/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(x1)))))) -> a(a(a(a(a(b(a(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(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(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(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(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(a(b(a(a(a(a(x))))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
308, 309, 315, 317, 319, 321, 323, 325, 327, 328, 329, 330, 331, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353

Node 308 is start node and node 309 is final node.

Those nodes are connected through the following edges:

* 308 to 315 labelled b_1(0)* 309 to 309 labelled #_1(0)* 315 to 317 labelled a_1(0)* 317 to 319 labelled a_1(0)* 319 to 321 labelled b_1(0)* 321 to 323 labelled a_1(0)* 323 to 325 labelled a_1(0)* 325 to 327 labelled a_1(0)* 327 to 328 labelled b_1(0)* 328 to 329 labelled a_1(0)* 328 to 343 labelled b_1(1)* 329 to 330 labelled a_1(0)* 329 to 343 labelled b_1(1)* 330 to 331 labelled a_1(0)* 330 to 343 labelled b_1(1)* 331 to 309 labelled a_1(0)* 331 to 343 labelled b_1(1)* 343 to 344 labelled a_1(1)* 344 to 345 labelled a_1(1)* 345 to 346 labelled b_1(1)* 346 to 347 labelled a_1(1)* 347 to 348 labelled a_1(1)* 348 to 349 labelled a_1(1)* 349 to 350 labelled b_1(1)* 350 to 351 labelled a_1(1)* 350 to 343 labelled b_1(1)* 351 to 352 labelled a_1(1)* 351 to 343 labelled b_1(1)* 352 to 353 labelled a_1(1)* 352 to 343 labelled b_1(1)* 353 to 309 labelled a_1(1)* 353 to 343 labelled b_1(1)


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(6)
YES