/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) Strip Symbols Proof [SOUND, 0 ms]
(4) QTRS
(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
(6) YES


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(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(b(a(a(a(a(a(x1))))))) -> a(a(a(a(a(a(b(a(a(a(a(b(x1))))))))))))

Q is empty.

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(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
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(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(a(a(a(a(b(a(x1))))))) -> b(a(a(a(a(b(a(a(a(a(a(a(x1))))))))))))

Q is empty.

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(3) Strip Symbols Proof (SOUND)
We were given the following TRS:

   a(a(a(a(a(b(a(x1))))))) -> b(a(a(a(a(b(a(a(a(a(a(a(x1))))))))))))

By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 

   a(a(a(a(a(b(x)))))) -> b(a(a(a(a(b(a(a(a(a(a(x)))))))))))

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(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(a(a(a(a(b(x)))))) -> b(a(a(a(a(b(a(a(a(a(a(x)))))))))))

Q is empty.

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(5) RFCMatchBoundsTRSProof (EQUIVALENT)
Termination of the TRS R could be shown with a Match Bound [MATCHBOUNDS1,MATCHBOUNDS2] of 1. This implies Q-termination of R.
The following rules were used to construct the certificate:

   a(a(a(a(a(b(x)))))) -> b(a(a(a(a(b(a(a(a(a(a(x)))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452

Node 420 is start node and node 421 is final node.

Those nodes are connected through the following edges:

* 420 to 422 labelled b_1(0)* 421 to 421 labelled #_1(0)* 422 to 423 labelled a_1(0)* 423 to 424 labelled a_1(0)* 424 to 425 labelled a_1(0)* 425 to 426 labelled a_1(0)* 426 to 427 labelled b_1(0)* 427 to 428 labelled a_1(0)* 427 to 443 labelled b_1(1)* 428 to 429 labelled a_1(0)* 428 to 443 labelled b_1(1)* 429 to 430 labelled a_1(0)* 429 to 443 labelled b_1(1)* 430 to 431 labelled a_1(0)* 430 to 443 labelled b_1(1)* 431 to 421 labelled a_1(0)* 431 to 443 labelled b_1(1)* 443 to 444 labelled a_1(1)* 444 to 445 labelled a_1(1)* 445 to 446 labelled a_1(1)* 446 to 447 labelled a_1(1)* 447 to 448 labelled b_1(1)* 448 to 449 labelled a_1(1)* 448 to 443 labelled b_1(1)* 449 to 450 labelled a_1(1)* 449 to 443 labelled b_1(1)* 450 to 451 labelled a_1(1)* 450 to 443 labelled b_1(1)* 451 to 452 labelled a_1(1)* 451 to 443 labelled b_1(1)* 452 to 421 labelled a_1(1)* 452 to 443 labelled b_1(1)


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(6)
YES