/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 (full) 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), 62 ms]
(4) CpxRelTRS
(5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(6) CpxTRS
    (7) CpxTrsMatchBoundsProof [FINISHED, 41 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 (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^1).


The TRS R consists of the following rules:

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

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

(1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID))
The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem:

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


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

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


The TRS R consists of the following rules:

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

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

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

Rewrite Strategy: FULL
----------------------------------------

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

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


The TRS R consists of the following rules:

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

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

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

Rewrite Strategy: FULL
----------------------------------------

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

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


The TRS R consists of the following rules:

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

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

(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.

"[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]
{(63,64,[0_1|0, 5_1|0, encArg_1|0, encode_0_1|0, encode_1_1|0, encode_2_1|0, encode_3_1|0, encode_4_1|0, encode_5_1|0]), (63,65,[0_1|1]), (63,68,[0_1|1]), (63,71,[0_1|1]), (63,74,[0_1|1]), (63,77,[0_1|1]), (63,81,[5_1|1]), (63,86,[0_1|1]), (63,90,[1_1|1]), (63,94,[0_1|1]), (63,98,[4_1|1]), (63,103,[4_1|1]), (63,108,[0_1|1]), (63,112,[0_1|1]), (63,116,[0_1|1]), (63,121,[3_1|1]), (63,126,[4_1|1]), (63,129,[4_1|1]), (63,133,[4_1|1]), (63,138,[0_1|1]), (63,143,[3_1|1]), (63,148,[4_1|1]), (63,153,[0_1|1]), (63,157,[1_1|1]), (63,161,[1_1|1]), (63,165,[3_1|1]), (63,169,[3_1|1]), (63,173,[0_1|1]), (63,178,[0_1|1]), (63,182,[0_1|1]), (63,187,[1_1|1, 2_1|1, 3_1|1, 4_1|1, 0_1|1, 