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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(b(a(a(a(a(x1)))))))))) -> a(a(a(a(a(b(a(a(a(b(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(b(a(a(a(b(a(x1)))))))))) -> b(a(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(a(a(b(a(x1)))))))))) -> b(a(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(a(a(a(b(x))))))))) -> b(a(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(a(a(a(b(x))))))))) -> b(a(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(a(a(a(b(x))))))))) -> b(a(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:
419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 442, 444, 446, 448

Node 419 is start node and node 420 is final node.

Those nodes are connected through the following edges:

* 419 to 421 labelled b_1(0)* 420 to 420 labelled #_1(0)* 421 to 422 labelled a_1(0)* 422 to 423 labelled a_1(0)* 423 to 424 labelled a_1(0)* 424 to 425 labelled b_1(0)* 425 to 426 labelled a_1(0)* 426 to 427 labelled a_1(0)* 427 to 428 labelled a_1(0)* 428 to 429 labelled b_1(0)* 429 to 430 labelled a_1(0)* 429 to 433 labelled b_1(1)* 430 to 431 labelled a_1(0)* 430 to 433 labelled b_1(1)* 431 to 432 labelled a_1(0)* 431 to 433 labelled b_1(1)* 432 to 420 labelled a_1(0)* 432 to 433 labelled b_1(1)* 433 to 434 labelled a_1(1)* 434 to 435 labelled a_1(1)* 435 to 436 labelled a_1(1)* 436 to 437 labelled b_1(1)* 437 to 438 labelled a_1(1)* 438 to 439 labelled a_1(1)* 439 to 440 labelled a_1(1)* 440 to 442 labelled b_1(1)* 442 to 444 labelled a_1(1)* 442 to 433 labelled b_1(1)* 444 to 446 labelled a_1(1)* 444 to 433 labelled b_1(1)* 446 to 448 labelled a_1(1)* 446 to 433 labelled b_1(1)* 448 to 420 labelled a_1(1)* 448 to 433 labelled b_1(1)


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(6)
YES