/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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), 89 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
    (7) CpxTrsMatchBoundsProof [FINISHED, 107 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))) -> 0(1(2(3(4(1(x1))))))
   0(1(1(x1))) -> 1(3(1(3(4(0(x1))))))
   0(1(1(x1))) -> 5(1(3(0(3(1(x1))))))
   0(1(4(x1))) -> 0(1(3(4(x1))))
   0(1(4(x1))) -> 1(3(4(2(0(x1)))))
   0(1(4(x1))) -> 1(5(3(4(0(x1)))))
   0(1(4(x1))) -> 3(1(3(4(0(x1)))))
   0(1(4(x1))) -> 1(1(5(3(4(0(x1))))))
   0(1(4(x1))) -> 1(2(3(4(3(0(x1))))))
   0(1(4(x1))) -> 1(3(3(4(4(0(x1))))))
   0(1(4(x1))) -> 1(3(4(5(0(5(x1))))))
   0(1(4(x1))) -> 3(4(5(5(0(1(x1))))))
   1(2(4(x1))) -> 1(2(3(4(1(x1)))))
   1(2(4(x1))) -> 5(3(4(1(2(x1)))))
   1(2(4(x1))) -> 1(5(2(3(4(3(x1))))))
   1(2(4(x1))) -> 2(3(3(4(5(1(x1))))))
   5(2(1(x1))) -> 1(2(2(3(5(4(x1))))))
   5(2(1(x1))) -> 1(3(2(5(3(4(x1))))))
   5(2(4(x1))) -> 0(5(2(3(4(x1)))))
   5(2(4(x1))) -> 5(5(3(4(2(x1)))))
   5(2(4(x1))) -> 0(3(4(4(5(2(x1))))))
   5(2(4(x1))) -> 2(2(5(3(4(4(x1))))))
   5(2(4(x1))) -> 2(3(3(4(5(5(x1))))))
   5(2(4(x1))) -> 2(3(4(3(5(3(x1))))))
   5(2(4(x1))) -> 2(5(3(4(0(5(x1))))))
   5(2(4(x1))) -> 3(1(2(5(3(4(x1))))))
   5(2(4(x1))) -> 5(2(3(4(0(3(x1))))))
   0(0(2(4(x1)))) -> 0(4(3(0(2(x1)))))
   0(1(1(5(x1)))) -> 0(1(3(5(1(2(x1))))))
   0(1(2(4(x1)))) -> 0(1(2(3(3(4(x1))))))
   0(1(4(5(x1)))) -> 3(4(0(5(1(x1)))))
   0(1(4(5(x1)))) -> 3(4(5(3(0(1(x1))))))
   0(4(2(1(x1)))) -> 0(4(1(2(3(4(x1))))))
   0(5(1(4(x1)))) -> 0(0(3(5(4(1(x1))))))
   1(0(1(4(x1)))) -> 3(4(0(1(2(1(x1))))))
   1(1(2(4(x1)))) -> 1(3(4(1(2(x1)))))
   1(2(2(4(x1)))) -> 2(2(2(3(4(1(x1))))))
   1(2(4(2(x1)))) -> 1(2(3(4(2(3(x1))))))
   1(5(2(1(x1)))) -> 1(0(3(5(1(2(x1))))))
   1(5(2(4(x1)))) -> 3(2(3(5(1(4(x1))))))
   1(5(2(4(x1)))) -> 5(2(3(3(1(4(x1))))))
   5(0(1(4(x1)))) -> 3(4(0(5(3(1(x1))))))
   5(2(5(1(x1)))) -> 3(5(1(5(2(x1)))))
   0(1(1(5(4(x1))))) -> 0(0(5(4(1(1(x1))))))
   1(0(0(2(4(x1))))) -> 0(2(0(4(4(1(x1))))))
   1(0(4(2(1(x1))))) -> 1(2(3(4(1(0(x1))))))
   1(2(5(0(1(x1))))) -> 2(3(5(1(0(1(x1))))))
   1(5(3(0(4(x1))))) -> 5(1(3(4(0(4(x1))))))
   5(0(5(2(4(x1))))) -> 4(0(0(5(5(2(x1))))))
   5(3(2(4(2(x1))))) -> 2(1(5(3(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(2(x_1)) -> 2(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))


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

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


The TRS R consists of the following rules:

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

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

   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))

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

(3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
proved innermost termination of relative rules
----------------------------------------

(4)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1).


The TRS R consists of the following rules:

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

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

   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))

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

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

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


The TRS R consists of the following rules:

   0(1(1(x1))) -> 0(1(2(3(4(1(x1))))))
   0(1(1(x1))) -> 1(3(1(3(4(0(x1))))))
   0(1(1(x1))) -> 5(1(3(0(3(1(x1))))))
   0(1(4(x1))) -> 0(1(3(4(x1))))
   0(1(4(x1))) -> 1(3(4(2(0(x1)))))
   0(1(4(x1))) -> 1(5(3(4(0(x1)))))
   0(1(4(x1))) -> 3(1(3(4(0(x1)))))
   0(1(4(x1))) -> 1(1(5(3(4(0(x1))))))
   0(1(4(x1))) -> 1(2(3(4(3(0(x1))))))
   0(1(4(x1))) -> 1(3(3(4(4(0(x1))))))
   0(1(4(x1))) -> 1(3(4(5(0(5(x1))))))
   0(1(4(x1))) -> 3(4(5(5(0(1(x1))))))
   1(2(4(x1))) -> 1(2(3(4(1(x1)))))
   1(2(4(x1))) -> 5(3(4(1(2(x1)))))
   1(2(4(x1))) -> 1(5(2(3(4(3(x1))))))
   1(2(4(x1))) -> 2(3(3(4(5(1(x1))))))
   5(2(1(x1))) -> 1(2(2(3(5(4(x1))))))
   5(2(1(x1))) -> 1(3(2(5(3(4(x1))))))
   5(2(4(x1))) -> 0(5(2(3(4(x1)))))
   5(2(4(x1))) -> 5(5(3(4(2(x1)))))
   5(2(4(x1))) -> 0(3(4(4(5(2(x1))))))
   5(2(4(x1))) -> 2(2(5(3(4(4(x1))))))
   5(2(4(x1))) -> 2(3(3(4(5(5(x1))))))
   5(2(4(x1))) -> 2(3(4(3(5(3(x1))))))
   5(2(4(x1))) -> 2(5(3(4(0(5(x1))))))
   5(2(4(x1))) -> 3(1(2(5(3(4(x1))))))
   5(2(4(x1))) -> 5(2(3(4(0(3(x1))))))
   0(0(2(4(x1)))) -> 0(4(3(0(2(x1)))))
   0(1(1(5(x1)))) -> 0(1(3(5(1(2(x1))))))
   0(1(2(4(x1)))) -> 0(1(2(3(3(4(x1))))))
   0(1(4(5(x1)))) -> 3(4(0(5(1(x1)))))
   0(1(4(5(x1)))) -> 3(4(5(3(0(1(x1))))))
   0(4(2(1(x1)))) -> 0(4(1(2(3(4(x1))))))
   0(5(1(4(x1)))) -> 0(0(3(5(4(1(x1))))))
   1(0(1(4(x1)))) -> 3(4(0(1(2(1(x1))))))
   1(1(2(4(x1)))) -> 1(3(4(1(2(x1)))))
   1(2(2(4(x1)))) -> 2(2(2(3(4(1(x1))))))
   1(2(4(2(x1)))) -> 1(2(3(4(2(3(x1))))))
   1(5(2(1(x1)))) -> 1(0(3(5(1(2(x1))))))
   1(5(2(4(x1)))) -> 3(2(3(5(1(4(x1))))))
   1(5(2(4(x1)))) -> 5(2(3(3(1(4(x1))))))
   5(0(1(4(x1)))) -> 3(4(0(5(3(1(x1))))))
   5(2(5(1(x1)))) -> 3(5(1(5(2(x1)))))
   0(1(1(5(4(x1))))) -> 0(0(5(4(1(1(x1))))))
   1(0(0(2(4(x1))))) -> 0(2(0(4(4(1(x1))))))
   1(0(4(2(1(x1))))) -> 1(2(3(4(1(0(x1))))))
   1(2(5(0(1(x1))))) -> 2(3(5(1(0(1(x1))))))
   1(5(3(0(4(x1))))) -> 5(1(3(4(0(4(x1))))))
   5(0(5(2(4(x1))))) -> 4(0(0(5(5(2(x1))))))
   5(3(2(4(2(x1))))) -> 2(1(5(3(4(2(x1))))))
   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))

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

(7) CpxTrsMatchBoundsProof (FINISHED)
A linear upper bound on the runtime complexity of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 3. 
The certificate found is represented by the following graph.

