YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(b(a(b(a(b(a(x1)))))))))) -> a(a(b(a(b(a(b(a(b(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(b(a(b(a(a(b(a(x1)))))))))) -> b(a(a(b(a(b(a(b(a(b(a(a(x1))))))))))))

Q is empty.

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603

Node 582 is start node and node 583 is final node.

Those nodes are connected through the following edges:

* 582 to 584 labelled b_1(0)* 583 to 583 labelled #_1(0)* 584 to 585 labelled a_1(0)* 585 to 586 labelled a_1(0)* 586 to 587 labelled b_1(0)* 587 to 588 labelled a_1(0)* 587 to 594 labelled b_1(1)* 588 to 589 labelled b_1(0)* 589 to 590 labelled a_1(0)* 589 to 594 labelled b_1(1)* 590 to 591 labelled b_1(0)* 591 to 592 labelled a_1(0)* 591 to 594 labelled b_1(1)* 592 to 593 labelled b_1(0)* 593 to 583 labelled a_1(0)* 593 to 594 labelled b_1(1)* 594 to 595 labelled a_1(1)* 595 to 596 labelled a_1(1)* 596 to 597 labelled b_1(1)* 597 to 598 labelled a_1(1)* 597 to 594 labelled b_1(1)* 598 to 599 labelled b_1(1)* 599 to 600 labelled a_1(1)* 599 to 594 labelled b_1(1)* 600 to 601 labelled b_1(1)* 601 to 602 labelled a_1(1)* 601 to 594 labelled b_1(1)* 602 to 603 labelled b_1(1)* 603 to 583 labelled a_1(1)* 603 to 594 labelled b_1(1)


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(6)
YES