/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

(0) QTRS
(1) QTRS Reverse [EQUIVALENT, 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(a(x1))))) -> a(a(b(b(a(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(b(a(a(b(x1))))) -> b(a(a(b(b(a(a(x1)))))))

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 2. This implies Q-termination of R.
The following rules were used to construct the certificate:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
171, 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

Node 171 is start node and node 172 is final node.

Those nodes are connected through the following edges:

* 171 to 173 labelled b_1(0)* 172 to 172 labelled #_1(0)* 173 to 174 labelled a_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)* 177 to 185 labelled b_1(1)* 178 to 172 labelled a_1(0)* 178 to 179 labelled b_1(1)* 179 to 180 labelled a_1(1)* 180 to 181 labelled a_1(1)* 181 to 182 labelled b_1(1)* 182 to 183 labelled b_1(1)* 183 to 184 labelled a_1(1)* 183 to 191 labelled b_1(2)* 184 to 172 labelled a_1(1)* 184 to 179 labelled b_1(1)* 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)* 189 to 191 labelled b_1(2)* 190 to 182 labelled a_1(1)* 190 to 179 labelled b_1(1)* 191 to 192 labelled a_1(2)* 192 to 193 labelled a_1(2)* 193 to 194 labelled b_1(2)* 194 to 195 labelled b_1(2)* 195 to 196 labelled a_1(2)* 195 to 191 labelled b_1(2)* 196 to 182 labelled a_1(2)* 196 to 179 labelled b_1(1)


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(4)
YES