/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

Q is empty.

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613

Node 575 is start node and node 576 is final node.

Those nodes are connected through the following edges:

* 575 to 577 labelled b_1(0)* 576 to 576 labelled #_1(0)* 577 to 578 labelled a_1(0)* 578 to 579 labelled a_1(0)* 579 to 580 labelled a_1(0)* 580 to 581 labelled b_1(0)* 581 to 582 labelled a_1(0)* 582 to 583 labelled a_1(0)* 582 to 602 labelled b_1(1)* 583 to 584 labelled b_1(0)* 584 to 585 labelled a_1(0)* 585 to 586 labelled a_1(0)* 585 to 602 labelled b_1(1)* 586 to 587 labelled b_1(0)* 587 to 588 labelled a_1(0)* 588 to 576 labelled a_1(0)* 588 to 602 labelled b_1(1)* 602 to 603 labelled a_1(1)* 603 to 604 labelled a_1(1)* 604 to 605 labelled a_1(1)* 605 to 606 labelled b_1(1)* 606 to 607 labelled a_1(1)* 607 to 608 labelled a_1(1)* 607 to 602 labelled b_1(1)* 608 to 609 labelled b_1(1)* 609 to 610 labelled a_1(1)* 610 to 611 labelled a_1(1)* 610 to 602 labelled b_1(1)* 611 to 612 labelled b_1(1)* 612 to 613 labelled a_1(1)* 613 to 576 labelled a_1(1)* 613 to 602 labelled b_1(1)


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(6)
YES