,[1_1|2]), (69,160,[0_1|2]), (69,164,[1_1|2]), (69,169,[1_1|2]), (69,173,[0_1|2]), (69,178,[0_1|2]), (69,182,[2_1|2]), (69,186,[1_1|2]), (69,190,[2_1|2]), (69,195,[0_1|2]), (69,200,[2_1|2]), (69,205,[2_1|2]), (69,210,[1_1|2]), (69,215,[0_1|2]), (69,219,[1_1|2]), (69,224,[4_1|2]), (69,229,[0_1|2]), (69,234,[0_1|2]), (69,239,[0_1|2]), (69,244,[0_1|2]), (69,249,[1_1|2]), (69,254,[4_1|2]), (69,259,[3_1|2]), (69,264,[0_1|2]), (69,269,[4_1|2]), (69,274,[1_1|2]), (69,278,[3_1|2]), (69,283,[3_1|2]), (69,288,[1_1|2]), (69,293,[0_1|2]), (69,298,[3_1|2]), (69,303,[1_1|2]), (69,308,[4_1|2]), (69,313,[1_1|2]), (69,318,[4_1|2]), (69,322,[4_1|2]), (69,327,[0_1|2]), (69,332,[4_1|2]), (69,337,[4_1|2]), (69,342,[4_1|2]), (69,347,[4_1|2]), (69,352,[1_1|2]), (70,70,[1_1|0, 2_1|0, 5_1|0, cons_0_1|0, cons_3_1|0, cons_4_1|0]), (71,72,[2_1|1]), (72,73,[1_1|1]), (73,74,[2_1|1]), (74,70,[0_1|1]), (74,71,[1_1|1]), (74,75,[1_1|1]), (74,80,[0_1|1]), (74,85,[0_1|1]), (74,90,[1_1|1]), (75,76,[2_1|1]), (76,77,[2_1|1]), (77,78,[5_1|1]), (78,79,[0_1|1]), (78,71,[1_1|1]), (78,75,[1_1|1]), (79,70,[1_1|1]), (80,81,[1_1|1]), (81,82,[2_1|1]), (82,83,[2_1|1]), (83,84,[5_1|1]), (84,70,[5_1|1]), (85,86,[5_1|1]), (86,87,[1_1|1]), (87,88,[1_1|1]), (88,89,[2_1|1]), (89,70,[5_1|1]), (90,91,[2_1|1]), (91,92,[5_1|1]), (92,93,[5_1|1]), (93,94,[0_1|1]), (93,106,[2_1|1]), (93,110,[1_1|1]), (93,114,[2_1|1]), (93,357,[1_1|2]), (94,70,[4_1|1]), (94,95,[4_1|1]), (94,100,[1_1|1]), (95,96,[4_1|1]), (96,97,[5_1|1]), (97,98,[1_1|1]), (98,99,[2_1|1]), (99,70,[1_1|1]), (100,101,[1_1|1]), (101,102,[2_1|1]), (102,103,[5_1|1]), (103,104,[4_1|1]), (103,95,[4_1|1]), (103,100,[1_1|1]), (104,70,[1_1|1]), (105,70,[encArg_1|1]), (105,105,[1_1|1, 2_1|1, 5_1|1, 0_1|1, 3_1|1, 4_1|1]), (105,119,[1_1|2]), (105,123,[0_1|2]), (105,128,[4_1|2]), (105,133,[0_1|2]), (105,138,[1_1|2]), (105,143,[0_1|2]), (105,147,[1_1|2]), (105,151,[3_1|2]), (105,155,[1_1|2]), (105,160,[0_1|2]), (105,164,[1_1|2]), (105,169,[1_1|2]), (105,173,[0_1|2]), (105,178,[0_1|2]), (105,182,[2_1|2]), (105,186,[1_1|2]), (105,190,[2_1|2]), (105,195,[0_1|2]), (105,200,[2_1|2]), (105,205,[2_1|2]), (105,210,[1_1|2]), (105,215,[0_1|2]), (105,219,[1_1|2]), (105,224,[4_1|2]), (105,229,[0_1|2]), (105,234,[0_1|2]), (105,239,[0_1|2]), (105,244,[0_1|2]), (105,249,[1_1|2]), (105,254,[4_1|2]), (105,259,[3_1|2]), (105,264,[0_1|2]), (105,269,[4_1|2]), (105,274,[1_1|2]), (105,278,[3_1|2]), (105,283,[3_1|2]), (105,288,[1_1|2]), (105,293,[0_1|2]), (105,298,[3_1|2]), (105,303,[1_1|2]), (105,308,[4_1|2]), (105,313,[1_1|2]), (105,318,[4_1|2]), (105,322,[4_1|2]), (105,327,[0_1|2]), (105,332,[4_1|2]), (105,337,[4_1|2]), (105,342,[4_1|2]), (105,347,[4_1|2]), (105,352,[1_1|2]), (106,107,[1_1|1]), (107,108,[2_1|1]), (108,109,[0_1|1]), (108,106,[2_1|1]), (108,110,[1_1|1]), (108,114,[2_1|1]), (108,357,[1_1|2]), (109,70,[4_1|1]), (109,95,[4_1|1]), (109,100,[1_1|1]), (110,111,[2_1|1]), (111,112,[5_1|1]), (112,113,[0_1|1]), (112,106,[2_1|1]), (112,110,[1_1|1]), (112,114,[2_1|1]), (112,357,[1_1|2]), (113,70,[4_1|1]), (113,95,[4_1|1]), (113,100,[1_1|1]), (114,115,[5_1|1]), (115,116,[4_1|1]), (116,117,[4_1|1]), (116,361,[0_1|1]), (117,118,[0_1|1]), (117,71,[1_1|1]), (117,75,[1_1|1]), (118,70,[1_1|1]), (119,120,[2_1|2]), (120,121,[1_1|2]), (121,122,[2_1|2]), (122,105,[0_1|2]), (122,119,[0_1|2, 