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


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YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
441, 442, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488

Node 441 is start node and node 442 is final node.

Those nodes are connected through the following edges:

* 441 to 469 labelled b_1(0)* 442 to 442 labelled #_1(0)* 469 to 470 labelled a_1(0)* 470 to 471 labelled a_1(0)* 471 to 472 labelled b_1(0)* 472 to 473 labelled a_1(0)* 473 to 474 labelled a_1(0)* 474 to 475 labelled b_1(0)* 475 to 476 labelled a_1(0)* 475 to 479 labelled b_1(1)* 476 to 477 labelled a_1(0)* 476 to 479 labelled b_1(1)* 477 to 478 labelled a_1(0)* 477 to 479 labelled b_1(1)* 478 to 442 labelled a_1(0)* 478 to 479 labelled b_1(1)* 479 to 480 labelled a_1(1)* 480 to 481 labelled a_1(1)* 481 to 482 labelled b_1(1)* 482 to 483 labelled a_1(1)* 483 to 484 labelled a_1(1)* 484 to 485 labelled b_1(1)* 485 to 486 labelled a_1(1)* 485 to 479 labelled b_1(1)* 486 to 487 labelled a_1(1)* 486 to 479 labelled b_1(1)* 487 to 488 labelled a_1(1)* 487 to 479 labelled b_1(1)* 488 to 442 labelled a_1(1)* 488 to 479 labelled b_1(1)


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(6)
YES