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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(b(a(a(a(a(x1))))))))) -> a(a(a(a(a(b(a(a(b(a(b(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(b(a(x1))))))))) -> b(a(a(b(a(b(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(b(a(x1))))))))) -> b(a(a(b(a(b(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(b(x)))))))) -> b(a(a(b(a(b(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(b(x)))))))) -> b(a(a(b(a(b(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(b(x)))))))) -> b(a(a(b(a(b(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:
526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551

Node 526 is start node and node 527 is final node.

Those nodes are connected through the following edges:

* 526 to 528 labelled b_1(0)* 527 to 527 labelled #_1(0)* 528 to 529 labelled a_1(0)* 529 to 530 labelled a_1(0)* 530 to 531 labelled b_1(0)* 531 to 532 labelled a_1(0)* 532 to 533 labelled b_1(0)* 533 to 534 labelled a_1(0)* 534 to 535 labelled a_1(0)* 535 to 536 labelled b_1(0)* 536 to 537 labelled a_1(0)* 536 to 540 labelled b_1(1)* 537 to 538 labelled a_1(0)* 537 to 540 labelled b_1(1)* 538 to 539 labelled a_1(0)* 538 to 540 labelled b_1(1)* 539 to 527 labelled a_1(0)* 539 to 540 labelled b_1(1)* 540 to 541 labelled a_1(1)* 541 to 542 labelled a_1(1)* 542 to 543 labelled b_1(1)* 543 to 544 labelled a_1(1)* 544 to 545 labelled b_1(1)* 545 to 546 labelled a_1(1)* 546 to 547 labelled a_1(1)* 547 to 548 labelled b_1(1)* 548 to 549 labelled a_1(1)* 548 to 540 labelled b_1(1)* 549 to 550 labelled a_1(1)* 549 to 540 labelled b_1(1)* 550 to 551 labelled a_1(1)* 550 to 540 labelled b_1(1)* 551 to 527 labelled a_1(1)* 551 to 540 labelled b_1(1)


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(6)
YES