1_1|2]), (122,138,[0_1|2, 1_1|2]), (122,147,[0_1|2, 1_1|2]), (122,155,[0_1|2, 1_1|2]), (122,164,[0_1|2, 1_1|2]), (122,169,[0_1|2, 1_1|2]), (122,186,[0_1|2, 1_1|2]), (122,210,[0_1|2, 1_1|2]), (122,219,[0_1|2, 1_1|2]), (122,249,[0_1|2, 1_1|2]), (122,274,[0_1|2]), (122,288,[0_1|2]), (122,303,[0_1|2]), (122,313,[0_1|2]), (122,352,[0_1|2]), (122,314,[0_1|2]), (122,123,[0_1|2]), (122,128,[4_1|2]), (122,133,[0_1|2]), (122,143,[0_1|2]), (122,151,[3_1|2]), (122,160,[0_1|2]), (122,173,[0_1|2]), (122,178,[0_1|2]), (122,182,[2_1|2]), (122,190,[2_1|2]), (122,195,[0_1|2]), (122,200,[2_1|2]), (122,205,[2_1|2]), (122,215,[0_1|2]), (122,224,[4_1|2]), (122,229,[0_1|2]), (122,234,[0_1|2]), (122,239,[0_1|2]), (122,244,[0_1|2]), (122,254,[4_1|2]), (122,376,[2_1|3]), (122,381,[1_1|3]), (122,385,[3_1|3]), (122,389,[1_1|3]), (122,394,[1_1|3]), (122,398,[2_1|3]), (123,124,[1_1|2]), (124,125,[2_1|2]), (125,126,[2_1|2]), (126,127,[4_1|2]), (126,303,[1_1|2]), (126,308,[4_1|2]), (126,313,[1_1|2]), (127,105,[1_1|2]), (127,119,[1_1|2]), (127,138,[1_1|2]), (127,147,[1_1|2]), (127,155,[1_1|2]), (127,164,[1_1|2]), (127,169,[1_1|2]), (127,186,[1_1|2]), (127,210,[1_1|2]), (127,219,[1_1|2]), (127,249,[1_1|2]), (127,274,[1_1|2]), (127,288,[1_1|2]), (127,303,[1_1|2]), (127,313,[1_1|2]), (127,352,[1_1|2]), (127,319,[1_1|2]), (127,348,[1_1|2]), (128,129,[0_1|2]), (129,130,[1_1|2]), (130,131,[2_1|2]), (131,132,[5_1|2]), (132,105,[4_1|2]), (132,255,[4_1|2]), (132,303,[1_1|2]), (132,308,[4_1|2]), (132,313,[1_1|2]), (132,318,[4_1|2]), (132,322,[4_1|2]), (132,327,[0_1|2]), (132,332,[4_1|2]), (132,337,[4_1|2]), (132,342,[4_1|2]), (132,347,[4_1|2]), (132,352,[1_1|2]), (133,134,[5_1|2]), (134,135,[1_1|2]), (135,136,[4_1|2]), (136,137,[2_1|2]), (137,105,[5_1|2]), (138,139,[2_1|2]), (139,140,[2_1|2]), (140,141,[5_1|2]), (141,142,[0_1|2]), (141,119,[1_1|2]), (141,123,[0_1|2]), (141,128,[4_1|2]), (141,133,[0_1|2]), (141,138,[1_1|2]), (141,143,[0_1|2]), (141,402,[1_1|3]), (141,406,[4_1|3]), (141,411,[0_1|3]), (142,105,[1_1|2]), (142,119,[1_1|2]), (142,138,[1_1|2]), (142,147,[1_1|2]), (142,155,[1_1|2]), (142,164,[1_1|2]), (142,169,[1_1|2]), (142,186,[1_1|2]), (142,210,[1_1|2]), (142,219,[1_1|2]), (142,249,[1_1|2]), (142,274,[1_1|2]), (142,288,[1_1|2]), (142,303,[1_1|2]), (142,313,[1_1|2]), (142,352,[1_1|2]), (143,144,[5_1|2]), (144,145,[3_1|2]), (145,146,[2_1|2]), (146,105,[1_1|2]), (146,151,[1_1|2]), (146,259,[1_1|2]), (146,278,[1_1|2]), (146,283,[1_1|2]), (146,298,[1_1|2]), (147,148,[3_1|2]), (148,149,[2_1|2]), (149,150,[2_1|2]), (150,105,[0_1|2]), (150,119,[0_1|2, 1_1|2]), (150,138,[0_1|2, 1_1|2]), (150,147,[0_1|2, 1_1|2]), (150,155,[0_1|2, 1_1|2]), (150,164,[0_1|2, 1_1|2]), (150,169,[0_1|2, 1_1|2]), (150,186,[0_1|2, 1_1|2]), (150,210,[0_1|2, 1_1|2]), (150,219,[0_1|2, 1_1|2]), (150,249,[0_1|2, 