/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(b(a(a(a(a(a(x1))))))))) -> a(a(a(a(a(a(b(a(b(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(b(a(x1))))))))) -> b(a(b(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(b(a(x1))))))))) -> b(a(b(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(a(b(x)))))))) -> b(a(b(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(a(b(x)))))))) -> b(a(b(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(a(b(x)))))))) -> b(a(b(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:
475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494

Node 475 is start node and node 476 is final node.

Those nodes are connected through the following edges:

* 475 to 477 labelled b_1(0)* 476 to 476 labelled #_1(0)* 477 to 478 labelled a_1(0)* 478 to 479 labelled b_1(0)* 479 to 480 labelled a_1(0)* 480 to 481 labelled b_1(0)* 481 to 482 labelled a_1(0)* 481 to 486 labelled b_1(1)* 482 to 483 labelled a_1(0)* 482 to 486 labelled b_1(1)* 483 to 484 labelled a_1(0)* 483 to 486 labelled b_1(1)* 484 to 485 labelled a_1(0)* 484 to 486 labelled b_1(1)* 485 to 476 labelled a_1(0)* 485 to 486 labelled b_1(1)* 486 to 487 labelled a_1(1)* 487 to 488 labelled b_1(1)* 488 to 489 labelled a_1(1)* 489 to 490 labelled b_1(1)* 490 to 491 labelled a_1(1)* 490 to 486 labelled b_1(1)* 491 to 492 labelled a_1(1)* 491 to 486 labelled b_1(1)* 492 to 493 labelled a_1(1)* 492 to 486 labelled b_1(1)* 493 to 494 labelled a_1(1)* 493 to 486 labelled b_1(1)* 494 to 476 labelled a_1(1)* 494 to 486 labelled b_1(1)


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(6)
YES