/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) Strip Symbols Proof [SOUND, 0 ms]
(4) QTRS
(5) RFCMatchBoundsTRSProof [EQUIVALENT, 1 ms]
(6) YES


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

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

Q is empty.

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

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

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

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

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(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(b(a(b(a(b(a(a(b(x))))))))) -> b(a(a(b(a(b(a(b(a(b(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(b(a(b(a(b(a(a(b(x))))))))) -> b(a(a(b(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:
158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201

Node 158 is start node and node 159 is final node.

Those nodes are connected through the following edges:

* 158 to 160 labelled b_1(0)* 159 to 159 labelled #_1(0)* 160 to 161 labelled a_1(0)* 161 to 162 labelled a_1(0)* 162 to 163 labelled b_1(0)* 163 to 164 labelled a_1(0)* 163 to 192 labelled b_1(1)* 164 to 165 labelled b_1(0)* 165 to 166 labelled a_1(0)* 165 to 192 labelled b_1(1)* 166 to 167 labelled b_1(0)* 167 to 168 labelled a_1(0)* 167 to 192 labelled b_1(1)* 168 to 169 labelled b_1(0)* 169 to 159 labelled a_1(0)* 169 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)* 195 to 196 labelled a_1(1)* 195 to 192 labelled b_1(1)* 196 to 197 labelled b_1(1)* 197 to 198 labelled a_1(1)* 197 to 192 labelled b_1(1)* 198 to 199 labelled b_1(1)* 199 to 200 labelled a_1(1)* 199 to 192 labelled b_1(1)* 200 to 201 labelled b_1(1)* 201 to 159 labelled a_1(1)* 201 to 192 labelled b_1(1)


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(6)
YES