5_1|1]), (63,188,[0_1|2]), (63,192,[0_1|2]), (63,195,[0_1|2]), (63,198,[0_1|2]), (63,201,[0_1|2]), (63,204,[0_1|2]), (63,208,[5_1|2]), (63,213,[0_1|2]), (63,217,[1_1|2]), (63,221,[0_1|2]), (63,225,[4_1|2]), (63,230,[4_1|2]), (63,235,[3_1|2]), (63,240,[1_1|2]), (63,244,[0_1|2]), (63,249,[5_1|2]), (63,254,[5_1|2]), (63,259,[0_1|2]), (63,263,[0_1|2]), (63,268,[3_1|2]), (63,273,[4_1|2]), (63,276,[4_1|2]), (63,280,[4_1|2]), (63,285,[0_1|2]), (63,290,[5_1|2]), (63,295,[4_1|2]), (63,300,[3_1|2]), (63,305,[4_1|2]), (63,310,[3_1|2]), (63,315,[1_1|2]), (63,320,[4_1|2]), (63,325,[0_1|2]), (63,330,[0_1|2]), (63,334,[1_1|2]), (63,338,[3_1|2]), (63,342,[3_1|2]), (63,346,[0_1|2]), (63,351,[2_1|2]), (63,356,[0_1|2]), (63,361,[0_1|2]), (63,365,[0_1|2]), (63,370,[5_1|2]), (63,375,[1_1|2]), (63,379,[5_1|2]), (63,384,[5_1|2]), (63,389,[0_1|2]), (63,394,[0_1|2]), (63,399,[0_1|3]), (64,64,[1_1|0, 2_1|0, 3_1|0, 4_1|0, cons_0_1|0, cons_5_1|0]), (65,66,[1_1|1]), (66,67,[3_1|1]), (67,64,[2_1|1]), (68,69,[2_1|1]), (69,70,[1_1|1]), (70,64,[0_1|1]), (70,65,[0_1|1]), (70,68,[0_1|1]), (70,71,[0_1|1]), (70,74,[0_1|1]), (70,77,[0_1|1]), (70,81,[5_1|1]), (70,86,[0_1|1]), (70,90,[1_1|1]), (70,94,[0_1|1]), (70,98,[4_1|1]), (70,103,[4_1|1]), (70,108,[0_1|1]), (70,112,[0_1|1]), (70,116,[0_1|1]), (70,121,[3_1|1]), (70,126,[4_1|1]), (70,129,[4_1|1]), (70,133,[4_1|1]), (70,138,[0_1|1]), (70,143,[3_1|1]), (70,148,[4_1|1]), (70,153,[0_1|1]), (70,157,[1_1|1]), (70,161,[1_1|1]), (70,165,[3_1|1]), (70,169,[3_1|1]), (70,173,[0_1|1]), (70,178,[0_1|1]), (70,182,[0_1|1]), (70,188,[0_1|2]), (71,72,[2_1|1]), (72,73,[1_1|1]), (73,64,[3_1|1]), (74,75,[2_1|1]), (75,76,[2_1|1]), (76,64,[1_1|1]), (77,78,[2_1|1]), (78,79,[2_1|1]), (79,80,[1_1|1]), (80,64,[4_1|1]), (81,82,[1_1|1]), (82,83,[0_1|1]), (83,84,[5_1|1]), (84,85,[2_1|1]), (85,64,[3_1|1]), (86,87,[2_1|1]), (87,88,[1_1|1]), (88,89,[0_1|1]), (88,112,[0_1|1]), (88,116,[0_1|1]), (88,121,[3_1|1]), (89,64,[2_1|1]), (90,91,[3_1|1]), (91,92,[0_1|1]), (92,93,[2_1|1]), (93,64,[2_1|1]), (94,95,[1_1|1]), (95,96,[4_1|1]), (96,97,[2_1|1]), (97,64,[3_1|1]), (98,99,[0_1|1]), (99,100,[2_1|1]), (100,101,[2_1|1]), (101,102,[1_1|1]), (102,64,[1_1|1]), (103,104,[0_1|1]), (104,105,[5_1|1]), (105,106,[5_1|1]), (106,107,[2_1|1]), (107,64,[1_1|1]), (108,109,[5_1|1]), (109,110,[2_1|1]), (110,111,[1_1|1]), (111,64,[4_1|1]), (112,113,[2_1|1]), (113,114,[1_1|1]), (114,115,[4_1|1]), (115,64,[3_1|1]), (116,117,[5_1|1]), (117,118,[4_1|1]), (118,119,[3_1|1]), (119,120,[2_1|1]), (120,64,[2_1|1]), (121,122,[2_1|1]), (122,123,[2_1|1]), (123,124,[3_1|1]), (124,125,[4_1|1]), (125,64,[0_1|1]), (125,65,[0_1|1]), (125,68,[0_1|1]), (125,71,[0_1|1]), (125,74,[0_1|1]), (125,77,[0_1|1]), (125,81,[5_1|1]), (125,86,[0_1|1]), (125,90,[1_1|1]), (125,94,[0_1|1]), (125,98,[4_1|1]), (125,103,[4_1|1]), (125,108,[0_1|1]), (125,112,[0_1|1]), (125,116,[0_1|1]), (125,121,[3_1|1]), (125,126,[4_1|1]), (125,129,[4_1|1]), (125,133,[4_1|1]), (125,138,[0_1|1]), (125,143,[3_1|1]), (125,148,[4_1|1]), (125,153,[0_1|1]), (125,157,[1_1|1]), (125,161,[1_1|1]), (125,165,[3_1|1]), (125,169,[3_1|1]), (125,173,[0_1|1]), (125,178,[0_1|1]), (125,182,[0_1|1]), (125,188,[0_1|2]), (126,127,[0_1|1]), (126,121,[3_1|1]), (127,128,[2_1|1]), (128,64,[3_1|1]), (129,130,[0_1|1]), (130,131,[