"[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, 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, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580]
{(55,56,[0_1|0, 1_1|0, 5_1|0, encArg_1|0, encode_0_1|0, encode_1_1|0, encode_2_1|0, encode_3_1|0, encode_4_1|0, encode_5_1|0]), (55,57,[1_1|1]), (55,61,[5_1|1]), (55,65,[1_1|1]), (55,70,[2_1|1]), (55,75,[1_1|1]), (55,80,[2_1|1]), (55,85,[0_1|1]), (55,89,[5_1|1]), (55,93,[0_1|1]), (55,98,[2_1|1]), (55,103,[2_1|1]), (55,108,[2_1|1]), (55,113,[2_1|1]), (55,118,[3_1|1]), (55,123,[5_1|1]), (55,128,[2_1|1]), (55,133,[2_1|1, 3_1|1, 4_1|1, 0_1|1, 1_1|1, 5_1|1]), (55,134,[0_1|2]), (55,139,[1_1|2]), (55,144,[5_1|2]), (55,149,[0_1|2]), (55,154,[0_1|2]), (55,159,[0_1|2]), (55,162,[1_1|2]), (55,166,[1_1|2]), (55,170,[3_1|2]), (55,174,[1_1|2]), (55,179,[1_1|2]), (55,184,[1_1|2]), (55,189,[1_1|2]), (55,194,[3_1|2]), (55,199,[3_1|2]), (55,203,[3_1|2]), (55,208,[0_1|2]), (55,213,[0_1|2]), (55,217,[0_1|2]), (55,222,[0_1|2]), (55,227,[1_1|2]), (55,231,[5_1|2]), (55,235,[1_1|2]), (55,240,[2_1|2]), (55,245,[1_1|2]), (55,250,[2_1|2]), (55,255,[2_1|2]), (55,260,[3_1|2]), (55,265,[0_1|2]), (55,270,[1_1|2]), (55,275,[1_1|2]), (55,279,[1_1|2]), (55,284,[3_1|2]), (55,289,[5_1|2]), (55,294,[5_1|2]), (55,299,[1_1|2]), (55,304,[1_1|2]), (55,309,[0_1|2]), (55,313,[5_1|2]), (55,317,[0_1|2]), (55,322,[2_1|2]), (55,327,[2_1|2]), (55,332,[2_1|2]), (55,337,[2_1|2]), (55,342,[3_1|2]), (55,347,[5_1|2]), (55,352,[3_1|2]), (55,356,[3_1|2]), (55,361,[4_1|2]), (55,366,[2_1|2]), (56,56,[2_1|0, 3_1|0, 4_1|0, cons_0_1|0, cons_1_1|0, cons_5_1|0]), (57,58,[2_1|1]), (58,59,[3_1|1]), (59,60,[4_1|1]), (60,56,[1_1|1]), (60,57,[1_1|1]), (60,61,[5_1|1]), (60,65,[1_1|1]), (60,70,[2_1|1]), (60,75,[1_1|1]), (60,80,[2_1|1]), (61,62,[3_1|1]), (62,63,[4_1|1]), (63,64,[1_1|1]), (63,57,[1_1|1]), (63,61,[5_1|1]), (63,65,[1_1|1]), (63,70,[2_1|1]), (63,75,[1_1|1]), (63,80,[2_1|1]), (64,56,[2_1|1]), (65,66,[5_1|1]), (66,67,[2_1|1]), (67,68,[3_1|1]), (68,69,[4_1|1]), (69,56,[3_1|1]), (70,71,[3_1|1]), (71,72,[3_1|1]), (72,73,[4_1|1]), (73,74,[5_1|1]), (74,56,[1_1|1]), (74,57,[1_1|1]), (74,61,[5_1|1]), (74,65,[1_1|1]), (74,70,[2_1|1]), (74,75,[1_1|1]), (74,80,[2_1|1]), (75,76,[2_1|1]), (76,77,[3_1|1]), (77,78,[4_1|1]), (78,79,[2_1|1]), (79,56,[3_1|1]), (80,81,[2_1|1]), (81,82,[2_1|1]), (82,83,[3_1|1]), (83,84,[4_1|1]), (84,56,[1_1|1]), (84,57,[1_1|1]), (84,61,[5_1|1]), (84,65,[1_1|1]), (84,70,[2_1|1]), (84,75,[1_1|1]), (84,80,[2_1|1]), (85,86,[5_1|1]), (86,87,[2_1|1]), (87,88,[3_1|1]), (88,56,[4_1|1]), (89,90,[5_1|1]), (90,91,[3_1|1]), (91,92,[4_1|1]), (92,56,[2_1|1]), (93,94,[3_1|1]), (94,95,[4_1|1]), (95,96,[4_1|1]), (96,97,[5_1|1]), (96,85,[0_1|1]), (96,89,[5_1|1]), (96,93,[0_1|1]), (96,98,[2_1|1]), (96,103,[2_1|1]), (96,108,[2_1|1]), (96,113,[2_1|1]), (96,118,[3_1|1]), (96,123,[5_1|1]), (97,56,[2_1|1]), (98,99,[2_1|1]), (99,100,[5_1|1]), (100,101,[3_1|1]), (101,102,[4_1|1]), (102,56,[4_1|1]), (103,104,[3_1|1]), (104,105,[3_1|1]), (105,106,[4_1|1]), (106,107,[5_1|1]), (106,371,[1_1|2]), (106,376,[1_1|2]), (107,56,[5_1|1]), (107,85,[0_1|1]), (107,89,[5_1|1]), (107,93,[0_1|1]), (107,98,[2_1|1]), (107,103,[2_1|1]), (107,108,[2_1|1]), (107,113,[2_1|1]), (107,118,[3_1|1]), (107,123,[5_1|1]), (107,128,[2_1|1]), (108,109,[3_1|1]), (109,110,[4_1|1]), (110,111,[3_1|1]), (111,112,[5_1|1]), (111,128,[2_1|1]), (112,56,[3_1|1]), (113,114,[5_1|1]), (114,115,[3_1|1]), (115,116,[4_1|1]), (116,117,[0_1|1]), (117,56,[5_1|1]), (117,85,[0_1|1]), (117,89,[5_1|1]), (117,93,[0_1|1]), (117,98,[2_1|1]), (117,103,[2_1|1]), (117,108,[2_1|1]), (117,113,[2_1|1]), (117,118,[3_1|1]), (117,123,[5_1|1]), (117,128,[2_1|1]), (118,119,[1_1|1]), (119,120,[2_1|1]), (120,121,[5_1|1]), (121,122,[3_1|1]), (122,56,[4_1|1]), (123,124,[2_1|1]), (124,125,[3_1|1]), (125,126,[4_1|1]), (126,127,[0_1|1]), (127,56,[3_1|1]), (128,129,[1_1|1]), (129,130,[5_1|1]), (130,131,[3_1|1]), (131,132,[4_1|1]), (132,56,[2_1|1]), (133,56,[encArg_1|1]), (133,133,[2_1|1, 