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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472

Node 447 is start node and node 448 is final node.

Those nodes are connected through the following edges:

* 447 to 449 labelled b_1(0)* 448 to 448 labelled #_1(0)* 449 to 450 labelled b_1(0)* 450 to 451 labelled a_1(0)* 451 to 452 labelled a_1(0)* 452 to 453 labelled b_1(0)* 453 to 454 labelled b_1(0)* 454 to 455 labelled a_1(0)* 455 to 456 labelled b_1(0)* 456 to 457 labelled b_1(0)* 457 to 458 labelled a_1(0)* 457 to 461 labelled b_1(1)* 458 to 459 labelled a_1(0)* 458 to 461 labelled b_1(1)* 459 to 460 labelled a_1(0)* 459 to 461 labelled b_1(1)* 460 to 448 labelled a_1(0)* 460 to 461 labelled b_1(1)* 461 to 462 labelled b_1(1)* 462 to 463 labelled a_1(1)* 463 to 464 labelled a_1(1)* 464 to 465 labelled b_1(1)* 465 to 466 labelled b_1(1)* 466 to 467 labelled a_1(1)* 467 to 468 labelled b_1(1)* 468 to 469 labelled b_1(1)* 469 to 470 labelled a_1(1)* 469 to 461 labelled b_1(1)* 470 to 471 labelled a_1(1)* 470 to 461 labelled b_1(1)* 471 to 472 labelled a_1(1)* 471 to 461 labelled b_1(1)* 472 to 448 labelled a_1(1)* 472 to 461 labelled b_1(1)


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(6)
YES