5_1|1]), (131,132,[5_1|1]), (132,64,[2_1|1]), (133,134,[1_1|1]), (134,135,[3_1|1]), (135,136,[2_1|1]), (136,137,[0_1|1]), (136,112,[0_1|1]), (136,116,[0_1|1]), (136,121,[3_1|1]), (137,64,[2_1|1]), (138,139,[2_1|1]), (139,140,[1_1|1]), (140,141,[4_1|1]), (141,142,[4_1|1]), (142,64,[4_1|1]), (143,144,[1_1|1]), (144,145,[4_1|1]), (145,146,[0_1|1]), (146,147,[2_1|1]), (147,64,[1_1|1]), (148,149,[1_1|1]), (149,150,[0_1|1]), (150,151,[2_1|1]), (151,152,[2_1|1]), (152,64,[3_1|1]), (153,154,[2_1|1]), (154,155,[1_1|1]), (155,156,[3_1|1]), (156,64,[2_1|1]), (157,158,[0_1|1]), (158,159,[2_1|1]), (159,160,[5_1|1]), (160,64,[3_1|1]), (161,162,[5_1|1]), (162,163,[0_1|1]), (162,121,[3_1|1]), (163,164,[2_1|1]), (164,64,[3_1|1]), (165,166,[0_1|1]), (166,167,[2_1|1]), (167,168,[2_1|1]), (168,64,[1_1|1]), (169,170,[2_1|1]), (170,171,[2_1|1]), (171,172,[1_1|1]), (172,64,[0_1|1]), (172,65,[0_1|1]), (172,68,[0_1|1]), (172,71,[0_1|1]), (172,74,[0_1|1]), (172,77,[0_1|1]), (172,81,[5_1|1]), (172,86,[0_1|1]), (172,90,[1_1|1]), (172,94,[0_1|1]), (172,98,[4_1|1]), (172,103,[4_1|1]), (172,108,[0_1|1]), (172,112,[0_1|1]), (172,116,[0_1|1]), (172,121,[3_1|1]), (172,126,[4_1|1]), (172,129,[4_1|1]), (172,133,[4_1|1]), (172,138,[0_1|1]), (172,143,[3_1|1]), (172,148,[4_1|1]), (172,153,[0_1|1]), (172,157,[1_1|1]), (172,161,[1_1|1]), (172,165,[3_1|1]), (172,169,[3_1|1]), (172,173,[0_1|1]), (172,178,[0_1|1]), (172,182,[0_1|1]), (172,188,[0_1|2]), (173,174,[3_1|1]), (174,175,[2_1|1]), (175,176,[3_1|1]), (176,177,[1_1|1]), (177,64,[3_1|1]), (178,179,[2_1|1]), (179,180,[2_1|1]), (180,181,[3_1|1]), (181,64,[4_1|1]), (182,183,[5_1|1]), (183,184,[3_1|1]), (184,185,[1_1|1]), (185,186,[4_1|1]), (186,64,[4_1|1]), (187,64,[encArg_1|1]), (187,187,[1_1|1, 2_1|1, 3_1|1, 4_1|1, 0_1|1, 5_1|1]), (187,192,[0_1|2]), (187,195,[0_1|2]), (187,198,[0_1|2]), (187,201,[0_1|2]), (187,204,[0_1|2]), (187,208,[5_1|2]), (187,213,[0_1|2]), (187,217,[1_1|2]), (187,221,[0_1|2]), (187,225,[4_1|2]), (187,230,[4_1|2]), (187,235,[3_1|2]), (187,188,[0_1|2]), (187,240,[1_1|2]), (187,244,[0_1|2]), (187,249,[5_1|2]), (187,254,[5_1|2]), (187,259,[0_1|2]), (187,263,[0_1|2]), (187,268,[3_1|2]), (187,273,[4_1|2]), (187,276,[4_1|2]), (187,280,[4_1|2]), (187,285,[0_1|2]), (187,290,[5_1|2]), (187,295,[4_1|2]), (187,300,[3_1|2]), (187,305,[4_1|2]), (187,310,[3_1|2]), (187,315,[1_1|2]), (187,320,[4_1|2]), (187,325,[0_1|2]), (187,330,[0_1|2]), (187,334,[1_1|2]), (187,338,[3_1|2]), (187,342,[3_1|2]), (187,346,[0_1|2]), (187,351,[2_1|2]), (187,356,[0_1|2]), (187,361,[0_1|2]), (187,365,[0_1|2]), (187,370,[5_1|2]), (187,375,[1_1|2]), (187,379,[5_1|2]), (187,384,[5_1|2]), (187,389,[0_1|2]), (187,394,[0_1|2]), (187,399,[0_1|3]), (188,189,[5_1|2]), (189,190,[2_1|2]), (190,191,[1_1|2]), (191,97,[4_1|2]), (191,187,[4_1|2]), (191,351,[4_1|2]), (191,317,[4_1|2]), (192,193,[1_1|2]), (193,194,[3_1|2]), (194,187,[2_1|2]), (194,351,[2_1|2]), (195,196,[2_1|2]), (196,197,[1_1|2]), (197,187,[0_1|2]), (197,351,[0_1|2, 