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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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

Q is empty.

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
18, 19, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94

Node 18 is start node and node 19 is final node.

Those nodes are connected through the following edges:

* 18 to 75 labelled b_1(0)* 19 to 19 labelled #_1(0)* 75 to 76 labelled a_1(0)* 76 to 77 labelled a_1(0)* 77 to 78 labelled a_1(0)* 78 to 79 labelled a_1(0)* 79 to 80 labelled b_1(0)* 80 to 81 labelled a_1(0)* 80 to 85 labelled b_1(1)* 81 to 82 labelled a_1(0)* 82 to 83 labelled b_1(0)* 83 to 84 labelled a_1(0)* 83 to 85 labelled b_1(1)* 84 to 19 labelled a_1(0)* 84 to 85 labelled b_1(1)* 85 to 86 labelled a_1(1)* 86 to 87 labelled a_1(1)* 87 to 88 labelled a_1(1)* 88 to 89 labelled a_1(1)* 89 to 90 labelled b_1(1)* 90 to 91 labelled a_1(1)* 90 to 85 labelled b_1(1)* 91 to 92 labelled a_1(1)* 92 to 93 labelled b_1(1)* 93 to 94 labelled a_1(1)* 93 to 85 labelled b_1(1)* 94 to 19 labelled a_1(1)* 94 to 85 labelled b_1(1)


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(6)
YES