3_1|1, 4_1|1, 0_1|1, 1_1|1, 5_1|1]), (133,134,[0_1|2]), (133,139,[1_1|2]), (133,144,[5_1|2]), (133,149,[0_1|2]), (133,154,[0_1|2]), (133,159,[0_1|2]), (133,162,[1_1|2]), (133,166,[1_1|2]), (133,170,[3_1|2]), (133,174,[1_1|2]), (133,179,[1_1|2]), (133,184,[1_1|2]), (133,189,[1_1|2]), (133,194,[3_1|2]), (133,199,[3_1|2]), (133,203,[3_1|2]), (133,208,[0_1|2]), (133,213,[0_1|2]), (133,217,[0_1|2]), (133,222,[0_1|2]), (133,227,[1_1|2]), (133,231,[5_1|2]), (133,235,[1_1|2]), (133,240,[2_1|2]), (133,245,[1_1|2]), (133,250,[2_1|2]), (133,255,[2_1|2]), (133,260,[3_1|2]), (133,265,[0_1|2]), (133,270,[1_1|2]), (133,275,[1_1|2]), (133,279,[1_1|2]), (133,284,[3_1|2]), (133,289,[5_1|2]), (133,294,[5_1|2]), (133,299,[1_1|2]), (133,304,[1_1|2]), (133,309,[0_1|2]), (133,313,[5_1|2]), (133,317,[0_1|2]), (133,322,[2_1|2]), (133,327,[2_1|2]), (133,332,[2_1|2]), (133,337,[2_1|2]), (133,342,[3_1|2]), (133,347,[5_1|2]), (133,352,[3_1|2]), (133,356,[3_1|2]), (133,361,[4_1|2]), (133,366,[2_1|2]), (134,135,[1_1|2]), (135,136,[2_1|2]), (136,137,[3_1|2]), (137,138,[4_1|2]), (138,133,[1_1|2]), (138,139,[1_1|2]), (138,162,[1_1|2]), (138,166,[1_1|2]), (138,174,[1_1|2]), (138,179,[1_1|2]), (138,184,[1_1|2]), (138,189,[1_1|2]), (138,227,[1_1|2]), (138,235,[1_1|2]), (138,245,[1_1|2]), (138,270,[1_1|2]), (138,275,[1_1|2]), (138,279,[1_1|2]), (138,299,[1_1|2]), (138,304,[1_1|2]), (138,175,[1_1|2]), (138,231,[5_1|2]), (138,240,[2_1|2]), (138,250,[2_1|2]), (138,255,[2_1|2]), (138,260,[3_1|2]), (138,265,[0_1|2]), (138,284,[3_1|2]), (138,289,[5_1|2]), (138,294,[5_1|2]), (139,140,[3_1|2]), (140,141,[1_1|2]), (141,142,[3_1|2]), (142,143,[4_1|2]), (143,133,[0_1|2]), (143,139,[0_1|2, 1_1|2]), (143,162,[0_1|2, 1_1|2]), (143,166,[0_1|2, 1_1|2]), (143,174,[0_1|2, 1_1|2]), (143,179,[0_1|2, 1_1|2]), (143,184,[0_1|2, 1_1|2]), (143,189,[0_1|2, 1_1|2]), (143,227,[0_1|2]), (143,235,[0_1|2]), (143,245,[0_1|2]), (143,270,[0_1|2]), (143,275,[0_1|2]), (143,279,[0_1|2]), (143,299,[0_1|2]), (143,304,[0_1|2]), (143,175,[0_1|2]), (143,134,[0_1|2]), (143,144,[5_1|2]), (143,149,[0_1|2]), (143,154,[0_1|2]), (143,159,[0_1|2]), (143,170,[3_1|2]), (143,194,[3_1|2]), (143,199,[3_1|2]), (143,203,[3_1|2]), (143,208,[0_1|2]), (143,213,[0_1|2]), (143,217,[0_1|2]), (143,222,[0_1|2]), (143,381,[0_1|3]), (143,386,[1_1|3]), (143,391,[5_1|3]), (143,396,[0_1|3]), (144,145,[1_1|2]), (145,146,[3_1|2]), (146,147,[0_1|2]), (147,148,[3_1|2]), (148,133,[1_1|2]), (148,139,[1_1|2]), (148,162,[1_1|2]), (148,166,[1_1|2]), (148,174,[1_1|2]), (148,179,[1_1|2]), (148,184,[1_1|2]), (148,189,[1_1|2]), (148,227,[1_1|2]), (148,235,[1_1|2]), (148,245,[1_1|2]), (148,270,[1_1|2]), (148,275,[1_1|2]), (148,279,[1_1|2]), (148,299,[1_1|2]), (148,304,[1_1|2]), (148,175,[1_1|2]), (148,231,[5_1|2]), (148,240,[2_1|2]), (148,250,[2_1|2]), (148,255,[2_1|2]), (148,260,[3_1|2]), (148,265,[0_1|2]), (148,284,[3_1|2]), (148,289,[5_1|2]), (148,294,[5_1|2]), (149,150,[1_1|2]), (150,151,[3_1|2]), (151,152,[5_1|2]), (152,153,[1_1|2]), (152,227,[1_1|2]), (152,231,[5_1|2]), (152,235,[1_1|2]), (152,240,[2_1|2]), (152,245,[1_1|2]), (152,250,[2_1|2]), (152,255,[2_1|2]), (152,401,[1_1|3]), (152,405,[5_1|3]), (152,409,[1_1|3]), (152,414,[2_1|3]), (153,133,[2_1|2]), (153,144,[2_1|2]), (153,231,[2_1|2]), (153,289,[2_1|2]), (153,294,[2_1|2]), (153,313,[2_1|2]), (153,347,[2_1|2]), (153,167,[2_1|2]), (153,236,[2_1|2]), (153,176,[2_1|2]), (154,155,[0_1|2]), (155,156,[5_1|2]), (156,157,[4_1|2]), (157,158,[1_1|2]), (157,275,[1_1|2]), (158,133,[1_1|2]), (158,361,[1_1|2]), (158,227,[1_1|2]), (158,231,[5_1|2]), (158,235,[1_1|2]), (158,240,[2_1|2]), (158,245,[1_1|2]), (158,250,[2_1|2]), (158,255,[2_1|2]), (158,260,[3_1|2]), (158,265,[0_1|2]), (158,270,[1_1|2]), (158,275,[1_1|2]), (158,279,[1_1|2]), (158,284,[3_1|2]), (158,289,[5_1|2]), (158,294,[5_1|2]), (159,160,[1_1|2]), (160,161,[3_1|2]), (161,133,[4_1|2]), (161,361,[4_1|2]), (162,163,[3_1|2]), (163,164,[4_1|2]), (164,165,[2_1|2]), (165,133,[0_1|2]), (165,361,[0_1|2]), (165,134,[0_1|2]), (165,139,[1_1|2]), (165,144,[5_1|2]), (165,149,[0_1|2]), (165,154,[0_1|2]), (165,159,[0_1|2]), (165,162,[1_1|2]), (165,166,[1_1|2]), (165,170,[3_1|2]), (165,174,[1_1|2]), (165,179,[1_1|2]), (165,184,[1_1|2]), (165,189,[1_1|2]), (165,194,[3_1|2]), (165,199,[3_1|2]), (165,203,[3_1|2]), (165,208,[0_1|2]), (165,213,[0_1|2]), (165,217,[0_1|2]), (165,222,[0_1|2]), (165,381,[0_1|3]), (165,386,[1_1|3]), (165,391,[5_1|3]), (165,396,[0_1|3]), (166,167,[5_1|2]), (167,168,[3_1|2]), (168,169,[4_1|2]), (169,133,[0_1|2]), (169,361,[0_1|2]), (169,134,[0_1|2]), (169,139,[1_1|2]), (169,144,[5_1|2]), (169,149,[0_1|2]), (169,154,[0_1|2]), (169,159,[0_1|2]), (169,162,[1_1|2]), (169,166,[1_1|2]), (169,170,[3_1|2]), (169,174,[1_1|2]), (169,179,[1_1|2]), (169,184,[1_1|2]), (169,189,[1_1|2]), (169,194,[3_1|2]), (169,199,[3_1|2]), (169,203,[3_1|2]), (169,208,[0_1|2]), (169,213,[0_1|2]), (169,217,[0_1|2]), (169,222,[0_1|2]), (169,381,[0_1|3]), (169,386,[1_1|3]), (169,391,[5_1|3]), (169,396,[0_1|3]), (170,171,[1_1|2]), (171,172,[3_1|2]), (172,173,[4_1|2]), (173,133,[0_1|2]), (173,361,[0_1|2]), (173,134,[0_1|2]), (173,139,[1_1|2]), (173,144,[5_1|2]), 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(330,331,[5_1|2]), (330,419,[1_1|3]), (330,424,[1_1|3]), (331,133,[5_1|2]), (331,361,[5_1|2, 4_1|2]), (331,299,[1_1|2]), (331,304,[1_1|2]), (331,309,[0_1|2]), (331,313,[5_1|2]), (331,317,[0_1|2]), (331,322,[2_1|2]), (331,327,[2_1|2]), (331,332,[2_1|2]), (331,337,[2_1|2]), (331,342,[3_1|2]), (331,347,[5_1|2]), (331,352,[3_1|2]), (331,356,[3_1|2]), (331,366,[2_1|2]), (331,419,[1_1|3]), (331,424,[1_1|3]), (332,333,[3_1|2]), (333,334,[4_1|2]), (334,335,[3_1|2]), (335,336,[5_1|2]), (335,366,[2_1|2]), (336,133,[3_1|2]), (336,361,[3_1|2]), (337,338,[5_1|2]), (338,339,[3_1|2]), (339,340,[4_1|2]), (340,341,[0_1|2]), (340,222,[0_1|2]), (341,133,[5_1|2]), (341,361,[5_1|2, 4_1|2]), (341,299,[1_1|2]), (341,304,[1_1|2]), (341,309,[0_1|2]), (341,313,[5_1|2]), (341,317,[0_1|2]), (341,322,[2_1|2]), (341,327,[2_1|2]), (341,332,[2_1|2]), (341,337,[2_1|2]), (341,342,[3_1|2]), (341,347,[5_1|2]), (341,352,[3_1|2]), (341,356,[3_1|2]), (341,366,[2_1|2]), (341,419,[1_1|3]), (341,424,[1_1|3]), (342,343,[1_1|2]), (343,344,[2_1|2]), (344,345,[5_1|2]), (345,346,[3_1|2]), (346,133,[4_1|2]), (346,361,[4_1|2]), (347,348,[2_1|2]), (348,349,[3_1|2]), (349,350,[4_1|2]), (350,351,[0_1|2]), (351,133,[3_1|2]), (351,361,[3_1|2]), (352,353,[5_1|2]), (353,354,[1_1|2]), (353,279,[1_1|2]), (353,284,[3_1|2]), (353,289,[5_1|2]), (353,566,[1_1|3]), (353,571,[3_1|3]), (353,576,[5_1|3]), (354,355,[5_1|2]), (354,299,[1_1|2]), (354,304,[1_1|2]), (354,309,[0_1|2]), (354,313,[5_1|2]), (354,317,[0_1|2]), (354,322,[2_1|2]), (354,327,[2_1|2]), (354,332,[2_1|2]), (354,337,[2_1|2]), (354,342,[3_1|2]), (354,347,[5_1|2]), (354,352,[3_1|2]), (354,509,[1_1|3]), (354,514,[1_1|3]), (354,519,[3_1|3]), (354,523,[0_1|3]), (354,527,[5_1|3]), (354,531,[0_1|3]), (354,536,[2_1|3]), (354,541,[2_1|3]), (354,546,[2_1|3]), (354,551,[2_1|3]), (354,556,[3_1|3]), (354,561,[5_1|3]), (355,133,[2_1|2]), (355,139,[2_1|2]), (355,162,[2_1|2]), (355,166,[2_1|2]), (355,174,[2_1|2]), (355,179,[2_1|2]), (355,184,[2_1|2]), (355,189,[2_1|2]), (355,227,[2_1|2]), (355,235,[2_1|2]), (355,245,[2_1|2]), (355,270,[2_1|2]), (355,275,[2_1|2]), (355,279,[2_1|2]), (355,299,[2_1|2]), (355,304,[2_1|2]), (355,145,[2_1|2]), (355,295,[2_1|2]), (356,357,[4_1|2]), (357,358,[0_1|2]), (358,359,[5_1|2]), (359,360,[3_1|2]), (360,133,[1_1|2]), (360,361,[1_1|2]), (360,227,[1_1|2]), (360,231,[5_1|2]), (360,235,[1_1|2]), (360,240,[2_1|2]), (360,245,[1_1|2]), (360,250,[2_1|2]), (360,255,[2_1|2]), (360,260,[3_1|2]), (360,265,[0_1|2]), (360,270,[1_1|2]), (360,275,[1_1|2]), (360,279,[1_1|2]), (360,284,[3_1|2]), (360,289,[5_1|2]), (360,294,[5_1|2]), (361,362,[0_1|2]), (362,363,[0_1|2]), (363,364,[5_1|2]), (364,365,[5_1|2]), (364,299,[1_1|2]), (364,304,[1_1|2]), (364,309,[0_1|2]), (364,313,[5_1|2]), (364,317,[0_1|2]), (364,322,[2_1|2]), (364,327,[2_1|2]), (364,332,[2_1|2]), (364,337,[2_1|2]), (364,342,[3_1|2]), (364,347,[5_1|2]), (364,352,[3_1|2]), (364,509,[1_1|3]), (364,514,[1_1|3]), (364,519,[3_1|3]), (364,523,[0_1|3]), (364,527,[5_1|3]), (364,531,[0_1|3]), (364,536,[2_1|3]), (364,541,[2_1|3]), (364,546,[2_1|3]), (364,551,[2_1|3]), (364,556,[3_1|3]), (364,561,[5_1|3]), (365,133,[2_1|2]), (365,361,[2_1|2]), (366,367,[1_1|2]), (367,368,[5_1|2]), (368,369,[3_1|2]), (369,370,[4_1|2]), (370,133,[2_1|2]), (370,240,[2_1|2]), (370,250,[2_1|2]), (370,255,[2_1|2]), (370,322,[2_1|2]), (370,327,[2_1|2]), (370,332,[2_1|2]), (370,337,[2_1|2]), (370,366,[2_1|2]), (371,372,[2_1|2]), (372,373,[2_1|2]), (373,374,[3_1|2]), (374,375,[5_1|2]), (375,129,[4_1|2]), (376,377,[3_1|2]), (377,378,[2_1|2]), (378,379,[5_1|2]), (379,380,[3_1|2]), (380,129,[4_1|2]), (381,382,[1_1|3]), (382,383,[2_1|3]), (383,384,[3_1|3]), (384,385,[4_1|3]), (385,175,[1_1|3]), (386,387,[3_1|3]), (387,388,[1_1|3]), (388,389,[3_1|3]), (389,390,[4_1|3]), (390,175,[0_1|3]), (391,392,[1_1|3]), (392,393,[3_1|3]), (393,394,[0_1|3]), (394,395,[3_1|3]), (395,175,[1_1|3]), (396,397,[1_1|3]), (397,398,[3_1|3]), (398,399,[5_1|3]), (399,400,[1_1|3]), (400,176,[2_1|3]), (401,402,[2_1|3]), (402,403,[3_1|3]), (403,404,[4_1|3]), (404,361,[1_1|3]), (405,406,[3_1|3]), (406,407,[4_1|3]), (407,408,[1_1|3]), (408,361,[2_1|3]), (409,410,[5_1|3]), (410,411,[2_1|3]), (411,412,[3_1|3]), (412,413,[4_1|3]), (413,361,[3_1|3]), (414,415,[3_1|3]), (415,416,[3_1|3]), (416,417,[4_1|3]), (417,418,[5_1|3]), (418,361,[1_1|3]), (419,420,[2_1|3]), (420,421,[2_1|3]), (421,422,[3_1|3]), (422,423,[5_1|3]), (423,367,[4_1|3]), (424,425,[3_1|3]), (425,426,[2_1|3]), (426,427,[5_1|3]), (427,428,[3_1|3]), (428,367,[4_1|3]), (429,430,[4_1|3]), (430,431,[0_1|3]), (431,432,[5_1|3]), (432,433,[3_1|3]), (433,361,[1_1|3]), (434,435,[1_1|3]), (435,436,[2_1|3]), (436,437,[3_1|3]), (437,438,[4_1|3]), (438,139,[1_1|3]), (438,162,[1_1|3]), (438,166,[1_1|3]), (438,174,[1_1|3]), (438,179,[1_1|3]), (438,184,[1_1|3]), (438,189,[1_1|3]), (438,227,[1_1|3]), (438,235,[1_1|3]), (438,245,[1_1|3]), (438,270,[1_1|3]), (438,275,[1_1|3]), (438,279,[1_1|3]), (438,299,[1_1|3]), (438,304,[1_1|3]), (438,145,[1_1|3]), (438,295,[1_1|3]), (438,175,[1_1|3]), (439,440,[3_1|3]), (440,441,[1_1|3]), (441,442,[3_1|3]), (442,443,[4_1|3]), (443,139,[0_1|3]), (443,162,[0_1|3]), (443,166,[0_1|3]), (443,174,[0_1|3]), (443,179,[0_1|3]), (443,184,[0_1|3]), (443,189,[0_1|3]), (443,227,[0_1|3]), (443,235,[0_1|3]), (443,245,[0_1|3]), (443,270,[0_1|3]), (443,275,[0_1|3]), (443,279,[0_1|3]), (443,299,[0_1|3]), (443,304,[0_1|3]), (443,145,[0_1|3]), (443,295,