/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(a(a(a(x1)))))) -> a(a(a(a(a(b(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(x1)))))) -> b(a(a(b(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(x1)))))) -> b(a(a(b(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(x))))) -> b(a(a(b(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(x))))) -> b(a(a(b(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(x))))) -> b(a(a(b(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:
424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475

Node 424 is start node and node 425 is final node.

Those nodes are connected through the following edges:

* 424 to 426 labelled b_1(0)* 425 to 425 labelled #_1(0)* 426 to 427 labelled a_1(0)* 427 to 428 labelled a_1(0)* 428 to 429 labelled b_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 464 labelled b_1(1)* 435 to 436 labelled a_1(0)* 435 to 464 labelled b_1(1)* 436 to 437 labelled a_1(0)* 436 to 464 labelled b_1(1)* 437 to 425 labelled a_1(0)* 437 to 464 labelled b_1(1)* 464 to 465 labelled a_1(1)* 465 to 466 labelled a_1(1)* 466 to 467 labelled b_1(1)* 467 to 468 labelled a_1(1)* 468 to 469 labelled a_1(1)* 469 to 470 labelled b_1(1)* 470 to 471 labelled a_1(1)* 471 to 472 labelled b_1(1)* 472 to 473 labelled a_1(1)* 472 to 464 labelled b_1(1)* 473 to 474 labelled a_1(1)* 473 to 464 labelled b_1(1)* 474 to 475 labelled a_1(1)* 474 to 464 labelled b_1(1)* 475 to 425 labelled a_1(1)* 475 to 464 labelled b_1(1)


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(6)
YES