1_1|2]), (150,274,[0_1|2]), (150,288,[0_1|2]), (150,303,[0_1|2]), (150,313,[0_1|2]), (150,352,[0_1|2]), (150,260,[0_1|2]), (150,123,[0_1|2]), (150,128,[4_1|2]), (150,133,[0_1|2]), (150,143,[0_1|2]), (150,151,[3_1|2]), (150,160,[0_1|2]), (150,173,[0_1|2]), (150,178,[0_1|2]), (150,182,[2_1|2]), (150,190,[2_1|2]), (150,195,[0_1|2]), (150,200,[2_1|2]), (150,205,[2_1|2]), (150,215,[0_1|2]), (150,224,[4_1|2]), (150,229,[0_1|2]), (150,234,[0_1|2]), (150,239,[0_1|2]), (150,244,[0_1|2]), (150,254,[4_1|2]), (150,376,[2_1|3]), (150,381,[1_1|3]), (150,385,[3_1|3]), (150,389,[1_1|3]), (150,394,[1_1|3]), (150,398,[2_1|3]), (151,152,[2_1|2]), (152,153,[1_1|2]), (153,154,[2_1|2]), (154,105,[0_1|2]), (154,119,[0_1|2, 1_1|2]), (154,138,[0_1|2, 1_1|2]), (154,147,[0_1|2, 1_1|2]), (154,155,[0_1|2, 1_1|2]), (154,164,[0_1|2, 1_1|2]), (154,169,[0_1|2, 1_1|2]), (154,186,[0_1|2, 1_1|2]), (154,210,[0_1|2, 1_1|2]), (154,219,[0_1|2, 1_1|2]), (154,249,[0_1|2, 1_1|2]), (154,274,[0_1|2]), (154,288,[0_1|2]), (154,303,[0_1|2]), (154,313,[0_1|2]), (154,352,[0_1|2]), (154,260,[0_1|2]), (154,123,[0_1|2]), (154,128,[4_1|2]), (154,133,[0_1|2]), (154,143,[0_1|2]), (154,151,[3_1|2]), (154,160,[0_1|2]), (154,173,[0_1|2]), (154,178,[0_1|2]), (154,182,[2_1|2]), (154,190,[2_1|2]), (154,195,[0_1|2]), (154,200,[2_1|2]), (154,205,[2_1|2]), (154,215,[0_1|2]), (154,224,[4_1|2]), (154,229,[0_1|2]), (154,234,[0_1|2]), (154,239,[0_1|2]), (154,244,[0_1|2]), (154,254,[4_1|2]), (154,376,[2_1|3]), (154,381,[1_1|3]), (154,385,[3_1|3]), (154,389,[1_1|3]), (154,394,[1_1|3]), (154,398,[2_1|3]), (155,156,[3_1|2]), (156,157,[3_1|2]), (157,158,[3_1|2]), (158,159,[2_1|2]), (159,105,[0_1|2]), (159,119,[0_1|2, 1_1|2]), (159,138,[0_1|2, 1_1|2]), (159,147,[0_1|2, 1_1|2]), (159,155,[0_1|2, 1_1|2]), (159,164,[0_1|2, 1_1|2]), (159,169,[0_1|2, 1_1|2]), (159,186,[0_1|2, 1_1|2]), (159,210,[0_1|2, 1_1|2]), (159,219,[0_1|2, 1_1|2]), (159,249,[0_1|2, 1_1|2]), (159,274,[0_1|2]), (159,288,[0_1|2]), (159,303,[0_1|2]), (159,313,[0_1|2]), (159,352,[0_1|2]), (159,260,[0_1|2]), (159,123,[0_1|2]), (159,128,[4_1|2]), (159,133,[0_1|2]), (159,143,[0_1|2]), (159,151,[3_1|2]), (159,160,[0_1|2]), (159,173,[0_1|2]), (159,178,[0_1|2]), (159,182,[2_1|2]), (159,190,[2_1|2]), (159,195,[0_1|2]), (159,200,[2_1|2]), (159,205,[2_1|2]), (159,215,[0_1|2]), (159,224,[4_1|2]), (159,229,[0_1|2]), (159,234,[0_1|2]), (159,239,[0_1|2]), (159,244,[0_1|2]), (159,254,[4_1|2]), (159,376,[2_1|3]), (159,381,[1_1|3]), (159,385,[3_1|3]), (159,389,[1_1|3]), (159,394,[1_1|3]), (159,398,[2_1|3]), (160,161,[1_1|2]), (161,162,[2_1|2]), (162,163,[5_1|2]), (163,105,[3_1|2]), (163,259,[3_1|2]), (163,264,[0_1|2]), (163,269,[4_1|2]), (163,274,[1_1|2]), (163,278,[3_1|2]), (163,283,[3_1|2]), (163,288,[1_1|2]), (163,293,[0_1|2]), (163,298,[3_1|2]), (164,165,[2_1|2]), (165,166,[5_1|2]), (166,167,[3_1|2]), (167,168,[0_1|2]), (167,182,[2_1|2]), (167,186,[1_1|2]), (167,190,[2_1|2]), (167,195,[0_1|2]), (167,200,[2_1|2]), (167,205,[2_1|2]), (167,210,[1_1|2]), (167,416,[2_1|3]), (167,420,[2_1|3]), (167,394,[1_1|3]), (168,105,[4_1|2]), (168,303,[1_1|2]), (168,308,[4_1|2]), (168,313,[1_1|2]), (168,318,[4_1|2]), (168,322,[4_1|2]), (168,327,[0_1|2]), (168,332,[4_1|2]), (168,337,[4_1|2]), (168,342,[4_1|2]), (168,347,[4_1|2]), (168,352,[1_1|2]), (169,170,[2_1|2]), (170,171,[5_1|2]), (171,172,[3_1|2]), (171,259,[3_1|2]), (171,264,[0_1|2]), 