/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) Strip Symbols Proof [SOUND, 0 ms]
(4) QTRS
(5) RFCMatchBoundsTRSProof [EQUIVALENT, 0 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(a(a(a(b(a(a(x1)))))))))) -> a(a(a(b(a(a(a(b(a(a(a(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(a(b(a(a(a(a(a(b(a(x1)))))))))) -> b(a(a(a(a(a(b(a(a(a(b(a(a(a(x1))))))))))))))

Q is empty.

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
150, 151, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318

Node 150 is start node and node 151 is final node.

Those nodes are connected through the following edges:

* 150 to 178 labelled b_1(0)* 151 to 151 labelled #_1(0)* 178 to 179 labelled a_1(0)* 179 to 180 labelled a_1(0)* 180 to 181 labelled a_1(0)* 181 to 182 labelled a_1(0)* 182 to 183 labelled a_1(0)* 183 to 184 labelled b_1(0)* 184 to 185 labelled a_1(0)* 185 to 186 labelled a_1(0)* 185 to 307 labelled b_1(1)* 186 to 187 labelled a_1(0)* 187 to 188 labelled b_1(0)* 188 to 189 labelled a_1(0)* 188 to 307 labelled b_1(1)* 189 to 151 labelled a_1(0)* 189 to 307 labelled b_1(1)* 307 to 308 labelled a_1(1)* 308 to 309 labelled a_1(1)* 309 to 310 labelled a_1(1)* 310 to 311 labelled a_1(1)* 311 to 312 labelled a_1(1)* 312 to 313 labelled b_1(1)* 313 to 314 labelled a_1(1)* 314 to 315 labelled a_1(1)* 314 to 307 labelled b_1(1)* 315 to 316 labelled a_1(1)* 316 to 317 labelled b_1(1)* 317 to 318 labelled a_1(1)* 317 to 307 labelled b_1(1)* 318 to 151 labelled a_1(1)* 318 to 307 labelled b_1(1)


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(6)
YES