/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
(4) YES


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

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

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

Q is empty.

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(3) 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:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 4, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34

Node 3 is start node and node 4 is final node.

Those nodes are connected through the following edges:

* 3 to 23 labelled a_1(0)* 4 to 4 labelled #_1(0)* 23 to 24 labelled b_1(0)* 24 to 25 labelled b_1(0)* 24 to 29 labelled a_1(1)* 25 to 26 labelled b_1(0)* 26 to 27 labelled a_1(0)* 27 to 28 labelled b_1(0)* 28 to 4 labelled a_1(0)* 29 to 30 labelled b_1(1)* 30 to 31 labelled b_1(1)* 30 to 29 labelled a_1(1)* 31 to 32 labelled b_1(1)* 32 to 33 labelled a_1(1)* 33 to 34 labelled b_1(1)* 34 to 4 labelled a_1(1)


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(4)
YES