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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

Q is empty.

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(3) Strip Symbols Proof (SOUND)
We were given the following TRS:

   a(a(b(a(a(a(a(b(a(x1))))))))) -> b(a(a(a(a(b(a(a(b(a(a(a(x1))))))))))))

By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 

   a(a(b(a(a(a(a(b(x)))))))) -> b(a(a(a(a(b(a(a(b(a(a(x)))))))))))

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(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(a(b(a(a(a(a(b(x)))))))) -> b(a(a(a(a(b(a(a(b(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(b(a(a(a(a(b(x)))))))) -> b(a(a(a(a(b(a(a(b(a(a(x)))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
359, 360, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383

Node 359 is start node and node 360 is final node.

Those nodes are connected through the following edges:

* 359 to 364 labelled b_1(0)* 360 to 360 labelled #_1(0)* 364 to 365 labelled a_1(0)* 365 to 366 labelled a_1(0)* 366 to 367 labelled a_1(0)* 367 to 368 labelled a_1(0)* 368 to 369 labelled b_1(0)* 369 to 370 labelled a_1(0)* 369 to 374 labelled b_1(1)* 370 to 371 labelled a_1(0)* 371 to 372 labelled b_1(0)* 372 to 373 labelled a_1(0)* 372 to 374 labelled b_1(1)* 373 to 360 labelled a_1(0)* 373 to 374 labelled b_1(1)* 374 to 375 labelled a_1(1)* 375 to 376 labelled a_1(1)* 376 to 377 labelled a_1(1)* 377 to 378 labelled a_1(1)* 378 to 379 labelled b_1(1)* 379 to 380 labelled a_1(1)* 379 to 374 labelled b_1(1)* 380 to 381 labelled a_1(1)* 381 to 382 labelled b_1(1)* 382 to 383 labelled a_1(1)* 382 to 374 labelled b_1(1)* 383 to 360 labelled a_1(1)* 383 to 374 labelled b_1(1)


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(6)
YES