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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 4 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(a(a(x1))))))) -> a(a(a(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].
----------------------------------------

(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576

Node 561 is start node and node 562 is final node.

Those nodes are connected through the following edges:

* 561 to 563 labelled b_1(0)* 562 to 562 labelled #_1(0)* 563 to 564 labelled a_1(0)* 564 to 565 labelled b_1(0)* 565 to 566 labelled a_1(0)* 566 to 567 labelled b_1(0)* 567 to 568 labelled a_1(0)* 567 to 570 labelled b_1(1)* 568 to 569 labelled a_1(0)* 568 to 570 labelled b_1(1)* 569 to 562 labelled a_1(0)* 569 to 570 labelled b_1(1)* 570 to 571 labelled a_1(1)* 571 to 572 labelled b_1(1)* 572 to 573 labelled a_1(1)* 573 to 574 labelled b_1(1)* 574 to 575 labelled a_1(1)* 574 to 570 labelled b_1(1)* 575 to 576 labelled a_1(1)* 575 to 570 labelled b_1(1)* 576 to 562 labelled a_1(1)* 576 to 570 labelled b_1(1)


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(6)
YES