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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

Q is empty.

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676

Node 651 is start node and node 652 is final node.

Those nodes are connected through the following edges:

* 651 to 653 labelled c_1(0)* 652 to 652 labelled #_1(0)* 653 to 654 labelled a_1(0)* 654 to 655 labelled b_1(0)* 655 to 656 labelled a_1(0)* 656 to 657 labelled a_1(0)* 657 to 658 labelled c_1(0)* 658 to 659 labelled a_1(0)* 659 to 660 labelled b_1(0)* 660 to 661 labelled a_1(0)* 660 to 665 labelled c_1(1)* 661 to 662 labelled c_1(0)* 662 to 663 labelled a_1(0)* 663 to 664 labelled b_1(0)* 664 to 652 labelled a_1(0)* 664 to 665 labelled c_1(1)* 665 to 666 labelled a_1(1)* 666 to 667 labelled b_1(1)* 667 to 668 labelled a_1(1)* 668 to 669 labelled a_1(1)* 669 to 670 labelled c_1(1)* 670 to 671 labelled a_1(1)* 671 to 672 labelled b_1(1)* 672 to 673 labelled a_1(1)* 672 to 665 labelled c_1(1)* 673 to 674 labelled c_1(1)* 674 to 675 labelled a_1(1)* 675 to 676 labelled b_1(1)* 676 to 652 labelled a_1(1)* 676 to 665 labelled c_1(1)


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(6)
YES