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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538

Node 513 is start node and node 514 is final node.

Those nodes are connected through the following edges:

* 513 to 515 labelled c_1(0)* 514 to 514 labelled #_1(0)* 515 to 516 labelled c_1(0)* 516 to 517 labelled b_1(0)* 517 to 518 labelled a_1(0)* 518 to 519 labelled a_1(0)* 519 to 520 labelled c_1(0)* 520 to 521 labelled c_1(0)* 521 to 522 labelled b_1(0)* 522 to 523 labelled a_1(0)* 522 to 527 labelled c_1(1)* 523 to 524 labelled a_1(0)* 523 to 527 labelled c_1(1)* 524 to 525 labelled a_1(0)* 524 to 527 labelled c_1(1)* 525 to 526 labelled a_1(0)* 525 to 527 labelled c_1(1)* 526 to 514 labelled a_1(0)* 526 to 527 labelled c_1(1)* 527 to 528 labelled c_1(1)* 528 to 529 labelled b_1(1)* 529 to 530 labelled a_1(1)* 530 to 531 labelled a_1(1)* 531 to 532 labelled c_1(1)* 532 to 533 labelled c_1(1)* 533 to 534 labelled b_1(1)* 534 to 535 labelled a_1(1)* 534 to 527 labelled c_1(1)* 535 to 536 labelled a_1(1)* 535 to 527 labelled c_1(1)* 536 to 537 labelled a_1(1)* 536 to 527 labelled c_1(1)* 537 to 538 labelled a_1(1)* 537 to 527 labelled c_1(1)* 538 to 514 labelled a_1(1)* 538 to 527 labelled c_1(1)


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(6)
YES