/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1 ms]
(4) YES


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

   b(a(a(a(b(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(b(a(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 0. This implies Q-termination of R.
The following rules were used to construct the certificate:

   b(b(a(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:
15, 16, 17, 18, 19, 20, 21, 22

Node 15 is start node and node 16 is final node.

Those nodes are connected through the following edges:

* 15 to 17 labelled a_1(0)* 16 to 16 labelled #_1(0)* 17 to 18 labelled b_1(0)* 18 to 19 labelled b_1(0)* 19 to 20 labelled a_1(0)* 20 to 21 labelled a_1(0)* 21 to 22 labelled b_1(0)* 22 to 16 labelled a_1(0)


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(4)
YES