/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) 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(b(a(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(a(b(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(a(b(b(a(x1)))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52

Node 39 is start node and node 40 is final node.

Those nodes are connected through the following edges:

* 39 to 41 labelled a_1(0)* 40 to 40 labelled #_1(0)* 41 to 42 labelled b_1(0)* 42 to 43 labelled b_1(0)* 43 to 44 labelled a_1(0)* 44 to 45 labelled b_1(0)* 44 to 47 labelled a_1(1)* 45 to 46 labelled b_1(0)* 46 to 40 labelled a_1(0)* 47 to 48 labelled b_1(1)* 48 to 49 labelled b_1(1)* 49 to 50 labelled a_1(1)* 50 to 51 labelled b_1(1)* 50 to 47 labelled a_1(1)* 51 to 52 labelled b_1(1)* 52 to 40 labelled a_1(1)


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(4)
YES