/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 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(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(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(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(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(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(b(a(a(a(a(a(x))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
5, 6, 28, 30, 31, 33, 34, 36, 38, 40, 42, 65, 66, 67, 68, 69, 70, 71, 72, 73

Node 5 is start node and node 6 is final node.

Those nodes are connected through the following edges:

* 5 to 28 labelled b_1(0)* 6 to 6 labelled #_1(0)* 28 to 30 labelled a_1(0)* 30 to 31 labelled b_1(0)* 31 to 33 labelled a_1(0)* 33 to 34 labelled b_1(0)* 34 to 36 labelled a_1(0)* 34 to 65 labelled b_1(1)* 36 to 38 labelled a_1(0)* 36 to 65 labelled b_1(1)* 38 to 40 labelled a_1(0)* 38 to 65 labelled b_1(1)* 40 to 42 labelled a_1(0)* 40 to 65 labelled b_1(1)* 42 to 6 labelled a_1(0)* 42 to 65 labelled b_1(1)* 65 to 66 labelled a_1(1)* 66 to 67 labelled b_1(1)* 67 to 68 labelled a_1(1)* 68 to 69 labelled b_1(1)* 69 to 70 labelled a_1(1)* 69 to 65 labelled b_1(1)* 70 to 71 labelled a_1(1)* 70 to 65 labelled b_1(1)* 71 to 72 labelled a_1(1)* 71 to 65 labelled b_1(1)* 72 to 73 labelled a_1(1)* 72 to 65 labelled b_1(1)* 73 to 6 labelled a_1(1)* 73 to 65 labelled b_1(1)


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(6)
YES