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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

Q is empty.

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
149, 150, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184

Node 149 is start node and node 150 is final node.

Those nodes are connected through the following edges:

* 149 to 163 labelled a_1(0)* 150 to 150 labelled #_1(0)* 163 to 164 labelled a_1(0)* 164 to 165 labelled b_1(0)* 165 to 166 labelled a_1(0)* 166 to 167 labelled a_1(0)* 167 to 168 labelled a_1(0)* 168 to 169 labelled b_1(0)* 168 to 174 labelled a_1(1)* 169 to 170 labelled a_1(0)* 170 to 171 labelled b_1(0)* 170 to 174 labelled a_1(1)* 171 to 172 labelled a_1(0)* 172 to 173 labelled b_1(0)* 172 to 174 labelled a_1(1)* 173 to 150 labelled a_1(0)* 174 to 175 labelled a_1(1)* 175 to 176 labelled b_1(1)* 176 to 177 labelled a_1(1)* 177 to 178 labelled a_1(1)* 178 to 179 labelled a_1(1)* 179 to 180 labelled b_1(1)* 179 to 174 labelled a_1(1)* 180 to 181 labelled a_1(1)* 181 to 182 labelled b_1(1)* 181 to 174 labelled a_1(1)* 182 to 183 labelled a_1(1)* 183 to 184 labelled b_1(1)* 183 to 174 labelled a_1(1)* 184 to 150 labelled a_1(1)


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(4)
YES