2_1|2]), (197,192,[0_1|2]), (197,195,[0_1|2]), (197,198,[0_1|2]), (197,201,[0_1|2]), (197,204,[0_1|2]), (197,208,[5_1|2]), (197,213,[0_1|2]), (197,217,[1_1|2]), (197,221,[0_1|2]), (197,225,[4_1|2]), (197,230,[4_1|2]), (197,235,[3_1|2]), (197,188,[0_1|2]), (197,240,[1_1|2]), (197,244,[0_1|2]), (197,249,[5_1|2]), (197,254,[5_1|2]), (197,259,[0_1|2]), (197,263,[0_1|2]), (197,268,[3_1|2]), (197,273,[4_1|2]), (197,276,[4_1|2]), (197,280,[4_1|2]), (197,285,[0_1|2]), (197,290,[5_1|2]), (197,295,[4_1|2]), (197,300,[3_1|2]), (197,305,[4_1|2]), (197,310,[3_1|2]), (197,315,[1_1|2]), (197,320,[4_1|2]), (197,325,[0_1|2]), (197,330,[0_1|2]), (197,334,[1_1|2]), (197,338,[3_1|2]), (197,342,[3_1|2]), (197,346,[0_1|2]), (197,356,[0_1|2]), (197,361,[0_1|2]), (197,365,[0_1|2]), (197,370,[5_1|2]), (197,403,[0_1|3]), (198,199,[2_1|2]), (199,200,[1_1|2]), (200,187,[3_1|2]), (200,351,[3_1|2]), (201,202,[2_1|2]), (202,203,[2_1|2]), (203,187,[1_1|2]), (203,351,[1_1|2]), (204,205,[2_1|2]), (205,206,[2_1|2]), (206,207,[1_1|2]), (207,187,[4_1|2]), (207,351,[4_1|2]), (208,209,[1_1|2]), (209,210,[0_1|2]), (210,211,[5_1|2]), (211,212,[2_1|2]), (212,187,[3_1|2]), (212,351,[3_1|2]), (213,214,[2_1|2]), (214,215,[1_1|2]), (215,216,[0_1|2]), (215,259,[0_1|2]), (215,263,[0_1|2]), (215,268,[3_1|2]), (215,407,[0_1|3]), (216,187,[2_1|2]), (216,351,[2_1|2]), (217,218,[3_1|2]), (218,219,[0_1|2]), (219,220,[2_1|2]), (220,187,[2_1|2]), (220,351,[2_1|2]), (221,222,[1_1|2]), (222,223,[4_1|2]), (223,224,[2_1|2]), (224,187,[3_1|2]), (224,225,[3_1|2]), (224,230,[3_1|2]), (224,273,[3_1|2]), (224,276,[3_1|2]), (224,280,[3_1|2]), (224,295,[3_1|2]), (224,305,[3_1|2]), (224,320,[3_1|2]), (225,226,[0_1|2]), (226,227,[2_1|2]), (227,228,[2_1|2]), (228,229,[1_1|2]), (229,187,[1_1|2]), (229,225,[1_1|2]), (229,230,[1_1|2]), (229,273,[1_1|2]), (229,276,[1_1|2]), (229,280,[1_1|2]), (229,295,[1_1|2]), (229,305,[1_1|2]), (229,320,[1_1|2]), (230,231,[0_1|2]), (231,232,[5_1|2]), (232,233,[5_1|2]), (233,234,[2_1|2]), (234,187,[1_1|2]), (234,225,[1_1|2]), (234,230,[1_1|2]), (234,273,[1_1|2]), (234,276,[1_1|2]), (234,280,[1_1|2]), (234,295,[1_1|2]), (234,305,[1_1|2]), (234,320,[1_1|2]), (235,236,[5_1|2]), (236,237,[5_1|2]), (237,238,[2_1|2]), (238,239,[1_1|2]), (239,187,[0_1|2]), (239,208,[0_1|2, 5_1|2]), (239,249,[0_1|2, 5_1|2]), (239,254,[0_1|2, 5_1|2]), (239,290,[0_1|2, 5_1|2]), (239,370,[0_1|2, 5_1|2]), (239,379,[0_1|2]), (239,384,[0_1|2]), (239,192,[0_1|2]), (239,195,[0_1|2]), (239,198,[0_1|2]), (239,201,[0_1|2]), (239,204,[0_1|2]), (239,213,[0_1|2]), (239,217,[1_1|2]), (239,221,[0_1|2]), (239,225,[4_1|2]), (239,230,[4_1|2]), (239,235,[3_1|2]), (239,188,[0_1|2]), (239,240,[1_1|2]), (239,244,[0_1|2]), (239,259,[0_1|2]), (239,263,[0_1|2]), (239,268,[3_1|2]), (239,273,[4_1|2]), (239,276,[4_1|2]), (239,280,[4_1|2]), (239,285,[0_1|2]), (239