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(302,210,[1_1|2]), (302,219,[1_1|2]), (302,249,[1_1|2]), (302,274,[1_1|2]), (302,288,[1_1|2]), (302,303,[1_1|2]), (302,313,[1_1|2]), (302,352,[1_1|2]), (303,304,[2_1|2]), (304,305,[5_1|2]), (305,306,[3_1|2]), (306,307,[4_1|2]), (306,318,[4_1|2]), (307,105,[4_1|2]), (307,303,[1_1|2]), (307,308,[4_1|2]), (307,313,[1_1|2]), (307,318,[4_1|2]), (307,322,[4_1|2]), (307,327,[0_1|2]), (307,332,[4_1|2]), (307,337,[4_1|2]), (307,342,[4_1|2]), (307,347,[4_1|2]), (307,352,[1_1|2]), (308,309,[4_1|2]), (309,310,[5_1|2]), (310,311,[1_1|2]), (311,312,[2_1|2]), (312,105,[1_1|2]), (312,119,[1_1|2]), (312,138,[1_1|2]), (312,147,[1_1|2]), (312,155,[1_1|2]), (312,164,[1_1|2]), (312,169,[1_1|2]), (312,186,[1_1|2]), (312,210,[1_1|2]), (312,219,[1_1|2]), (312,249,[1_1|2]), (312,274,[1_1|2]), (312,288,[1_1|2]), (312,303,[1_1|2]), (312,313,[1_1|2]), (312,352,[1_1|2]), (313,314,[1_1|2]), (314,315,[2_1|2]), (315,316,[5_1|2]), (316,317,[4_1|2]), (316,303,[1_1|2]), (316,308,[4_1|2]), (316,313,[1_1|2]), (317,105,[1_1|2]), (317,119,[1_1|2]), (317,138,[1_1|2]), (317,147,[1_1|2]), (317,155,[1_1|2]), (317,164,[1_1|2]), (317,169,[1_1|2]), (317,186,[1_1|2]), (317,210,[1_1|2]), (317,219,[1_1|2]), (317,249,[1_1|2]), (317,274,[1_1|2]), (317,288,[1_1|2]), (317,303,[1_1|2]), (317,313,[1_1|2]), (317,352,[1_1|2]), (318,319,[1_1|2]), (319,320,[2_1|2]), (320,321,[5_1|2]), (321,105,[4_1|2]), (321,303,[1_1|2]), (321,308,[4_1|2]), (321,313,[1_1|2]), (321,318,[4_1|2]), (321,322,[4_1|2]), (321,327,[0_1|2]), (321,332,[4_1|2]), (321,337,[4_1|2]), (321,342,[4_1|2]), (321,347,[4_1|2]), (321,352,[1_1|2]), (322,323,[4_1|2]), (323,324,[0_1|2]), (324,325,[1_1|2]), (325,326,[3_1|2]), (326,105,[1_1|2]), (326,119,[1_1|2]), (326,138,[1_1|2]), (326,147,[1_1|2]), (326,155,[1_1|2]), (326,164,[1_1|2]), (326,169,[1_1|2]), (326,186,[1_1|2]), (326,210,[1_1|2]), (326,219,[1_1|2]), (326,249,[1_1|2]), (326,274,[1_1|2]), (326,288,[1_1|2]), (326,303,[1_1|2]), (326,313,[1_1|2]), (326,352,[1_1|2]), (326,319,[1_1|2]), (326,348,[1_1|2]), (327,328,[1_1|2]), (328,329,[2_1|2]), (329,330,[5_1|2]), (330,331,[4_1|2]), (330,303,[1_1|2]), (330,308,[4_1|2]), (330,313,[1_1|2]), (331,105,[1_1|2]), (331,119,[1_1|2]), (331,138,[1_1|2]), (331,147,[1_1|2]), (331,155,[1_1|2]), (331,164,[1_1|2]), (331,169,[1_1|2]), (331,186,[1_1|2]), (331,210,[1_1|2]), (331,219,[1_1|2]), (331,249,[1_1|2]), (331,274,[1_1|2]), (331,288,[1_1|2]), (331,303,[1_1|2]), (331,313,[1_1|2]), (331,352,[1_1|2]), (332,333,[0_1|2]), (333,334,[2_1|2]), (334,335,[5_1|2]), (335,336,[0_1|2]), (335,182,[2_1|2]), (335,186,[1_1|2]), (335,190,[2_1|2]), (335,195,[0_1|2]), (335,200,[2_1|2]), (335,205,[2_1|2]), (335,210,[1_1|2]), (335,416,[2_1|3]), (335,420,[2_1|3]), (335,394,[1_1|3]), (336,105,[4_1|2]), (336,255,[4_1|2]), (336,303,[1_1|2]), (336,308,[4_1|2]), (336,313,[1_1|2]), (336,318,[4_1|2]), (336,322,[4_1|2]), (336,327,[0_1|2]), (336,332,[4_1|2]), (336,337,[4_1|2]), (336,342,[4_1|2]), (336,347,[