/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 3 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(x1)))))) -> a(a(b(a(b(a(b(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(b(a(a(b(a(x1)))))) -> b(a(a(b(a(b(a(b(a(b(a(a(x1))))))))))))

Q is empty.

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(3) Strip Symbols Proof (SOUND)
We were given the following TRS:

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

By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 

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

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(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 429, 431, 432, 433, 434, 435, 436, 437, 438, 439

Node 396 is start node and node 397 is final node.

Those nodes are connected through the following edges:

* 396 to 398 labelled b_1(0)* 397 to 397 labelled #_1(0)* 398 to 399 labelled a_1(0)* 399 to 400 labelled a_1(0)* 400 to 401 labelled b_1(0)* 401 to 402 labelled a_1(0)* 402 to 403 labelled b_1(0)* 403 to 404 labelled a_1(0)* 404 to 405 labelled b_1(0)* 405 to 406 labelled a_1(0)* 405 to 429 labelled b_1(1)* 406 to 407 labelled b_1(0)* 407 to 397 labelled a_1(0)* 407 to 429 labelled b_1(1)* 429 to 431 labelled a_1(1)* 431 to 432 labelled a_1(1)* 432 to 433 labelled b_1(1)* 433 to 434 labelled a_1(1)* 434 to 435 labelled b_1(1)* 435 to 436 labelled a_1(1)* 436 to 437 labelled b_1(1)* 437 to 438 labelled a_1(1)* 437 to 429 labelled b_1(1)* 438 to 439 labelled b_1(1)* 439 to 397 labelled a_1(1)* 439 to 429 labelled b_1(1)


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(6)
YES