,295,[4_1|2]), (239,300,[3_1|2]), (239,305,[4_1|2]), (239,310,[3_1|2]), (239,315,[1_1|2]), (239,320,[4_1|2]), (239,325,[0_1|2]), (239,330,[0_1|2]), (239,334,[1_1|2]), (239,338,[3_1|2]), (239,342,[3_1|2]), (239,346,[0_1|2]), (239,351,[2_1|2]), (239,356,[0_1|2]), (239,361,[0_1|2]), (239,365,[0_1|2]), (239,403,[0_1|3]), (240,241,[5_1|2]), (241,242,[0_1|2]), (241,268,[3_1|2]), (242,243,[2_1|2]), (243,187,[3_1|2]), (243,351,[3_1|2]), (244,245,[2_1|2]), (245,246,[2_1|2]), (246,247,[1_1|2]), (247,248,[0_1|2]), (248,187,[5_1|2]), (248,351,[5_1|2]), (248,375,[1_1|2]), (248,379,[5_1|2]), (248,384,[5_1|2]), (248,389,[0_1|2]), (248,394,[0_1|2]), (249,250,[5_1|2]), (250,251,[0_1|2]), (251,252,[2_1|2]), (252,253,[1_1|2]), (253,187,[3_1|2]), (253,351,[3_1|2]), (254,255,[0_1|2]), (255,256,[2_1|2]), (256,257,[5_1|2]), (257,258,[1_1|2]), (258,187,[1_1|2]), (258,208,[1_1|2]), (258,249,[1_1|2]), (258,254,[1_1|2]), (258,290,[1_1|2]), (258,370,[1_1|2]), (258,379,[1_1|2]), (258,384,[1_1|2]), (259,260,[2_1|2]), (260,261,[1_1|2]), (261,262,[4_1|2]), (262,187,[3_1|2]), (262,225,[3_1|2]), (262,230,[3_1|2]), (262,273,[3_1|2]), (262,276,[3_1|2]), (262,280,[3_1|2]), (262,295,[3_1|2]), (262,305,[3_1|2]), (262,320,[3_1|2]), (263,264,[5_1|2]), (264,265,[4_1|2]), (265,266,[3_1|2]), (266,267,[2_1|2]), (267,187,[2_1|2]), (267,351,[2_1|2]), (268,269,[2_1|2]), (269,270,[2_1|2]), (270,271,[3_1|2]), (271,272,[4_1|2]), (272,187,[0_1|2]), (272,351,[0_1|2, 2_1|2]), (272,192,[0_1|2]), (272,195,[0_1|2]), (272,198,[0_1|2]), (272,201,[0_1|2]), (272,204,[0_1|2]), (272,208,[5_1|2]), (272,213,[0_1|2]), (272,217,[1_1|2]), (272,221,[0_1|2]), (272,225,[4_1|2]), (272,230,[4_1|2]), (272,235,[3_1|2]), (272,188,[0_1|2]), (272,240,[1_1|2]), (272,244,[0_1|2]), (272,249,[5_1|2]), (272,254,[5_1|2]), (272,259,[0_1|2]), (272,263,[0_1|2]), (272,268,[3_1|2]), (272,273,[4_1|2]), (272,276,[4_1|2]), (272,280,[4_1|2]), (272,285,[0_1|2]), (272,290,[5_1|2]), (272,295,[4_1|2]), (272,300,[3_1|2]), (272,305,[4_1|2]), (272,310,[3_1|2]), (272,315,[1_1|2]), (272,320,[4_1|2]), (272,325,[0_1|2]), (272,330,[0_1|2]), (272,334,[1_1|2]), (272,338,[3_1|2]), (272,342,[3_1|2]), (272,346,[0_1|2]), (272,356,[0_1|2]), (272,361,[0_1|2]), (272,365,[0_1|2]), (272,370,[5_1|2]), (272,403,[0_1|3]), (273,274,[0_1|2]), (273,268,[3_1|2]), (274,275,[2_1|2]), (275,187,[3_1|2]), (275,351,[3_1|2]), (276,277,[0_1|2]), (277,278,[5_1|2]), (278,279,[5_1|2]), (279,187,[2_1|2]), (279,351,[2_1|2]), (280,281,[1_1|2]), (281,282,[3_1|2]), (282,283,[2_1|2]), (283,284,[0_1|2]), (283,259,[0_1|2]), (283,263,[0_1|2]), (283,268,[3_1|2]), (283,407,[0_1|3]), (284,187,[2_1|2]), (284,351,[2_1|2]), (285,286,[2_1|2]), (286,287,[1_1|2]), (287,288,[4_1|2]), (288,289,[4_1|2]), (289,187,[4_1|2]), (289,225,[4_1|2]), (289,230,[4_1|2]), (289,273,[4_1|2]), (289,276,[4_1|2]), (289,280,[4_1|2]), (289,295,[4_1|2]), (289,305,[4_1|2]), (289,320,[4_1|2]), (289,316,[4_1|2]), (290,291,[4_1|2]), (291,292,[3_1|2]), (292,293,[2_1|2]), (293,294,[2_1|2]), (294,187,[0_1|2]), (294,351,[0_1|2, 