/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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, 2 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(x1)))))) -> a(a(a(a(a(b(a(b(a(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(a(a(a(b(a(x1)))))) -> b(a(a(b(a(a(b(a(b(a(a(a(a(a(x1))))))))))))))

Q is empty.

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
33, 34, 251, 255, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290

Node 33 is start node and node 34 is final node.

Those nodes are connected through the following edges:

* 33 to 251 labelled b_1(0)* 34 to 34 labelled #_1(0)* 251 to 255 labelled a_1(0)* 255 to 257 labelled a_1(0)* 257 to 258 labelled b_1(0)* 258 to 259 labelled a_1(0)* 259 to 260 labelled a_1(0)* 260 to 261 labelled b_1(0)* 261 to 262 labelled a_1(0)* 262 to 263 labelled b_1(0)* 263 to 264 labelled a_1(0)* 263 to 279 labelled b_1(1)* 264 to 265 labelled a_1(0)* 264 to 279 labelled b_1(1)* 265 to 266 labelled a_1(0)* 265 to 279 labelled b_1(1)* 266 to 34 labelled a_1(0)* 266 to 279 labelled b_1(1)* 279 to 280 labelled a_1(1)* 280 to 281 labelled a_1(1)* 281 to 282 labelled b_1(1)* 282 to 283 labelled a_1(1)* 283 to 284 labelled a_1(1)* 284 to 285 labelled b_1(1)* 285 to 286 labelled a_1(1)* 286 to 287 labelled b_1(1)* 287 to 288 labelled a_1(1)* 287 to 279 labelled b_1(1)* 288 to 289 labelled a_1(1)* 288 to 279 labelled b_1(1)* 289 to 290 labelled a_1(1)* 289 to 279 labelled b_1(1)* 290 to 34 labelled a_1(1)* 290 to 279 labelled b_1(1)


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(6)
YES