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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

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

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 2. This implies Q-termination of R.
The following rules were used to construct the certificate:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 4, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 141, 142, 143, 144, 145, 146, 147, 148

Node 1 is start node and node 4 is final node.

Those nodes are connected through the following edges:

* 1 to 85 labelled a_1(0)* 4 to 4 labelled #_1(0)* 85 to 86 labelled a_1(0)* 86 to 87 labelled b_1(0)* 87 to 88 labelled b_1(0)* 88 to 89 labelled a_1(0)* 89 to 90 labelled a_1(0)* 90 to 91 labelled a_1(0)* 91 to 92 labelled b_1(0)* 91 to 101 labelled a_1(1)* 92 to 4 labelled b_1(0)* 92 to 93 labelled a_1(1)* 93 to 94 labelled a_1(1)* 94 to 95 labelled b_1(1)* 95 to 96 labelled b_1(1)* 96 to 97 labelled a_1(1)* 97 to 98 labelled a_1(1)* 98 to 99 labelled a_1(1)* 99 to 100 labelled b_1(1)* 99 to 141 labelled a_1(2)* 100 to 4 labelled b_1(1)* 100 to 93 labelled a_1(1)* 101 to 102 labelled a_1(1)* 102 to 103 labelled b_1(1)* 103 to 104 labelled b_1(1)* 104 to 105 labelled a_1(1)* 105 to 106 labelled a_1(1)* 106 to 107 labelled a_1(1)* 107 to 108 labelled b_1(1)* 107 to 141 labelled a_1(2)* 108 to 97 labelled b_1(1)* 108 to 93 labelled a_1(1)* 141 to 142 labelled a_1(2)* 142 to 143 labelled b_1(2)* 143 to 144 labelled b_1(2)* 144 to 145 labelled a_1(2)* 145 to 146 labelled a_1(2)* 146 to 147 labelled a_1(2)* 147 to 148 labelled b_1(2)* 147 to 141 labelled a_1(2)* 148 to 97 labelled b_1(2)* 148 to 93 labelled a_1(1)


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(2)
YES