2_1|2]), (294,192,[0_1|2]), (294,195,[0_1|2]), (294,198,[0_1|2]), (294,201,[0_1|2]), (294,204,[0_1|2]), (294,208,[5_1|2]), (294,213,[0_1|2]), (294,217,[1_1|2]), (294,221,[0_1|2]), (294,225,[4_1|2]), (294,230,[4_1|2]), (294,235,[3_1|2]), (294,188,[0_1|2]), (294,240,[1_1|2]), (294,244,[0_1|2]), (294,249,[5_1|2]), (294,254,[5_1|2]), (294,259,[0_1|2]), (294,263,[0_1|2]), (294,268,[3_1|2]), (294,273,[4_1|2]), (294,276,[4_1|2]), (294,280,[4_1|2]), (294,285,[0_1|2]), (294,290,[5_1|2]), (294,295,[4_1|2]), (294,300,[3_1|2]), (294,305,[4_1|2]), (294,310,[3_1|2]), (294,315,[1_1|2]), (294,320,[4_1|2]), (294,325,[0_1|2]), (294,330,[0_1|2]), (294,334,[1_1|2]), (294,338,[3_1|2]), (294,342,[3_1|2]), (294,346,[0_1|2]), (294,356,[0_1|2]), (294,361,[0_1|2]), (294,365,[0_1|2]), (294,370,[5_1|2]), (294,403,[0_1|3]), (295,296,[4_1|2]), (296,297,[0_1|2]), (297,298,[0_1|2]), (298,299,[2_1|2]), (299,187,[2_1|2]), (299,351,[2_1|2]), (300,301,[1_1|2]), (301,302,[4_1|2]), (302,303,[0_1|2]), (303,304,[2_1|2]), (304,187,[1_1|2]), (304,351,[1_1|2]), (305,306,[1_1|2]), (306,307,[0_1|2]), (307,308,[2_1|2]), (308,309,[2_1|2]), (309,187,[3_1|2]), (309,351,[3_1|2]), (310,311,[4_1|2]), (311,312,[1_1|2]), (312,313,[0_1|2]), (313,314,[2_1|2]), (314,187,[5_1|2]), (314,208,[5_1|2]), (314,249,[5_1|2]), (314,254,[5_1|2]), (314,290,[5_1|2]), (314,370,[5_1|2]), (314,379,[5_1|2]), (314,384,[5_1|2]), (314,375,[1_1|2]), (314,389,[0_1|2]), (314,394,[0_1|2]), (315,316,[4_1|2]), (316,317,[2_1|2]), (317,318,[0_1|2]), (318,319,[5_1|2]), (319,187,[5_1|2]), (319,351,[5_1|2]), (319,375,[1_1|2]), (319,379,[5_1|2]), (319,384,[5_1|2]), (319,389,[0_1|2]), (319,394,[0_1|2]), (320,321,[0_1|2]), (321,322,[2_1|2]), (322,323,[5_1|2]), (323,324,[1_1|2]), (324,187,[1_1|2]), (324,351,[1_1|2]), (325,326,[0_1|2]), (326,327,[2_1|2]), (327,328,[2_1|2]), (328,329,[3_1|2]), (329,187,[4_1|2]), (329,351,[4_1|2]), (330,331,[2_1|2]), (331,332,[1_1|2]), (332,333,[3_1|2]), (333,187,[2_1|2]), (333,351,[2_1|2]), (334,335,[0_1|2]), (335,336,[2_1|2]), (336,337,[5_1|2]), (337,187,[3_1|2]), (337,351,[3_1|2]), (338,339,[0_1|2]), (339,340,[2_1|2]), (340,341,[2_1|2]), (341,187,[1_1|2]), (341,351,[1_1|2]), (342,343,[2_1|2]), (343,344,[2_1|2]), (344,345,[1_1|2]), (345,187,[0_1|2]), (345,351,[0_1|2, 2_1|2]), (345,192,[0_1|2]), (345,195,[0_1|2]), (345,198,[0_1|2]), (345,201,[0_1|2]), (345,204,[0_1|2]), (345,208,[5_1|2]), (345,213,[0_1|2]), (345,217,[1_1|2]), (345,221,[0_1|2]), (345,225,[4_1|2]), (345,230,[4_1|2]), (345,235,[3_1|2]), (345,188,[0_1|2]), (345,240,[1_1|2]), (345,244,[0_1|2]), (345,249,[5_1|2]), (345,254,[5_1|2]), (345,259,[0_1|2]), (345,263,[0_1|2]), (345,268,[3_1|2]), (345,273,[4_1|2]), (345,276,[4_1|2]), (345,280,[4_1|2]), (345,285,[0_1|2]), (345,290,[5_1|2]), (345,295,[4_1|2]), (345,300,[3_1|2]), (345,305,[4_1|