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


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YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
344, 345, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538

Node 344 is start node and node 345 is final node.

Those nodes are connected through the following edges:

* 344 to 502 labelled b_1(0)* 345 to 345 labelled #_1(0)* 502 to 503 labelled c_1(0)* 503 to 504 labelled b_1(0)* 504 to 505 labelled a_1(0)* 505 to 506 labelled a_1(0)* 506 to 507 labelled a_1(0)* 507 to 508 labelled b_1(0)* 508 to 509 labelled c_1(0)* 509 to 510 labelled b_1(0)* 510 to 511 labelled a_1(0)* 510 to 527 labelled b_1(1)* 511 to 525 labelled a_1(0)* 511 to 527 labelled b_1(1)* 525 to 526 labelled a_1(0)* 525 to 527 labelled b_1(1)* 526 to 345 labelled a_1(0)* 526 to 527 labelled b_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 a_1(1)* 532 to 533 labelled b_1(1)* 533 to 534 labelled c_1(1)* 534 to 535 labelled b_1(1)* 535 to 536 labelled a_1(1)* 535 to 527 labelled b_1(1)* 536 to 537 labelled a_1(1)* 536 to 527 labelled b_1(1)* 537 to 538 labelled a_1(1)* 537 to 527 labelled b_1(1)* 538 to 345 labelled a_1(1)* 538 to 527 labelled b_1(1)


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(6)
YES