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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(b(a(b(b(a(a(a(a(a(x1))))))))))) -> a(a(a(a(a(a(b(b(a(b(b(a(b(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(b(a(b(b(a(x1))))))))))) -> b(b(a(b(b(a(b(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(b(a(b(b(a(x1))))))))))) -> b(b(a(b(b(a(b(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(b(a(b(b(x)))))))))) -> b(b(a(b(b(a(b(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(b(a(b(b(x)))))))))) -> b(b(a(b(b(a(b(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(b(a(b(b(x)))))))))) -> b(b(a(b(b(a(b(b(a(a(a(a(a(x)))))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574

Node 549 is start node and node 550 is final node.

Those nodes are connected through the following edges:

* 549 to 551 labelled b_1(0)* 550 to 550 labelled #_1(0)* 551 to 552 labelled b_1(0)* 552 to 553 labelled a_1(0)* 553 to 554 labelled b_1(0)* 554 to 555 labelled b_1(0)* 555 to 556 labelled a_1(0)* 556 to 557 labelled b_1(0)* 557 to 558 labelled b_1(0)* 558 to 559 labelled a_1(0)* 558 to 563 labelled b_1(1)* 559 to 560 labelled a_1(0)* 559 to 563 labelled b_1(1)* 560 to 561 labelled a_1(0)* 560 to 563 labelled b_1(1)* 561 to 562 labelled a_1(0)* 561 to 563 labelled b_1(1)* 562 to 550 labelled a_1(0)* 562 to 563 labelled b_1(1)* 563 to 564 labelled b_1(1)* 564 to 565 labelled a_1(1)* 565 to 566 labelled b_1(1)* 566 to 567 labelled b_1(1)* 567 to 568 labelled a_1(1)* 568 to 569 labelled b_1(1)* 569 to 570 labelled b_1(1)* 570 to 571 labelled a_1(1)* 570 to 563 labelled b_1(1)* 571 to 572 labelled a_1(1)* 571 to 563 labelled b_1(1)* 572 to 573 labelled a_1(1)* 572 to 563 labelled b_1(1)* 573 to 574 labelled a_1(1)* 573 to 563 labelled b_1(1)* 574 to 550 labelled a_1(1)* 574 to 563 labelled b_1(1)


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(6)
YES