/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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, 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(c(a(a(a(a(a(x1))))))))) -> a(a(a(a(a(a(b(b(c(a(a(b(b(c(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(c(b(b(a(x1))))))))) -> c(b(b(a(a(c(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(c(b(b(a(x1))))))))) -> c(b(b(a(a(c(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(c(b(b(x)))))))) -> c(b(b(a(a(c(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(c(b(b(x)))))))) -> c(b(b(a(a(c(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(c(b(b(x)))))))) -> c(b(b(a(a(c(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:
357, 358, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395

Node 357 is start node and node 358 is final node.

Those nodes are connected through the following edges:

* 357 to 372 labelled c_1(0)* 358 to 358 labelled #_1(0)* 372 to 373 labelled b_1(0)* 373 to 374 labelled b_1(0)* 374 to 375 labelled a_1(0)* 375 to 376 labelled a_1(0)* 376 to 377 labelled c_1(0)* 377 to 378 labelled b_1(0)* 378 to 379 labelled b_1(0)* 379 to 380 labelled a_1(0)* 379 to 384 labelled c_1(1)* 380 to 381 labelled a_1(0)* 380 to 384 labelled c_1(1)* 381 to 382 labelled a_1(0)* 381 to 384 labelled c_1(1)* 382 to 383 labelled a_1(0)* 382 to 384 labelled c_1(1)* 383 to 358 labelled a_1(0)* 383 to 384 labelled c_1(1)* 384 to 385 labelled b_1(1)* 385 to 386 labelled b_1(1)* 386 to 387 labelled a_1(1)* 387 to 388 labelled a_1(1)* 388 to 389 labelled c_1(1)* 389 to 390 labelled b_1(1)* 390 to 391 labelled b_1(1)* 391 to 392 labelled a_1(1)* 391 to 384 labelled c_1(1)* 392 to 393 labelled a_1(1)* 392 to 384 labelled c_1(1)* 393 to 394 labelled a_1(1)* 393 to 384 labelled c_1(1)* 394 to 395 labelled a_1(1)* 394 to 384 labelled c_1(1)* 395 to 358 labelled a_1(1)* 395 to 384 labelled c_1(1)


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(6)
YES