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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 7 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(b(x1)))))) -> a(b(a(b(a(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(a(a(b(x1)))))) -> a(b(a(b(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:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
15, 16, 23, 24, 25, 26, 27, 28, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 77, 78, 79, 80, 81, 82

Node 15 is start node and node 16 is final node.

Those nodes are connected through the following edges:

* 15 to 23 labelled a_1(0)* 16 to 16 labelled #_1(0)* 23 to 24 labelled b_1(0)* 23 to 47 labelled a_1(1)* 24 to 25 labelled a_1(0)* 25 to 26 labelled b_1(0)* 25 to 41 labelled a_1(1)* 26 to 27 labelled a_1(0)* 27 to 28 labelled b_1(0)* 27 to 41 labelled a_1(1)* 28 to 16 labelled a_1(0)* 41 to 42 labelled b_1(1)* 41 to 59 labelled a_1(2)* 42 to 43 labelled a_1(1)* 43 to 44 labelled b_1(1)* 43 to 41 labelled a_1(1)* 44 to 45 labelled a_1(1)* 45 to 46 labelled b_1(1)* 45 to 41 labelled a_1(1)* 46 to 16 labelled a_1(1)* 47 to 48 labelled b_1(1)* 48 to 49 labelled a_1(1)* 49 to 50 labelled b_1(1)* 49 to 65 labelled a_1(2)* 50 to 51 labelled a_1(1)* 51 to 52 labelled b_1(1)* 52 to 42 labelled a_1(1)* 59 to 60 labelled b_1(2)* 60 to 61 labelled a_1(2)* 61 to 62 labelled b_1(2)* 61 to 65 labelled a_1(2)* 62 to 63 labelled a_1(2)* 63 to 64 labelled b_1(2)* 64 to 42 labelled a_1(2)* 65 to 66 labelled b_1(2)* 66 to 67 labelled a_1(2)* 67 to 68 labelled b_1(2)* 67 to 77 labelled a_1(2)* 68 to 69 labelled a_1(2)* 69 to 70 labelled b_1(2)* 70 to 44 labelled a_1(2)* 77 to 78 labelled b_1(2)* 78 to 79 labelled a_1(2)* 79 to 80 labelled b_1(2)* 79 to 41 labelled a_1(1)* 80 to 81 labelled a_1(2)* 81 to 82 labelled b_1(2)* 82 to 46 labelled a_1(2)


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(4)
YES