2]), (345,310,[3_1|2]), (345,315,[1_1|2]), (345,320,[4_1|2]), (345,325,[0_1|2]), (345,330,[0_1|2]), (345,334,[1_1|2]), (345,338,[3_1|2]), (345,342,[3_1|2]), (345,346,[0_1|2]), (345,356,[0_1|2]), (345,361,[0_1|2]), (345,365,[0_1|2]), (345,370,[5_1|2]), (345,403,[0_1|3]), (346,347,[3_1|2]), (347,348,[2_1|2]), (348,349,[3_1|2]), (349,350,[1_1|2]), (350,187,[3_1|2]), (350,351,[3_1|2]), (351,352,[3_1|2]), (352,353,[1_1|2]), (353,354,[3_1|2]), (354,355,[0_1|2]), (355,187,[5_1|2]), (355,208,[5_1|2]), (355,249,[5_1|2]), (355,254,[5_1|2]), (355,290,[5_1|2]), (355,370,[5_1|2]), (355,379,[5_1|2]), (355,384,[5_1|2]), (355,375,[1_1|2]), (355,389,[0_1|2]), (355,394,[0_1|2]), (356,357,[3_1|2]), (357,358,[2_1|2]), (358,359,[5_1|2]), (359,360,[1_1|2]), (360,187,[2_1|2]), (360,351,[2_1|2]), (361,362,[2_1|2]), (362,363,[2_1|2]), (363,364,[3_1|2]), (364,187,[4_1|2]), (364,351,[4_1|2]), (365,366,[5_1|2]), (366,367,[3_1|2]), (367,368,[1_1|2]), (368,369,[4_1|2]), (369,187,[4_1|2]), (369,225,[4_1|2]), (369,230,[4_1|2]), (369,273,[4_1|2]), (369,276,[4_1|2]), (369,280,[4_1|2]), (369,295,[4_1|2]), (369,305,[4_1|2]), (369,320,[4_1|2]), (369,316,[4_1|2]), (370,371,[5_1|2]), (371,372,[3_1|2]), (372,373,[2_1|2]), (373,374,[1_1|2]), (374,187,[0_1|2]), (374,351,[0_1|2, 2_1|2]), (374,192,[0_1|2]), (374,195,[0_1|2]), (374,198,[0_1|2]), (374,201,[0_1|2]), (374,204,[0_1|2]), (374,208,[5_1|2]), (374,213,[0_1|2]), (374,217,[1_1|2]), (374,221,[0_1|2]), (374,225,[4_1|2]), (374,230,[4_1|2]), (374,235,[3_1|2]), (374,188,[0_1|2]), (374,240,[1_1|2]), (374,244,[0_1|2]), (374,249,[5_1|2]), (374,254,[5_1|2]), (374,259,[0_1|2]), (374,263,[0_1|2]), (374,268,[3_1|2]), (374,273,[4_1|2]), (374,276,[4_1|2]), (374,280,[4_1|2]), (374,285,[0_1|2]), (374,290,[5_1|2]), (374,295,[4_1|2]), (374,300,[3_1|2]), (374,305,[4_1|2]), (374,310,[3_1|2]), (374,315,[1_1|2]), (374,320,[4_1|2]), (374,325,[0_1|2]), (374,330,[0_1|2]), (374,334,[1_1|2]), (374,338,[3_1|2]), (374,342,[3_1|2]), (374,346,[0_1|2]), (374,356,[0_1|2]), (374,361,[0_1|2]), (374,365,[0_1|2]), (374,370,[5_1|2]), (374,403,[0_1|3]), (375,376,[3_1|2]), (376,377,[2_1|2]), (377,378,[5_1|2]), (377,375,[1_1|2]), (377,379,[5_1|2]), (377,384,[5_1|2]), (377,389,[0_1|2]), (377,394,[0_1|2]), (378,187,[0_1|2]), (378,351,[0_1|2, 2_1|2]), (378,192,[0_1|2]), (378,195,[0_1|2]), (378,198,[0_1|2]), (378,201,[0_1|2]), (378,204,[0_1|2]), (378,208,[5_1|2]), (378,213,[0_1|2]), (378,217,[1_1|2]), (378,221,[0_1|2]), (378,225,[4_1|2]), (378,230,[4_1|2]), (378,235,[3_1|2]), (378,188,[0_1|2]), (378,240,[1_1|2]), (378,244,[0_1|2]), (378,249,[5_1|2]), (378,254,[5_1|2]), (378,259,[0_1|2]), (378,263,[0_1|2]), (378,268,[3_1|2]), (378,273,[4_1|2]), (378,276,[4_1|2]), (378,280,[4_1|2]), (378,285,[0_1|2]), (378,290,[5_1|2]), (378,295,[4_1|2]), (378,300,[3_1|2]), (378,305,[4_1|2]), (378,310,[3_1|2]), (378,315,[1_1|2]), (378,320,[4_1|2]), (378,325,[0_1|2]), (378,330,[0_1|2]), (378,334