/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 0 ms]
(6) YES


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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
135, 136, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 332, 333, 334, 335, 336, 337, 338, 339, 340, 341, 342

Node 135 is start node and node 136 is final node.

Those nodes are connected through the following edges:

* 135 to 275 labelled b_1(0)* 136 to 136 labelled #_1(0)* 275 to 276 labelled b_1(0)* 276 to 277 labelled a_1(0)* 277 to 278 labelled a_1(0)* 278 to 279 labelled a_1(0)* 279 to 280 labelled b_1(0)* 280 to 281 labelled b_1(0)* 281 to 282 labelled a_1(0)* 281 to 332 labelled b_1(1)* 282 to 283 labelled a_1(0)* 282 to 332 labelled b_1(1)* 283 to 284 labelled a_1(0)* 283 to 332 labelled b_1(1)* 284 to 285 labelled a_1(0)* 284 to 332 labelled b_1(1)* 285 to 136 labelled a_1(0)* 285 to 332 labelled b_1(1)* 332 to 333 labelled b_1(1)* 333 to 334 labelled a_1(1)* 334 to 335 labelled a_1(1)* 335 to 336 labelled a_1(1)* 336 to 337 labelled b_1(1)* 337 to 338 labelled b_1(1)* 338 to 339 labelled a_1(1)* 338 to 332 labelled b_1(1)* 339 to 340 labelled a_1(1)* 339 to 332 labelled b_1(1)* 340 to 341 labelled a_1(1)* 340 to 332 labelled b_1(1)* 341 to 342 labelled a_1(1)* 341 to 332 labelled b_1(1)* 342 to 136 labelled a_1(1)* 342 to 332 labelled b_1(1)


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(6)
YES