/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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:

   a(a(b(b(a(b(x1)))))) -> a(b(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(b(a(a(x1)))))) -> a(b(b(a(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 2. This implies Q-termination of R.
The following rules were used to construct the certificate:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
17, 18, 21, 22, 23, 24, 25, 26, 27, 34, 35, 36, 37, 38, 39, 40, 54, 55, 56, 57, 58, 59, 60, 91, 92, 93, 94, 95, 96, 97

Node 17 is start node and node 18 is final node.

Those nodes are connected through the following edges:

* 17 to 21 labelled a_1(0)* 18 to 18 labelled #_1(0)* 21 to 22 labelled b_1(0)* 22 to 23 labelled b_1(0)* 23 to 24 labelled a_1(0)* 24 to 25 labelled a_1(0)* 25 to 26 labelled b_1(0)* 25 to 54 labelled a_1(1)* 26 to 27 labelled b_1(0)* 26 to 34 labelled a_1(1)* 27 to 18 labelled a_1(0)* 34 to 35 labelled b_1(1)* 35 to 36 labelled b_1(1)* 36 to 37 labelled a_1(1)* 37 to 38 labelled a_1(1)* 38 to 39 labelled b_1(1)* 38 to 91 labelled a_1(2)* 39 to 40 labelled b_1(1)* 39 to 34 labelled a_1(1)* 40 to 18 labelled a_1(1)* 54 to 55 labelled b_1(1)* 55 to 56 labelled b_1(1)* 56 to 57 labelled a_1(1)* 57 to 58 labelled a_1(1)* 58 to 59 labelled b_1(1)* 58 to 91 labelled a_1(2)* 59 to 60 labelled b_1(1)* 59 to 34 labelled a_1(1)* 60 to 38 labelled a_1(1)* 91 to 92 labelled b_1(2)* 92 to 93 labelled b_1(2)* 93 to 94 labelled a_1(2)* 94 to 95 labelled a_1(2)* 95 to 96 labelled b_1(2)* 95 to 91 labelled a_1(2)* 96 to 97 labelled b_1(2)* 96 to 34 labelled a_1(1)* 97 to 38 labelled a_1(2)


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(4)
YES