/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1 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(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(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(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(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(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(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:
235, 236, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 374, 377, 379, 381, 382, 384, 386, 388, 390, 392, 393

Node 235 is start node and node 236 is final node.

Those nodes are connected through the following edges:

* 235 to 361 labelled c_1(0)* 236 to 236 labelled #_1(0)* 361 to 362 labelled c_1(0)* 362 to 363 labelled b_1(0)* 363 to 364 labelled a_1(0)* 364 to 365 labelled c_1(0)* 365 to 366 labelled c_1(0)* 366 to 367 labelled b_1(0)* 367 to 368 labelled a_1(0)* 367 to 374 labelled c_1(1)* 368 to 369 labelled a_1(0)* 368 to 374 labelled c_1(1)* 369 to 370 labelled a_1(0)* 369 to 374 labelled c_1(1)* 370 to 371 labelled a_1(0)* 370 to 374 labelled c_1(1)* 371 to 236 labelled a_1(0)* 371 to 374 labelled c_1(1)* 374 to 377 labelled c_1(1)* 377 to 379 labelled b_1(1)* 379 to 381 labelled a_1(1)* 381 to 382 labelled c_1(1)* 382 to 384 labelled c_1(1)* 384 to 386 labelled b_1(1)* 386 to 388 labelled a_1(1)* 386 to 374 labelled c_1(1)* 388 to 390 labelled a_1(1)* 388 to 374 labelled c_1(1)* 390 to 392 labelled a_1(1)* 390 to 374 labelled c_1(1)* 392 to 393 labelled a_1(1)* 392 to 374 labelled c_1(1)* 393 to 236 labelled a_1(1)* 393 to 374 labelled c_1(1)


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(6)
YES