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


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YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(b(a(a(a(a(a(x1))))))))))) -> a(a(a(a(a(a(b(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(b(a(x1))))))))))) -> b(a(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(b(a(x1))))))))))) -> b(a(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(a(b(x)))))))))) -> b(a(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(a(b(x)))))))))) -> b(a(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(a(b(x)))))))))) -> b(a(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:
268, 269, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611

Node 268 is start node and node 269 is final node.

Those nodes are connected through the following edges:

* 268 to 535 labelled b_1(0)* 269 to 269 labelled #_1(0)* 535 to 536 labelled a_1(0)* 536 to 537 labelled b_1(0)* 537 to 538 labelled a_1(0)* 538 to 539 labelled b_1(0)* 539 to 540 labelled a_1(0)* 540 to 541 labelled b_1(0)* 541 to 542 labelled a_1(0)* 541 to 601 labelled b_1(1)* 542 to 543 labelled a_1(0)* 542 to 601 labelled b_1(1)* 543 to 544 labelled a_1(0)* 543 to 601 labelled b_1(1)* 544 to 545 labelled a_1(0)* 544 to 601 labelled b_1(1)* 545 to 269 labelled a_1(0)* 545 to 601 labelled b_1(1)* 601 to 602 labelled a_1(1)* 602 to 603 labelled b_1(1)* 603 to 604 labelled a_1(1)* 604 to 605 labelled b_1(1)* 605 to 606 labelled a_1(1)* 606 to 607 labelled b_1(1)* 607 to 608 labelled a_1(1)* 607 to 601 labelled b_1(1)* 608 to 609 labelled a_1(1)* 608 to 601 labelled b_1(1)* 609 to 610 labelled a_1(1)* 609 to 601 labelled b_1(1)* 610 to 611 labelled a_1(1)* 610 to 601 labelled b_1(1)* 611 to 269 labelled a_1(1)* 611 to 601 labelled b_1(1)


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(6)
YES