/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) Strip Symbols Proof [SOUND, 0 ms]
(2) QTRS
(3) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
(4) YES


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(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

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

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

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

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(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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(3) 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:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192

Node 173 is start node and node 174 is final node.

Those nodes are connected through the following edges:

* 173 to 175 labelled a_1(0)* 174 to 174 labelled #_1(0)* 175 to 176 labelled a_1(0)* 176 to 177 labelled b_1(0)* 177 to 178 labelled b_1(0)* 178 to 179 labelled a_1(0)* 179 to 180 labelled a_1(0)* 180 to 181 labelled b_1(0)* 180 to 184 labelled a_1(1)* 181 to 182 labelled a_1(0)* 182 to 183 labelled a_1(0)* 183 to 174 labelled b_1(0)* 183 to 184 labelled a_1(1)* 184 to 185 labelled a_1(1)* 185 to 186 labelled b_1(1)* 186 to 187 labelled b_1(1)* 187 to 188 labelled a_1(1)* 188 to 189 labelled a_1(1)* 189 to 190 labelled b_1(1)* 189 to 184 labelled a_1(1)* 190 to 191 labelled a_1(1)* 191 to 192 labelled a_1(1)* 192 to 174 labelled b_1(1)* 192 to 184 labelled a_1(1)


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(4)
YES