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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(b(a(a(a(a(a(x1)))))))) -> a(a(a(a(a(a(b(b(a(b(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(a(b(b(a(x1)))))))) -> b(b(a(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(b(b(a(x1)))))))) -> b(b(a(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(b(b(x))))))) -> b(b(a(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(b(b(x))))))) -> b(b(a(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(b(b(x))))))) -> b(b(a(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:
349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368

Node 349 is start node and node 350 is final node.

Those nodes are connected through the following edges:

* 349 to 351 labelled b_1(0)* 350 to 350 labelled #_1(0)* 351 to 352 labelled b_1(0)* 352 to 353 labelled a_1(0)* 353 to 354 labelled b_1(0)* 354 to 355 labelled b_1(0)* 355 to 356 labelled a_1(0)* 355 to 360 labelled b_1(1)* 356 to 357 labelled a_1(0)* 356 to 360 labelled b_1(1)* 357 to 358 labelled a_1(0)* 357 to 360 labelled b_1(1)* 358 to 359 labelled a_1(0)* 358 to 360 labelled b_1(1)* 359 to 350 labelled a_1(0)* 359 to 360 labelled b_1(1)* 360 to 361 labelled b_1(1)* 361 to 362 labelled a_1(1)* 362 to 363 labelled b_1(1)* 363 to 364 labelled b_1(1)* 364 to 365 labelled a_1(1)* 364 to 360 labelled b_1(1)* 365 to 366 labelled a_1(1)* 365 to 360 labelled b_1(1)* 366 to 367 labelled a_1(1)* 366 to 360 labelled b_1(1)* 367 to 368 labelled a_1(1)* 367 to 360 labelled b_1(1)* 368 to 350 labelled a_1(1)* 368 to 360 labelled b_1(1)


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(6)
YES