/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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) RFCMatchBoundsTRSProof [EQUIVALENT, 16 ms]
(2) YES


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

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

Q is empty.

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 8, 9, 12, 13

Node 1 is start node and node 2 is final node.

Those nodes are connected through the following edges:

* 1 to 8 labelled a_1(0)* 2 to 2 labelled #_1(0)* 8 to 9 labelled b_1(0)* 9 to 2 labelled a_1(0)* 9 to 12 labelled a_1(1)* 12 to 13 labelled b_1(1)* 13 to 2 labelled a_1(1)* 13 to 12 labelled a_1(1)


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(2)
YES