/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(b(a(b(a(a(a(a(x1)))))))) -> a(a(a(a(a(b(a(b(a(a(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(b(a(b(a(x1)))))))) -> b(a(b(a(a(a(b(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(b(a(x1)))))))) -> b(a(b(a(a(a(b(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(b(x))))))) -> b(a(b(a(a(a(b(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(b(x))))))) -> b(a(b(a(a(a(b(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(b(x))))))) -> b(a(b(a(a(a(b(a(b(a(a(a(a(x)))))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
376, 377, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449

Node 376 is start node and node 377 is final node.

Those nodes are connected through the following edges:

* 376 to 426 labelled b_1(0)* 377 to 377 labelled #_1(0)* 426 to 427 labelled a_1(0)* 427 to 428 labelled b_1(0)* 428 to 429 labelled a_1(0)* 429 to 430 labelled a_1(0)* 430 to 431 labelled a_1(0)* 431 to 432 labelled b_1(0)* 432 to 433 labelled a_1(0)* 433 to 434 labelled b_1(0)* 434 to 435 labelled a_1(0)* 434 to 438 labelled b_1(1)* 435 to 436 labelled a_1(0)* 435 to 438 labelled b_1(1)* 436 to 437 labelled a_1(0)* 436 to 438 labelled b_1(1)* 437 to 377 labelled a_1(0)* 437 to 438 labelled b_1(1)* 438 to 439 labelled a_1(1)* 439 to 440 labelled b_1(1)* 440 to 441 labelled a_1(1)* 441 to 442 labelled a_1(1)* 442 to 443 labelled a_1(1)* 443 to 444 labelled b_1(1)* 444 to 445 labelled a_1(1)* 445 to 446 labelled b_1(1)* 446 to 447 labelled a_1(1)* 446 to 438 labelled b_1(1)* 447 to 448 labelled a_1(1)* 447 to 438 labelled b_1(1)* 448 to 449 labelled a_1(1)* 448 to 438 labelled b_1(1)* 449 to 377 labelled a_1(1)* 449 to 438 labelled b_1(1)


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(6)
YES