/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 1 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(a(x1))))))) -> a(a(a(a(a(a(b(a(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(a(b(a(x1))))))) -> b(a(b(a(a(a(a(b(a(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(a(b(a(x1))))))) -> b(a(b(a(a(a(a(b(a(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(a(b(x)))))) -> b(a(b(a(a(a(a(b(a(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(a(b(x)))))) -> b(a(b(a(a(a(a(b(a(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(a(b(x)))))) -> b(a(b(a(a(a(a(b(a(a(a(a(a(x)))))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 7, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 70, 71, 72, 73, 74, 75, 76, 77, 78, 129, 130, 131

Node 3 is start node and node 7 is final node.

Those nodes are connected through the following edges:

* 3 to 33 labelled b_1(0)* 7 to 7 labelled #_1(0)* 33 to 34 labelled a_1(0)* 34 to 35 labelled b_1(0)* 35 to 36 labelled a_1(0)* 36 to 37 labelled a_1(0)* 37 to 38 labelled a_1(0)* 38 to 39 labelled a_1(0)* 39 to 40 labelled b_1(0)* 40 to 41 labelled a_1(0)* 40 to 70 labelled b_1(1)* 41 to 42 labelled a_1(0)* 41 to 70 labelled b_1(1)* 42 to 43 labelled a_1(0)* 42 to 70 labelled b_1(1)* 43 to 44 labelled a_1(0)* 43 to 70 labelled b_1(1)* 44 to 7 labelled a_1(0)* 44 to 70 labelled b_1(1)* 70 to 71 labelled a_1(1)* 71 to 72 labelled b_1(1)* 72 to 73 labelled a_1(1)* 73 to 74 labelled a_1(1)* 74 to 75 labelled a_1(1)* 75 to 76 labelled a_1(1)* 76 to 77 labelled b_1(1)* 77 to 78 labelled a_1(1)* 77 to 70 labelled b_1(1)* 78 to 129 labelled a_1(1)* 78 to 70 labelled b_1(1)* 129 to 130 labelled a_1(1)* 129 to 70 labelled b_1(1)* 130 to 131 labelled a_1(1)* 130 to 70 labelled b_1(1)* 131 to 7 labelled a_1(1)* 131 to 70 labelled b_1(1)


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(6)
YES