[0_1|3]), (443,175,[0_1|3]), (444,445,[1_1|3]), (445,446,[3_1|3]), (446,447,[0_1|3]), (447,448,[3_1|3]), (448,139,[1_1|3]), (448,162,[1_1|3]), (448,166,[1_1|3]), (448,174,[1_1|3]), (448,179,[1_1|3]), (448,184,[1_1|3]), (448,189,[1_1|3]), (448,227,[1_1|3]), (448,235,[1_1|3]), (448,245,[1_1|3]), (448,270,[1_1|3]), (448,275,[1_1|3]), (448,279,[1_1|3]), (448,299,[1_1|3]), (448,304,[1_1|3]), (448,145,[1_1|3]), (448,295,[1_1|3]), (448,175,[1_1|3]), (449,450,[1_1|3]), (450,451,[3_1|3]), (451,452,[5_1|3]), (452,453,[1_1|3]), (453,167,[2_1|3]), (453,236,[2_1|3]), (453,176,[2_1|3]), (454,455,[1_1|3]), (455,456,[3_1|3]), (456,361,[4_1|3]), (457,458,[3_1|3]), (458,459,[4_1|3]), (459,460,[2_1|3]), (460,361,[0_1|3]), (461,462,[5_1|3]), (462,463,[3_1|3]), (463,464,[4_1|3]), (464,361,[0_1|3]), (465,466,[1_1|3]), (466,467,[3_1|3]), (467,468,[4_1|3]), (468,361,[0_1|3]), (469,470,[1_1|3]), (470,471,[5_1|3]), (471,472,[3_1|3]), (472,473,[4_1|3]), (473,361,[0_1|3]), (474,475,[2_1|3]), (475,476,[3_1|3]), (476,477,[4_1|3]), (477,478,[3_1|3]), (478,361,[0_1|3]), (479,480,[3_1|3]), (480,481,[3_1|3]), (481,482,[4_1|3]), (482,483,[4_1|3]), (483,361,[0_1|3]), (484,485,[3_1|3]), (485,486,[4_1|3]), (486,487,[5_1|3]), (487,488,[0_1|3]), (488,361,[5_1|3]), (489,490,[4_1|3]), (490,491,[5_1|3]), (491,492,[5_1|3]), (492,493,[0_1|3]), (493,361,[1_1|3]), (494,495,[0_1|3]), (495,496,[3_1|3]), (496,497,[5_1|3]), (497,498,[4_1|3]), (498,361,[1_1|3]), (499,500,[4_1|3]), (500,501,[0_1|3]), (501,502,[1_1|3]), (502,503,[2_1|3]), (503,361,[1_1|3]), (504,505,[4_1|3]), (505,506,[1_1|3]), (506,507,[2_1|3]), (507,508,[3_1|3]), (508,367,[4_1|3]), (509,510,[2_1|3]), (510,511,[2_1|3]), (511,512,[3_1|3]), (512,513,[5_1|3]), (513,139,[4_1|3]), (513,162,[4_1|3]), (513,166,[4_1|3]), (513,174,[4_1|3]), (513,179,[4_1|3]), (513,184,[4_1|3]), (513,189,[4_1|3]), (513,227,[4_1|3]), (513,235,[4_1|3]), (513,245,[4_1|3]), (513,270,[4_1|3]), (513,275,[4_1|3]), (513,279,[4_1|3]), (513,299,[4_1|3]), (513,304,[4_1|3]), (513,175,[4_1|3]), (514,515,[3_1|3]), (515,516,[2_1|3]), (516,517,[5_1|3]), (517,518,[3_1|3]), (518,139,[4_1|3]), (518,162,[4_1|3]), (518,166,[4_1|3]), (518,174,[4_1|3]), (518,179,[4_1|3]), (518,184,[4_1|3]), (518,189,[4_1|3]), (518,227,[4_1|3]), (518,235,[4_1|3]), (518,245,[4_1|3]), (518,270,[4_1|3]), (518,275,[4_1|3]), (518,279,[4_1|3]), (518,299,[4_1|3]), (518,304,[4_1|3]), (518,175,[4_1|3]), (519,520,[5_1|3]), (520,521,[1_1|3]), (521,522,[5_1|3]), (522,145,[2_1|3]), (522,295,[2_1|3]), (523,524,[5_1|3]), (524,525,[2_1|3]), (525,526,[3_1|3]), (526,361,[4_1|3]), (527,528,[5_1|3]), (528,529,[3_1|3]), (529,530,[4_1|3]), (530,361,[2_1|3]), (531,532,[3_1|3]), (532,533,[4_1|3]), (533,534,[4_1|3]), (534,535,[5_1|3]), (535,361,[2_1|3]), (536,537,[2_1|3]), (537,538,[5_1|3]), (538,539,[3_1|3]), (539,540,[4_1|3]), (540,361,[4_1|3]), (541,542,[3_1|3]), (542,543,[3_1|3]), (543,544,[4_1|3]), (544,545,[5_1|3]), (545,361,[5_1|3]), (546,547,[3_1|3]), (547,548,[4_1|3]), (548,549,[3_1|3]), (549,550,[5_1|3]), (550,361,[3_1|3]), (551,552,[5_1|3]), (552,553,[3_1|3]), (553,554,[4_1|3]), (554,555,[0_1|3]), (555,361,[5_1|3]), (556,557,[1_1|3]), (557,558,[2_1|3]), (558,559,[5_1|3]), (559,560,[3_1|3]), (560,361,[4_1|3]), (561,562,[2_1|3]), (562,563,[3_1|3]), (563,564,[4_1|3]), (564,565,[0_1|3]), (565,361,[3_1|3]), (566,567,[0_1|3]), (567,568,[3_1|3]), (568,569,[5_1|3]), (569,570,[1_1|3]), (570,139,[2_1|3]), (570,162,[2_1|3]), (570,166,[2_1|3]), (570,174,[2_1|3]), (570,179,[2_1|3]), (570,184,[2_1|3]), (570,189,[2_1|3]), (570,227,[2_1|3]), (570,235,[2_1|3]), (570,245,[2_1|3]), (570,270,[2_1|3]), (570,275,[2_1|3]), (570,279,[2_1|3]), (570,299,[2_1|3]), (570,304,[2_1|3]), (570,175,[2_1|3]), (571,572,[2_1|3]), (572,573,[3_1|3]), (573,574,[5_1|3]), (574,575,[1_1|3]), (575,361,[4_1|3]), (576,577,[2_1|3]), (577,578,[3_1|3]), (578,579,[3_1|3]), (579,580,[1_1|3]), (580,361,[4_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))) -> 0(1(2(3(4(1(x1))))))
