YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(a(b(b(a(a(b(x1)))))))) -> a(a(b(b(a(a(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(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(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(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(a(a(b(x)))))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197

Node 172 is start node and node 173 is final node.

Those nodes are connected through the following edges:

* 172 to 174 labelled a_1(0)* 173 to 173 labelled #_1(0)* 174 to 175 labelled a_1(0)* 175 to 176 labelled b_1(0)* 176 to 177 labelled b_1(0)* 177 to 178 labelled a_1(0)* 178 to 179 labelled a_1(0)* 179 to 180 labelled b_1(0)* 180 to 181 labelled a_1(0)* 181 to 182 labelled a_1(0)* 182 to 183 labelled b_1(0)* 182 to 186 labelled a_1(1)* 183 to 184 labelled a_1(0)* 184 to 185 labelled a_1(0)* 185 to 173 labelled b_1(0)* 185 to 186 labelled a_1(1)* 186 to 187 labelled a_1(1)* 187 to 188 labelled b_1(1)* 188 to 189 labelled b_1(1)* 189 to 190 labelled a_1(1)* 190 to 191 labelled a_1(1)* 191 to 192 labelled b_1(1)* 192 to 193 labelled a_1(1)* 193 to 194 labelled a_1(1)* 194 to 195 labelled b_1(1)* 194 to 186 labelled a_1(1)* 195 to 196 labelled a_1(1)* 196 to 197 labelled a_1(1)* 197 to 173 labelled b_1(1)* 197 to 186 labelled a_1(1)


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(4)
YES