,[1_1|2]), (378,338,[3_1|2]), (378,342,[3_1|2]), (378,346,[0_1|2]), (378,356,[0_1|2]), (378,361,[0_1|2]), (378,365,[0_1|2]), (378,370,[5_1|2]), (378,403,[0_1|3]), (379,380,[0_1|2]), (380,381,[2_1|2]), (381,382,[1_1|2]), (382,383,[3_1|2]), (383,187,[3_1|2]), (383,351,[3_1|2]), (384,385,[0_1|2]), (385,386,[2_1|2]), (386,387,[2_1|2]), (387,388,[1_1|2]), (388,187,[2_1|2]), (388,351,[2_1|2]), (389,390,[2_1|2]), (390,391,[2_1|2]), (391,392,[5_1|2]), (392,393,[1_1|2]), (393,187,[4_1|2]), (393,351,[4_1|2]), (394,395,[5_1|2]), (395,396,[2_1|2]), (396,397,[5_1|2]), (397,398,[4_1|2]), (398,187,[4_1|2]), (398,351,[4_1|2]), (399,400,[5_1|3]), (400,401,[2_1|3]), (401,402,[1_1|3]), (402,224,[4_1|3]), (403,404,[5_1|3]), (404,405,[2_1|3]), (405,406,[1_1|3]), (406,317,[4_1|3]), (406,224,[4_1|3]), (407,408,[2_1|3]), (408,409,[1_1|3]), (409,410,[4_1|3]), (410,225,[3_1|3]), (410,230,[3_1|3]), (410,273,[3_1|3]), (410,276,[3_1|3]), (410,280,[3_1|3]), (410,295,[3_1|3]), (410,305,[3_1|3]), (410,320,[3_1|3])}"
----------------------------------------

(8)
BOUNDS(1, n^1)

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

(9) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
Transformed a relative TRS into a decreasing-loop problem.
----------------------------------------

(10)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

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

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

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

Rewrite Strategy: FULL
----------------------------------------

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

The rewrite sequence

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

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

The pumping substitution is [x1 / 1(2(x1))].

The result substitution is [ ].




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

(12)
Complex Obligation (BEST)

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

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

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


The TRS R consists of the following rules:

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

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

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

Rewrite Strategy: FULL
----------------------------------------

(14) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
----------------------------------------

(15)
BOUNDS(n^1, INF)

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

(16)
Obligation:
Analyzing the following TRS for decreasing loops:

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


The TRS R consists of the following rules:

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

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

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

Rewrite Strategy: FULL