/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(b(a(a(b(c(b(a(x1)))))))))) -> a(a(b(c(b(a(b(c(b(a(a(b(c(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(b(c(b(a(a(b(c(b(a(x1)))))))))) -> b(c(b(a(a(b(c(b(a(b(c(b(a(a(x1))))))))))))))

Q is empty.

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
586, 587, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624

Node 586 is start node and node 587 is final node.

Those nodes are connected through the following edges:

* 586 to 601 labelled b_1(0)* 587 to 587 labelled #_1(0)* 601 to 602 labelled c_1(0)* 602 to 603 labelled b_1(0)* 603 to 604 labelled a_1(0)* 604 to 605 labelled a_1(0)* 605 to 606 labelled b_1(0)* 606 to 607 labelled c_1(0)* 607 to 608 labelled b_1(0)* 608 to 609 labelled a_1(0)* 608 to 613 labelled b_1(1)* 609 to 610 labelled b_1(0)* 610 to 611 labelled c_1(0)* 611 to 612 labelled b_1(0)* 612 to 587 labelled a_1(0)* 612 to 613 labelled b_1(1)* 613 to 614 labelled c_1(1)* 614 to 615 labelled b_1(1)* 615 to 616 labelled a_1(1)* 616 to 617 labelled a_1(1)* 617 to 618 labelled b_1(1)* 618 to 619 labelled c_1(1)* 619 to 620 labelled b_1(1)* 620 to 621 labelled a_1(1)* 620 to 613 labelled b_1(1)* 621 to 622 labelled b_1(1)* 622 to 623 labelled c_1(1)* 623 to 624 labelled b_1(1)* 624 to 587 labelled a_1(1)* 624 to 613 labelled b_1(1)


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(6)
YES