/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 4 ms]
(6) YES


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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
327, 328, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389

Node 327 is start node and node 328 is final node.

Those nodes are connected through the following edges:

* 327 to 342 labelled c_1(0)* 328 to 328 labelled #_1(0)* 342 to 343 labelled c_1(0)* 343 to 344 labelled b_1(0)* 344 to 345 labelled a_1(0)* 345 to 346 labelled a_1(0)* 346 to 347 labelled c_1(0)* 347 to 348 labelled c_1(0)* 348 to 349 labelled b_1(0)* 349 to 350 labelled a_1(0)* 349 to 378 labelled c_1(1)* 350 to 351 labelled a_1(0)* 350 to 378 labelled c_1(1)* 351 to 352 labelled a_1(0)* 351 to 378 labelled c_1(1)* 352 to 353 labelled a_1(0)* 352 to 378 labelled c_1(1)* 353 to 328 labelled a_1(0)* 353 to 378 labelled c_1(1)* 378 to 379 labelled c_1(1)* 379 to 380 labelled b_1(1)* 380 to 381 labelled a_1(1)* 381 to 382 labelled a_1(1)* 382 to 383 labelled c_1(1)* 383 to 384 labelled c_1(1)* 384 to 385 labelled b_1(1)* 385 to 386 labelled a_1(1)* 385 to 378 labelled c_1(1)* 386 to 387 labelled a_1(1)* 386 to 378 labelled c_1(1)* 387 to 388 labelled a_1(1)* 387 to 378 labelled c_1(1)* 388 to 389 labelled a_1(1)* 388 to 378 labelled c_1(1)* 389 to 328 labelled a_1(1)* 389 to 378 labelled c_1(1)


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(6)
YES