4_1|2]), (336,352,[1_1|2]), (337,338,[4_1|2]), (338,339,[1_1|2]), (339,340,[2_1|2]), (340,341,[1_1|2]), (341,105,[5_1|2]), (341,119,[5_1|2]), (341,138,[5_1|2]), (341,147,[5_1|2]), (341,155,[5_1|2]), (341,164,[5_1|2]), (341,169,[5_1|2]), (341,186,[5_1|2]), (341,210,[5_1|2]), (341,219,[5_1|2]), (341,249,[5_1|2]), (341,274,[5_1|2]), (341,288,[5_1|2]), (341,303,[5_1|2]), (341,313,[5_1|2]), (341,352,[5_1|2]), (341,319,[5_1|2]), (341,348,[5_1|2]), (342,343,[3_1|2]), (343,344,[1_1|2]), (344,345,[2_1|2]), (345,346,[2_1|2]), (346,105,[5_1|2]), (346,119,[5_1|2]), (346,138,[5_1|2]), (346,147,[5_1|2]), (346,155,[5_1|2]), (346,164,[5_1|2]), (346,169,[5_1|2]), (346,186,[5_1|2]), (346,210,[5_1|2]), (346,219,[5_1|2]), (346,249,[5_1|2]), (346,274,[5_1|2]), (346,288,[5_1|2]), (346,303,[5_1|2]), (346,313,[5_1|2]), (346,352,[5_1|2]), (346,260,[5_1|2]), (347,348,[1_1|2]), (348,349,[2_1|2]), (349,350,[5_1|2]), (350,351,[3_1|2]), (350,298,[3_1|2]), (351,105,[4_1|2]), (351,119,[4_1|2]), (351,138,[4_1|2]), (351,147,[4_1|2]), (351,155,[4_1|2]), (351,164,[4_1|2]), (351,169,[4_1|2]), (351,186,[4_1|2]), (351,210,[4_1|2]), (351,219,[4_1|2]), (351,249,[4_1|2]), (351,274,[4_1|2]), (351,288,[4_1|2]), (351,303,[4_1|2, 1_1|2]), (351,313,[4_1|2, 1_1|2]), (351,352,[4_1|2, 1_1|2]), (351,260,[4_1|2]), (351,344,[4_1|2]), (351,308,[4_1|2]), (351,318,[4_1|2]), (351,322,[4_1|2]), (351,327,[0_1|2]), (351,332,[4_1|2]), (351,337,[4_1|2]), (351,342,[4_1|2]), (351,347,[4_1|2]), (352,353,[3_1|2]), (353,354,[2_1|2]), (354,355,[5_1|2]), (355,356,[5_1|2]), (356,105,[4_1|2]), (356,119,[4_1|2]), (356,138,[4_1|2]), (356,147,[4_1|2]), (356,155,[4_1|2]), (356,164,[4_1|2]), (356,169,[4_1|2]), (356,186,[4_1|2]), (356,210,[4_1|2]), (356,219,[4_1|2]), (356,249,[4_1|2]), (356,274,[4_1|2]), (356,288,[4_1|2]), (356,303,[4_1|2, 1_1|2]), (356,313,[4_1|2, 1_1|2]), (356,352,[4_1|2, 1_1|2]), (356,260,[4_1|2]), (356,308,[4_1|2]), (356,318,[4_1|2]), (356,322,[4_1|2]), (356,327,[0_1|2]), (356,332,[4_1|2]), (356,337,[4_1|2]), (356,342,[4_1|2]), (356,347,[4_1|2]), (357,358,[2_1|2]), (358,359,[1_1|2]), (359,360,[2_1|2]), (360,101,[0_1|2]), (361,362,[1_1|1]), (362,363,[2_1|1]), (363,364,[5_1|1]), (364,365,[4_1|1]), (364,95,[4_1|1]), (364,100,[1_1|1]), (365,70,[1_1|1]), (376,377,[0_1|3]), (377,378,[4_1|3]), (378,379,[4_1|3]), (379,380,[0_1|3]), (380,130,[1_1|3]), (381,382,[3_1|3]), (382,383,[2_1|3]), (383,384,[2_1|3]), (384,260,[0_1|3]), (385,386,[2_1|3]), (386,387,[1_1|3]), (387,388,[2_1|3]), (388,260,[0_1|3]), (389,390,[3_1|3]), (390,391,[3_1|3]), (391,392,[3_1|3]), (392,393,[2_1|3]), (393,260,[0_1|3]), (394,395,[2_1|3]), (395,396,[1_1|3]), (396,397,[2_1|3]), (397,314,[0_1|3]), (398,399,[1_1|3]), (399,400,[2_1|3]), (400,401,[0_1|3]), (401,319,[4_1|3]), (401,348,[4_1|3]), (402,403,[2_1|3]), (403,404,[1_1|3]), (404,405,[2_1|3]), (405,119,[0_1|3]), (405,138,[0_1|3]), (405,147,[0_1|3]), (405,155,[0_1|3]), (405,164,[0_1|3]), (405,169,[0_1|3]), (405,186,[0_1|3]), (405,210,[0_1|3]), (405,219,[0_1|3]), (405,249,[0_1|3]), (405,274,[0_1|3]), (405,288,[0_1|3]), (405,303,[0_1|3]), (405,313,[0_1|3]), (405,352,[0_1|3]), (405,314,[0_1|3]), (406,407,[0_1|3]), (407,408,[1_1|3]), (408,409,[2_1|3]), (409,410,[5_1|3]), (410,255,[4_1|3]), (411,412,[1_1|3]), (412,413,[2_1|3]), (413,414,[2_1|3]), (414,415,[4_1|3]), (415,319,[1_1|3]), (415,348,[1_1|3]), (416,417,[1_1|3]), (417,418,[2_1|3]), (418,419,[0_1|3]), (418,416,[2_1|3]), (419,119,[4_1|3]), (419,138,[4_1|3]), (419,147,[4_1|3]), (419,155,[4_1|3]), (419,164,[4_1|3]), (419,169,[4_1|3]), (419,186,[4_1|3]), (419,210,[4_1|3]), (419,219,[4_1|3]), (419,249,[4_1|3]), (419,274,[4_1|3]), (419,288,[4_1|3]), (419,303,[4_1|3]), (419,313,[4_1|3]), (419,352,[4_1|3]), (419,319,[4_1|3]), (419,348,[4_1|3]), (419,314,[4_1|3]), (420,421,[0_1|3]), (421,422,[4_1|3]), (422,423,[4_1|3]), (423,424,[0_1|3]), (424,124,[1_1|3]), (424,161,[1_1|3]), (424,240,[1_1|3]), (424,294,[1_1|3]), (424,328,[1_1|3]), (425,426,[3_1|3]), (426,427,[3_1|3]), (427,428,[2_1|3]), (428,260,[0_1|3]), (429,430,[4_1|3]), (430,431,[0_1|3]), (431,432,[1_1|3]), (432,433,[3_1|3]), (433,319,[1_1|3]), (433,348,[1_1|3]), (434,435,[2_1|3]), (435,436,[1_1|3]), (436,437,[2_1|3]), (437,105,[0_1|3]), (437,119,[0_1|3, 1_1|2]), (437,138,[0_1|3, 1_1|2]), (437,147,[0_1|3, 1_1|2]), (437,155,[0_1|3, 1_1|2]), (437,164,[0_1|3, 1_1|2]), (437,169,[0_1|3, 1_1|2]), (437,186,[0_1|3, 1_1|2]), (437,210,[0_1|3, 1_1|2]), (437,219,[0_1|3, 1_1|2]), (437,249,[0_1|3, 1_1|2]), (437,274,[0_1|3]), (437,288,[0_1|3]), (437,303,[0_1|3]), (437,313,[0_1|3]), (437,352,[0_1|3]), (437,319,[0_1|3]), (437,348,[0_1|3]), (437,123,[0_1|2]), (437,128,[4_1|2]), (437,133,[0_1|2]), (437,143,[0_1|2]), (437,151,[3_1|2]), (437,160,[0_1|2]), (437,173,[0_1|2]), (437,178,[0_1|2]), (437,182,[2_1|2]), (437,190,[2_1|2]), (437,195,[0_1|2]), (437,200,[2_1|2]), (437,205,[2_1|2]), (437,215,[0_1|2]), (437,224,[4_1|2]), (437,229,[0_1|2]), (437,234,[0_1|2]), (437,239,[0_1|2]), (437,244,[0_1|2]), (437,254,[4_1|2]), (437,376,[2_1|3]), (437,381,[1_1|3]), (437,385,[3_1|3]), (437,389,[1_1|3]), (437,394,[1_1|3]), (437,398,[2_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(1(x1))) -> 1(2(1(2(0(x1)))))
   0(3(1(x1))) -> 1(3(2(2(0(x1)))))
   0(3(1(x1))) -> 3(2(1(2(0(x1)))))
   0(3(1(x1))) -> 1(3(3(3(2(0(x1))))))
   0(4(1(x1))) -> 2(1(2(0(4(x1)))))
   0(0(4(5(x1)))) -> 0(0(2(5(4(x1)))))
   0(1(4(1(x1)))) -> 0(1(2(2(4(1(x1))))))
   0(1(4(5(x1)))) -> 4(0(1(2(5(4(x1))))))
   0(1(5(1(x1)))) -> 1(2(2(5(0(1(x1))))))
   0(1(5(3(x1)))) -> 0(5(3(2(1(x1)))))
   0(2(4(1(x1)))) -> 1(3(3(2(0(4(x1))))))
   0(2(4(1(x1)))) -> 4(2(1(2(0(4(x1))))))
   0(2(4(5(x1)))) -> 0(2(2(5(0(4(x1))))))
   0(3(1(5(x1)))) -> 0(1(2(5(3(x1)))))
   0(3(1(5(x1)))) -> 1(2(5(3(0(4(x1))))))
   0(3(5(1(x1)))) -> 1(2(5(3(0(x1)))))
   0(3(5(1(x1)))) -> 0(5(2(1(2(3(x1))))))
   0(3(5(5(x1)))) -> 0(3(2(5(5(x1)))))
   0(4(0(1(x1)))) -> 2(0(4(4(0(1(x1))))))
   0(4(1(5(x1)))) -> 1(2(5(0(4(x1)))))
   0(4(3(5(x1)))) -> 0(4(3(2(5(4(x1))))))
   0(4(5(1(x1)))) -> 2(5(4(4(0(1(x1))))))
   3(0(1(5(x1)))) -> 3(1(4(0(5(4(x1))))))
   3(0(3(1(x1)))) -> 1(3(3(2(0(x1)))))
   3(0(3(5(x1)))) -> 3(2(5(0(2(3(x1))))))
   3(3(0(1(x1)))) -> 0(1(3(2(2(3(x1))))))
   3(4(5(1(x1)))) -> 3(2(5(4(2(1(x1))))))
   4(1(3(5(x1)))) -> 1(2(5(3(4(4(x1))))))
