/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 2 ms]
(6) YES


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(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
330, 331, 332, 333, 334, 335, 336, 337, 338, 570, 571, 572, 573, 574, 575, 576

Node 330 is start node and node 331 is final node.

Those nodes are connected through the following edges:

* 330 to 332 labelled b_1(0)* 331 to 331 labelled #_1(0)* 332 to 333 labelled a_1(0)* 333 to 334 labelled b_1(0)* 334 to 335 labelled a_1(0)* 335 to 336 labelled b_1(0)* 336 to 337 labelled a_1(0)* 336 to 570 labelled b_1(1)* 337 to 338 labelled a_1(0)* 337 to 570 labelled b_1(1)* 338 to 331 labelled a_1(0)* 338 to 570 labelled b_1(1)* 570 to 571 labelled a_1(1)* 571 to 572 labelled b_1(1)* 572 to 573 labelled a_1(1)* 573 to 574 labelled b_1(1)* 574 to 575 labelled a_1(1)* 574 to 570 labelled b_1(1)* 575 to 576 labelled a_1(1)* 575 to 570 labelled b_1(1)* 576 to 331 labelled a_1(1)* 576 to 570 labelled b_1(1)


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(6)
YES