/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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, 2 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(a(a(x1))))))))) -> a(a(a(a(a(a(b(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].
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(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
436, 437, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471

Node 436 is start node and node 437 is final node.

Those nodes are connected through the following edges:

* 436 to 450 labelled b_1(0)* 437 to 437 labelled #_1(0)* 450 to 451 labelled a_1(0)* 451 to 452 labelled b_1(0)* 452 to 453 labelled a_1(0)* 453 to 454 labelled b_1(0)* 454 to 455 labelled a_1(0)* 455 to 456 labelled b_1(0)* 456 to 457 labelled a_1(0)* 456 to 461 labelled b_1(1)* 457 to 458 labelled a_1(0)* 457 to 461 labelled b_1(1)* 458 to 459 labelled a_1(0)* 458 to 461 labelled b_1(1)* 459 to 460 labelled a_1(0)* 459 to 461 labelled b_1(1)* 460 to 437 labelled a_1(0)* 460 to 461 labelled b_1(1)* 461 to 462 labelled a_1(1)* 462 to 463 labelled b_1(1)* 463 to 464 labelled a_1(1)* 464 to 465 labelled b_1(1)* 465 to 466 labelled a_1(1)* 466 to 467 labelled b_1(1)* 467 to 468 labelled a_1(1)* 467 to 461 labelled b_1(1)* 468 to 469 labelled a_1(1)* 468 to 461 labelled b_1(1)* 469 to 470 labelled a_1(1)* 469 to 461 labelled b_1(1)* 470 to 471 labelled a_1(1)* 470 to 461 labelled b_1(1)* 471 to 437 labelled a_1(1)* 471 to 461 labelled b_1(1)


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(6)
YES