YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(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:
588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611

Node 588 is start node and node 589 is final node.

Those nodes are connected through the following edges:

* 588 to 590 labelled b_1(0)* 589 to 589 labelled #_1(0)* 590 to 591 labelled a_1(0)* 591 to 592 labelled b_1(0)* 592 to 593 labelled a_1(0)* 593 to 594 labelled b_1(0)* 594 to 595 labelled a_1(0)* 595 to 596 labelled b_1(0)* 596 to 597 labelled a_1(0)* 596 to 601 labelled b_1(1)* 597 to 598 labelled a_1(0)* 597 to 601 labelled b_1(1)* 598 to 599 labelled a_1(0)* 598 to 601 labelled b_1(1)* 599 to 600 labelled a_1(0)* 599 to 601 labelled b_1(1)* 600 to 589 labelled a_1(0)* 600 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 589 labelled a_1(1)* 611 to 601 labelled b_1(1)


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(6)
YES