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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(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:
614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639

Node 614 is start node and node 615 is final node.

Those nodes are connected through the following edges:

* 614 to 616 labelled b_1(0)* 615 to 615 labelled #_1(0)* 616 to 617 labelled a_1(0)* 617 to 618 labelled a_1(0)* 618 to 619 labelled a_1(0)* 619 to 620 labelled b_1(0)* 620 to 621 labelled a_1(0)* 621 to 622 labelled a_1(0)* 621 to 628 labelled b_1(1)* 622 to 623 labelled b_1(0)* 623 to 624 labelled a_1(0)* 624 to 625 labelled a_1(0)* 624 to 628 labelled b_1(1)* 625 to 626 labelled b_1(0)* 626 to 627 labelled a_1(0)* 627 to 615 labelled a_1(0)* 627 to 628 labelled b_1(1)* 628 to 629 labelled a_1(1)* 629 to 630 labelled a_1(1)* 630 to 631 labelled a_1(1)* 631 to 632 labelled b_1(1)* 632 to 633 labelled a_1(1)* 633 to 634 labelled a_1(1)* 633 to 628 labelled b_1(1)* 634 to 635 labelled b_1(1)* 635 to 636 labelled a_1(1)* 636 to 637 labelled a_1(1)* 636 to 628 labelled b_1(1)* 637 to 638 labelled b_1(1)* 638 to 639 labelled a_1(1)* 639 to 615 labelled a_1(1)* 639 to 628 labelled b_1(1)


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(6)
YES