   4(1(5(1(x1)))) -> 4(4(5(1(2(1(x1))))))
   4(4(1(5(x1)))) -> 4(1(2(5(4(x1)))))
   0(1(4(5(5(x1))))) -> 0(5(1(4(2(5(x1))))))
   0(2(1(4(5(x1))))) -> 0(0(1(2(5(4(x1))))))
   0(2(1(5(5(x1))))) -> 0(1(2(2(5(5(x1))))))
   0(4(2(4(1(x1))))) -> 1(3(2(0(4(4(x1))))))
   0(4(5(4(3(x1))))) -> 2(5(0(4(4(3(x1))))))
   0(5(1(5(1(x1))))) -> 0(5(1(1(2(5(x1))))))
   0(5(2(1(5(x1))))) -> 1(2(5(5(0(4(x1))))))
   0(5(2(4(1(x1))))) -> 4(5(2(1(2(0(x1))))))
   3(0(1(4(1(x1))))) -> 0(4(4(1(3(1(x1))))))
   3(0(1(4(1(x1))))) -> 4(3(2(0(1(1(x1))))))
   3(0(3(5(5(x1))))) -> 3(3(2(5(0(5(x1))))))
   3(0(5(3(1(x1))))) -> 1(0(3(3(2(5(x1))))))
   4(0(1(4(1(x1))))) -> 4(4(0(1(3(1(x1))))))
   4(0(1(5(1(x1))))) -> 0(1(2(5(4(1(x1))))))
   4(0(2(4(5(x1))))) -> 4(0(2(5(0(4(x1))))))
   4(1(1(5(1(x1))))) -> 1(1(2(5(4(1(x1))))))
   4(5(1(4(1(x1))))) -> 4(4(1(2(1(5(x1))))))
   4(5(2(3(1(x1))))) -> 4(3(1(2(2(5(x1))))))
   4(5(4(3(1(x1))))) -> 4(1(2(5(3(4(x1))))))
   4(5(5(3(1(x1))))) -> 1(3(2(5(5(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(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))
   encArg(cons_4(x_1)) -> 4(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(5(1(x1)))) ->^+ 1(2(2(5(0(1(x1))))))

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

The pumping substitution is [x1 / 5(1(x1))].

The result substitution is [ ].




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

(12)
Complex Obligation (BEST)

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

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

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


The TRS R consists of the following rules:

   0(1(1(x1))) -> 1(2(1(2(0(x1)))))
   0(3(1(x1))) -> 1(3(2(2(0(x1)))))
   0(3(1(x1))) -> 3(2(1(2(0(x1)))))
   0(3(1(x1))) -> 1(3(3(3(2(0(x1))))))
   0(4(1(x1))) -> 2(1(2(0(4(x1)))))
   0(0(4(5(x1)))) -> 0(0(2(5(4(x1)))))
   0(1(4(1(x1)))) -> 0(1(2(2(4(1(x1))))))
   0(1(4(5(x1)))) -> 4(0(1(2(5(4(x1))))))
   0(1(5(1(x1)))) -> 1(2(2(5(0(1(x1))))))
   0(1(5(3(x1)))) -> 0(5(3(2(1(x1)))))
   0(2(4(1(x1)))) -> 1(3(3(2(0(4(x1))))))
   0(2(4(1(x1)))) -> 4(2(1(2(0(4(x1))))))
   0(2(4(5(x1)))) -> 0(2(2(5(0(4(x1))))))
   0(3(1(5(x1)))) -> 0(1(2(5(3(x1)))))
   0(3(1(5(x1)))) -> 1(2(5(3(0(4(x1))))))
   0(3(5(1(x1)))) -> 1(2(5(3(0(x1)))))
   0(3(5(1(x1)))) -> 0(5(2(1(2(3(x1))))))
   0(3(5(5(x1)))) -> 0(3(2(5(5(x1)))))
   0(4(0(1(x1)))) -> 2(0(4(4(0(1(x1))))))
   0(4(1(5(x1)))) -> 1(2(5(0(4(x1)))))
   0(4(3(5(x1)))) -> 0(4(3(2(5(4(x1))))))
   0(4(5(1(x1)))) -> 2(5(4(4(0(1(x1))))))
   3(0(1(5(x1)))) -> 3(1(4(0(5(4(x1))))))
   3(0(3(1(x1)))) -> 1(3(3(2(0(x1)))))
   3(0(3(5(x1)))) -> 3(2(5(0(2(3(x1))))))
   3(3(0(1(x1)))) -> 0(1(3(2(2(3(x1))))))
   3(4(5(1(x1)))) -> 3(2(5(4(2(1(x1))))))
   4(1(3(5(x1)))) -> 1(2(5(3(4(4(x1))))))
   4(1(5(1(x1)))) -> 4(4(5(1(2(1(x1))))))
   4(4(1(5(x1)))) -> 4(1(2(5(4(x1)))))
   0(1(4(5(5(x1))))) -> 0(5(1(4(2(5(x1))))))
   0(2(1(4(5(x1))))) -> 0(0(1(2(5(4(x1))))))
   0(2(1(5(5(x1))))) -> 0(1(2(2(5(5(x1))))))
   0(4(2(4(1(x1))))) -> 1(3(2(0(4(4(x1))))))
   0(4(5(4(3(x1))))) -> 2(5(0(4(4(3(x1))))))
   0(5(1(5(1(x1))))) -> 0(5(1(1(2(5(x1))))))
