/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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(b(a(a(a(x1))))))) -> a(a(a(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(b(a(b(a(x1))))))) -> b(a(b(a(b(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(b(a(b(a(x1))))))) -> b(a(b(a(b(a(a(a(a(x1)))))))))

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512

Node 497 is start node and node 498 is final node.

Those nodes are connected through the following edges:

* 497 to 499 labelled b_1(0)* 498 to 498 labelled #_1(0)* 499 to 500 labelled a_1(0)* 500 to 501 labelled b_1(0)* 501 to 502 labelled a_1(0)* 502 to 503 labelled b_1(0)* 503 to 504 labelled a_1(0)* 503 to 506 labelled b_1(1)* 504 to 505 labelled a_1(0)* 504 to 506 labelled b_1(1)* 505 to 498 labelled a_1(0)* 505 to 506 labelled b_1(1)* 506 to 507 labelled a_1(1)* 507 to 508 labelled b_1(1)* 508 to 509 labelled a_1(1)* 509 to 510 labelled b_1(1)* 510 to 511 labelled a_1(1)* 510 to 506 labelled b_1(1)* 511 to 512 labelled a_1(1)* 511 to 506 labelled b_1(1)* 512 to 498 labelled a_1(1)* 512 to 506 labelled b_1(1)


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(6)
YES