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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


Termination w.r.t. Q of the given QTRS could be proven:

(0) QTRS
(1) RFCMatchBoundsTRSProof [EQUIVALENT, 0 ms]
(2) YES


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

   b(a(b(a(a(a(x1)))))) -> a(a(a(a(b(a(b(a(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 3. This implies Q-termination of R.
The following rules were used to construct the certificate:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100

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

Those nodes are connected through the following edges:

* 1 to 3 labelled a_1(0)* 2 to 2 labelled #_1(0)* 3 to 4 labelled a_1(0)* 4 to 5 labelled a_1(0)* 5 to 6 labelled a_1(0)* 6 to 7 labelled b_1(0)* 6 to 69 labelled a_1(1)* 7 to 8 labelled a_1(0)* 8 to 9 labelled b_1(0)* 8 to 61 labelled a_1(1)* 9 to 10 labelled a_1(0)* 10 to 2 labelled b_1(0)* 10 to 61 labelled a_1(1)* 61 to 62 labelled a_1(1)* 62 to 63 labelled a_1(1)* 63 to 64 labelled a_1(1)* 64 to 65 labelled b_1(1)* 64 to 77 labelled a_1(2)* 65 to 66 labelled a_1(1)* 66 to 67 labelled b_1(1)* 66 to 61 labelled a_1(1)* 67 to 68 labelled a_1(1)* 68 to 2 labelled b_1(1)* 68 to 61 labelled a_1(1)* 69 to 70 labelled a_1(1)* 70 to 71 labelled a_1(1)* 71 to 72 labelled a_1(1)* 72 to 73 labelled b_1(1)* 73 to 74 labelled a_1(1)* 74 to 75 labelled b_1(1)* 74 to 85 labelled a_1(2)* 75 to 76 labelled a_1(1)* 76 to 62 labelled b_1(1)* 77 to 78 labelled a_1(2)* 78 to 79 labelled a_1(2)* 79 to 80 labelled a_1(2)* 80 to 81 labelled b_1(2)* 81 to 82 labelled a_1(2)* 82 to 83 labelled b_1(2)* 82 to 85 labelled a_1(2)* 83 to 84 labelled a_1(2)* 84 to 62 labelled b_1(2)* 85 to 86 labelled a_1(2)* 86 to 87 labelled a_1(2)* 87 to 88 labelled a_1(2)* 88 to 89 labelled b_1(2)* 89 to 90 labelled a_1(2)* 90 to 91 labelled b_1(2)* 90 to 93 labelled a_1(3)* 91 to 92 labelled a_1(2)* 92 to 77 labelled b_1(2)* 93 to 94 labelled a_1(3)* 94 to 95 labelled a_1(3)* 95 to 96 labelled a_1(3)* 96 to 97 labelled b_1(3)* 97 to 98 labelled a_1(3)* 98 to 99 labelled b_1(3)* 99 to 100 labelled a_1(3)* 100 to 80 labelled b_1(3)


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(2)
YES