/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1 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(b(a(a(a(a(a(x1)))))))) -> a(a(a(a(a(a(b(b(a(b(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(b(a(x1)))))))) -> b(b(a(b(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(b(a(x1)))))))) -> b(b(a(b(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(b(x))))))) -> b(b(a(b(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(b(x))))))) -> b(b(a(b(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(b(x))))))) -> b(b(a(b(b(a(a(a(a(a(x))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 116, 117, 118, 119, 120, 121, 122, 123, 124

Node 95 is start node and node 96 is final node.

Those nodes are connected through the following edges:

* 95 to 97 labelled b_1(0)* 96 to 96 labelled #_1(0)* 97 to 98 labelled b_1(0)* 98 to 99 labelled a_1(0)* 99 to 100 labelled b_1(0)* 100 to 101 labelled b_1(0)* 101 to 102 labelled a_1(0)* 101 to 116 labelled b_1(1)* 102 to 103 labelled a_1(0)* 102 to 116 labelled b_1(1)* 103 to 104 labelled a_1(0)* 103 to 116 labelled b_1(1)* 104 to 105 labelled a_1(0)* 104 to 116 labelled b_1(1)* 105 to 96 labelled a_1(0)* 105 to 116 labelled b_1(1)* 116 to 117 labelled b_1(1)* 117 to 118 labelled a_1(1)* 118 to 119 labelled b_1(1)* 119 to 120 labelled b_1(1)* 120 to 121 labelled a_1(1)* 120 to 116 labelled b_1(1)* 121 to 122 labelled a_1(1)* 121 to 116 labelled b_1(1)* 122 to 123 labelled a_1(1)* 122 to 116 labelled b_1(1)* 123 to 124 labelled a_1(1)* 123 to 116 labelled b_1(1)* 124 to 96 labelled a_1(1)* 124 to 116 labelled b_1(1)


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(6)
YES