/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) 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(a(b(a(b(x1)))))) -> a(b(a(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(a(b(a(a(b(x1)))))) -> a(b(b(a(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(a(b(a(a(b(x1)))))) -> a(b(b(a(a(b(a(x1)))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 3, 5, 6, 7, 8, 9, 10, 17, 18, 19, 20, 21, 22

Node 1 is start node and node 3 is final node.

Those nodes are connected through the following edges:

* 1 to 5 labelled a_1(0)* 3 to 3 labelled #_1(0)* 5 to 6 labelled b_1(0)* 6 to 7 labelled b_1(0)* 7 to 8 labelled a_1(0)* 8 to 9 labelled a_1(0)* 9 to 10 labelled b_1(0)* 9 to 17 labelled a_1(1)* 10 to 3 labelled a_1(0)* 17 to 18 labelled b_1(1)* 18 to 19 labelled b_1(1)* 19 to 20 labelled a_1(1)* 20 to 21 labelled a_1(1)* 21 to 22 labelled b_1(1)* 21 to 17 labelled a_1(1)* 22 to 3 labelled a_1(1)


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(4)
YES