/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 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(x1))))) -> a(a(b(b(a(a(b(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:

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 4, 11, 12, 13, 14, 15, 16, 23, 25, 26, 28, 30, 32, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94

Node 2 is start node and node 4 is final node.

Those nodes are connected through the following edges:

* 2 to 11 labelled b_1(0)* 4 to 4 labelled #_1(0)* 11 to 12 labelled a_1(0)* 12 to 13 labelled a_1(0)* 13 to 14 labelled b_1(0)* 14 to 15 labelled b_1(0)* 15 to 16 labelled a_1(0)* 15 to 83 labelled b_1(1)* 16 to 4 labelled a_1(0)* 16 to 23 labelled b_1(1)* 23 to 25 labelled a_1(1)* 25 to 26 labelled a_1(1)* 26 to 28 labelled b_1(1)* 28 to 30 labelled b_1(1)* 30 to 32 labelled a_1(1)* 30 to 89 labelled b_1(2)* 32 to 4 labelled a_1(1)* 32 to 23 labelled b_1(1)* 83 to 84 labelled a_1(1)* 84 to 85 labelled a_1(1)* 85 to 86 labelled b_1(1)* 86 to 87 labelled b_1(1)* 87 to 88 labelled a_1(1)* 87 to 89 labelled b_1(2)* 88 to 28 labelled a_1(1)* 88 to 23 labelled b_1(1)* 89 to 90 labelled a_1(2)* 90 to 91 labelled a_1(2)* 91 to 92 labelled b_1(2)* 92 to 93 labelled b_1(2)* 93 to 94 labelled a_1(2)* 93 to 89 labelled b_1(2)* 94 to 28 labelled a_1(2)* 94 to 23 labelled b_1(1)


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(4)
YES