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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 4, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 69, 70, 71, 72, 73, 74, 75, 76, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108

Node 3 is start node and node 4 is final node.

Those nodes are connected through the following edges:

* 3 to 37 labelled b_1(0)* 4 to 4 labelled #_1(0)* 37 to 38 labelled a_1(0)* 38 to 39 labelled a_1(0)* 39 to 40 labelled b_1(0)* 40 to 41 labelled b_1(0)* 41 to 42 labelled a_1(0)* 41 to 69 labelled b_1(1)* 42 to 43 labelled a_1(0)* 42 to 45 labelled b_1(1)* 43 to 44 labelled b_1(0)* 44 to 4 labelled a_1(0)* 44 to 45 labelled b_1(1)* 45 to 46 labelled a_1(1)* 46 to 47 labelled a_1(1)* 47 to 48 labelled b_1(1)* 48 to 49 labelled b_1(1)* 49 to 50 labelled a_1(1)* 49 to 93 labelled b_1(2)* 50 to 51 labelled a_1(1)* 50 to 45 labelled b_1(1)* 51 to 52 labelled b_1(1)* 52 to 4 labelled a_1(1)* 52 to 45 labelled b_1(1)* 69 to 70 labelled a_1(1)* 70 to 71 labelled a_1(1)* 71 to 72 labelled b_1(1)* 72 to 73 labelled b_1(1)* 73 to 74 labelled a_1(1)* 74 to 75 labelled a_1(1)* 75 to 76 labelled b_1(1)* 76 to 48 labelled a_1(1)* 76 to 101 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)* 96 to 97 labelled b_1(2)* 97 to 98 labelled a_1(2)* 98 to 99 labelled a_1(2)* 99 to 100 labelled b_1(2)* 100 to 48 labelled a_1(2)* 100 to 101 labelled b_1(2)* 101 to 102 labelled a_1(2)* 102 to 103 labelled a_1(2)* 103 to 104 labelled b_1(2)* 104 to 105 labelled b_1(2)* 105 to 106 labelled a_1(2)* 105 to 93 labelled b_1(2)* 106 to 107 labelled a_1(2)* 106 to 45 labelled b_1(1)* 107 to 108 labelled b_1(2)* 108 to 52 labelled a_1(2)* 108 to 93 labelled b_1(2)


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(4)
YES