/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(a(a(a(a(a(a(x1)))))))) -> a(a(a(a(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(a(a(a(a(b(a(x1)))))))) -> b(a(a(a(a(a(b(a(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(a(b(a(x1)))))))) -> b(a(a(a(a(a(b(a(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(a(b(x))))))) -> b(a(a(a(a(a(b(a(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(a(b(x))))))) -> b(a(a(a(a(a(b(a(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(a(b(x))))))) -> b(a(a(a(a(a(b(a(a(a(a(a(a(x)))))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 4, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374

Node 3 is start node and node 4 is final node.

Those nodes are connected through the following edges:

* 3 to 339 labelled b_1(0)* 4 to 4 labelled #_1(0)* 339 to 340 labelled a_1(0)* 340 to 341 labelled a_1(0)* 341 to 342 labelled a_1(0)* 342 to 343 labelled a_1(0)* 343 to 344 labelled a_1(0)* 344 to 345 labelled b_1(0)* 345 to 346 labelled a_1(0)* 345 to 363 labelled b_1(1)* 346 to 347 labelled a_1(0)* 346 to 363 labelled b_1(1)* 347 to 348 labelled a_1(0)* 347 to 363 labelled b_1(1)* 348 to 349 labelled a_1(0)* 348 to 363 labelled b_1(1)* 349 to 350 labelled a_1(0)* 349 to 363 labelled b_1(1)* 350 to 4 labelled a_1(0)* 350 to 363 labelled b_1(1)* 363 to 364 labelled a_1(1)* 364 to 365 labelled a_1(1)* 365 to 366 labelled a_1(1)* 366 to 367 labelled a_1(1)* 367 to 368 labelled a_1(1)* 368 to 369 labelled b_1(1)* 369 to 370 labelled a_1(1)* 369 to 363 labelled b_1(1)* 370 to 371 labelled a_1(1)* 370 to 363 labelled b_1(1)* 371 to 372 labelled a_1(1)* 371 to 363 labelled b_1(1)* 372 to 373 labelled a_1(1)* 372 to 363 labelled b_1(1)* 373 to 374 labelled a_1(1)* 373 to 363 labelled b_1(1)* 374 to 4 labelled a_1(1)* 374 to 363 labelled b_1(1)


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(6)
YES