/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(a(a(a(x1))))))) -> a(a(a(a(a(b(b(a(b(b(a(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(b(b(a(x1))))))) -> b(b(a(a(b(b(a(b(b(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(b(b(a(x1))))))) -> b(b(a(a(b(b(a(b(b(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(b(b(x)))))) -> b(b(a(a(b(b(a(b(b(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(b(b(x)))))) -> b(b(a(a(b(b(a(b(b(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(b(b(x)))))) -> b(b(a(a(b(b(a(b(b(a(a(a(a(x)))))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550

Node 512 is start node and node 513 is final node.

Those nodes are connected through the following edges:

* 512 to 514 labelled b_1(0)* 513 to 513 labelled #_1(0)* 514 to 515 labelled b_1(0)* 515 to 516 labelled a_1(0)* 516 to 517 labelled a_1(0)* 517 to 518 labelled b_1(0)* 518 to 519 labelled b_1(0)* 519 to 520 labelled a_1(0)* 520 to 521 labelled b_1(0)* 521 to 522 labelled b_1(0)* 522 to 523 labelled a_1(0)* 522 to 539 labelled b_1(1)* 523 to 524 labelled a_1(0)* 523 to 539 labelled b_1(1)* 524 to 525 labelled a_1(0)* 524 to 539 labelled b_1(1)* 525 to 513 labelled a_1(0)* 525 to 539 labelled b_1(1)* 539 to 540 labelled b_1(1)* 540 to 541 labelled a_1(1)* 541 to 542 labelled a_1(1)* 542 to 543 labelled b_1(1)* 543 to 544 labelled b_1(1)* 544 to 545 labelled a_1(1)* 545 to 546 labelled b_1(1)* 546 to 547 labelled b_1(1)* 547 to 548 labelled a_1(1)* 547 to 539 labelled b_1(1)* 548 to 549 labelled a_1(1)* 548 to 539 labelled b_1(1)* 549 to 550 labelled a_1(1)* 549 to 539 labelled b_1(1)* 550 to 513 labelled a_1(1)* 550 to 539 labelled b_1(1)


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(6)
YES