   0(5(2(1(5(x1))))) -> 1(2(5(5(0(4(x1))))))
   0(5(2(4(1(x1))))) -> 4(5(2(1(2(0(x1))))))
   3(0(1(4(1(x1))))) -> 0(4(4(1(3(1(x1))))))
   3(0(1(4(1(x1))))) -> 4(3(2(0(1(1(x1))))))
   3(0(3(5(5(x1))))) -> 3(3(2(5(0(5(x1))))))
   3(0(5(3(1(x1))))) -> 1(0(3(3(2(5(x1))))))
   4(0(1(4(1(x1))))) -> 4(4(0(1(3(1(x1))))))
   4(0(1(5(1(x1))))) -> 0(1(2(5(4(1(x1))))))
   4(0(2(4(5(x1))))) -> 4(0(2(5(0(4(x1))))))
   4(1(1(5(1(x1))))) -> 1(1(2(5(4(1(x1))))))
   4(5(1(4(1(x1))))) -> 4(4(1(2(1(5(x1))))))
   4(5(2(3(1(x1))))) -> 4(3(1(2(2(5(x1))))))
   4(5(4(3(1(x1))))) -> 4(1(2(5(3(4(x1))))))
   4(5(5(3(1(x1))))) -> 1(3(2(5(5(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(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))
   encArg(cons_4(x_1)) -> 4(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(1(x1))) -> 1(2(1(2(0(x1)))))
   0(3(1(x1))) -> 1(3(2(2(0(x1)))))
   0(3(1(x1))) -> 3(2(1(2(0(x1)))))
   0(3(1(x1))) -> 1(3(3(3(2(0(x1))))))
   0(4(1(x1))) -> 2(1(2(0(4(x1)))))
   0(0(4(5(x1)))) -> 0(0(2(5(4(x1)))))
   0(1(4(1(x1)))) -> 0(1(2(2(4(1(x1))))))
   0(1(4(5(x1)))) -> 4(0(1(2(5(4(x1))))))
   0(1(5(1(x1)))) -> 1(2(2(5(0(1(x1))))))
   0(1(5(3(x1)))) -> 0(5(3(2(1(x1)))))
   0(2(4(1(x1)))) -> 1(3(3(2(0(4(x1))))))
   0(2(4(1(x1)))) -> 4(2(1(2(0(4(x1))))))
   0(2(4(5(x1)))) -> 0(2(2(5(0(4(x1))))))
   0(3(1(5(x1)))) -> 0(1(2(5(3(x1)))))
   0(3(1(5(x1)))) -> 1(2(5(3(0(4(x1))))))
   0(3(5(1(x1)))) -> 1(2(5(3(0(x1)))))
   0(3(5(1(x1)))) -> 0(5(2(1(2(3(x1))))))
   0(3(5(5(x1)))) -> 0(3(2(5(5(x1)))))
   0(4(0(1(x1)))) -> 2(0(4(4(0(1(x1))))))
   0(4(1(5(x1)))) -> 1(2(5(0(4(x1)))))
   0(4(3(5(x1)))) -> 0(4(3(2(5(4(x1))))))
   0(4(5(1(x1)))) -> 2(5(4(4(0(1(x1))))))
   3(0(1(5(x1)))) -> 3(1(4(0(5(4(x1))))))
   3(0(3(1(x1)))) -> 1(3(3(2(0(x1)))))
   3(0(3(5(x1)))) -> 3(2(5(0(2(3(x1))))))
   3(3(0(1(x1)))) -> 0(1(3(2(2(3(x1))))))
   3(4(5(1(x1)))) -> 3(2(5(4(2(1(x1))))))
   4(1(3(5(x1)))) -> 1(2(5(3(4(4(x1))))))
   4(1(5(1(x1)))) -> 4(4(5(1(2(1(x1))))))
   4(4(1(5(x1)))) -> 4(1(2(5(4(x1)))))
   0(1(4(5(5(x1))))) -> 0(5(1(4(2(5(x1))))))
   0(2(1(4(5(x1))))) -> 0(0(1(2(5(4(x1))))))
   0(2(1(5(5(x1))))) -> 0(1(2(2(5(5(x1))))))
   0(4(2(4(1(x1))))) -> 1(3(2(0(4(4(x1))))))
   0(4(5(4(3(x1))))) -> 2(5(0(4(4(3(x1))))))
   0(5(1(5(1(x1))))) -> 0(5(1(1(2(5(x1))))))
   0(5(2(1(5(x1))))) -> 1(2(5(5(0(4(x1))))))
   0(5(2(4(1(x1))))) -> 4(5(2(1(2(0(x1))))))
   3(0(1(4(1(x1))))) -> 0(4(4(1(3(1(x1))))))
   3(0(1(4(1(x1))))) -> 4(3(2(0(1(1(x1))))))
   3(0(3(5(5(x1))))) -> 3(3(2(5(0(5(x1))))))
   3(0(5(3(1(x1))))) -> 1(0(3(3(2(5(x1))))))
   4(0(1(4(1(x1))))) -> 4(4(0(1(3(1(x1))))))
   4(0(1(5(1(x1))))) -> 0(1(2(5(4(1(x1))))))
   4(0(2(4(5(x1))))) -> 4(0(2(5(0(4(x1))))))
   4(1(1(5(1(x1))))) -> 1(1(2(5(4(1(x1))))))
   4(5(1(4(1(x1))))) -> 4(4(1(2(1(5(x1))))))
   4(5(2(3(1(x1))))) -> 4(3(1(2(2(5(x1))))))
   4(5(4(3(1(x1))))) -> 4(1(2(5(3(4(x1))))))
   4(5(5(3(1(x1))))) -> 1(3(2(5(5(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(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))
   encArg(cons_4(x_1)) -> 4(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