   0(1(1(x1))) -> 1(3(1(3(4(0(x1))))))
   0(1(1(x1))) -> 5(1(3(0(3(1(x1))))))
   0(1(4(x1))) -> 0(1(3(4(x1))))
   0(1(4(x1))) -> 1(3(4(2(0(x1)))))
   0(1(4(x1))) -> 1(5(3(4(0(x1)))))
   0(1(4(x1))) -> 3(1(3(4(0(x1)))))
   0(1(4(x1))) -> 1(1(5(3(4(0(x1))))))
   0(1(4(x1))) -> 1(2(3(4(3(0(x1))))))
   0(1(4(x1))) -> 1(3(3(4(4(0(x1))))))
   0(1(4(x1))) -> 1(3(4(5(0(5(x1))))))
   0(1(4(x1))) -> 3(4(5(5(0(1(x1))))))
   1(2(4(x1))) -> 1(2(3(4(1(x1)))))
   1(2(4(x1))) -> 5(3(4(1(2(x1)))))
   1(2(4(x1))) -> 1(5(2(3(4(3(x1))))))
   1(2(4(x1))) -> 2(3(3(4(5(1(x1))))))
   5(2(1(x1))) -> 1(2(2(3(5(4(x1))))))
   5(2(1(x1))) -> 1(3(2(5(3(4(x1))))))
   5(2(4(x1))) -> 0(5(2(3(4(x1)))))
   5(2(4(x1))) -> 5(5(3(4(2(x1)))))
   5(2(4(x1))) -> 0(3(4(4(5(2(x1))))))
   5(2(4(x1))) -> 2(2(5(3(4(4(x1))))))
   5(2(4(x1))) -> 2(3(3(4(5(5(x1))))))
   5(2(4(x1))) -> 2(3(4(3(5(3(x1))))))
   5(2(4(x1))) -> 2(5(3(4(0(5(x1))))))
   5(2(4(x1))) -> 3(1(2(5(3(4(x1))))))
   5(2(4(x1))) -> 5(2(3(4(0(3(x1))))))
   0(0(2(4(x1)))) -> 0(4(3(0(2(x1)))))
   0(1(1(5(x1)))) -> 0(1(3(5(1(2(x1))))))
   0(1(2(4(x1)))) -> 0(1(2(3(3(4(x1))))))
   0(1(4(5(x1)))) -> 3(4(0(5(1(x1)))))
   0(1(4(5(x1)))) -> 3(4(5(3(0(1(x1))))))
   0(4(2(1(x1)))) -> 0(4(1(2(3(4(x1))))))
   0(5(1(4(x1)))) -> 0(0(3(5(4(1(x1))))))
   1(0(1(4(x1)))) -> 3(4(0(1(2(1(x1))))))
   1(1(2(4(x1)))) -> 1(3(4(1(2(x1)))))
   1(2(2(4(x1)))) -> 2(2(2(3(4(1(x1))))))
   1(2(4(2(x1)))) -> 1(2(3(4(2(3(x1))))))
   1(5(2(1(x1)))) -> 1(0(3(5(1(2(x1))))))
   1(5(2(4(x1)))) -> 3(2(3(5(1(4(x1))))))
   1(5(2(4(x1)))) -> 5(2(3(3(1(4(x1))))))
   5(0(1(4(x1)))) -> 3(4(0(5(3(1(x1))))))
   5(2(5(1(x1)))) -> 3(5(1(5(2(x1)))))
   0(1(1(5(4(x1))))) -> 0(0(5(4(1(1(x1))))))
   1(0(0(2(4(x1))))) -> 0(2(0(4(4(1(x1))))))
   1(0(4(2(1(x1))))) -> 1(2(3(4(1(0(x1))))))
   1(2(5(0(1(x1))))) -> 2(3(5(1(0(1(x1))))))
   1(5(3(0(4(x1))))) -> 5(1(3(4(0(4(x1))))))
   5(0(5(2(4(x1))))) -> 4(0(0(5(5(2(x1))))))
   5(3(2(4(2(x1))))) -> 2(1(5(3(4(2(x1))))))

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

   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))

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

The rewrite sequence

1(2(4(x1))) ->^+ 2(3(3(4(5(1(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 / 2(4(x1))].

The result substitution is [ ].




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(12)
Complex Obligation (BEST)

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

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

   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))

Rewrite Strategy: INNERMOST
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(14) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
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(15)
BOUNDS(n^1, INF)

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

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

   encArg(2(x_1)) -> 2(encArg(x_1))
   encArg(3(x_1)) -> 3(encArg(x_1))
   encArg(4(x_1)) -> 4(encArg(x_1))
   encArg(cons_0(x_1)) -> 0(encArg(x_1))
   encArg(cons_1(x_1)) -> 1(encArg(x_1))
   encArg(cons_5(x_1)) -> 5(encArg(x_1))
   encode_0(x_1) -> 0(encArg(x_1))
   encode_1(x_1) -> 1(encArg(x_1))
   encode_2(x_1) -> 2(encArg(x_1))
   encode_3(x_1) -> 3(encArg(x_1))
   encode_4(x_1) -> 4(encArg(x_1))
   encode_5(x_1) -> 5(encArg(x_1))

Rewrite Strategy: INNERMOST