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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(b(b(b(b(x1)))))) -> a(b(b(b(b(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(b(b(b(a(b(x1)))))) -> a(b(b(b(b(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 1. This implies Q-termination of R.
The following rules were used to construct the certificate:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76

Node 63 is start node and node 64 is final node.

Those nodes are connected through the following edges:

* 63 to 65 labelled a_1(0)* 64 to 64 labelled #_1(0)* 65 to 66 labelled b_1(0)* 66 to 67 labelled b_1(0)* 66 to 71 labelled a_1(1)* 67 to 68 labelled b_1(0)* 68 to 69 labelled b_1(0)* 69 to 70 labelled b_1(0)* 70 to 64 labelled a_1(0)* 71 to 72 labelled b_1(1)* 72 to 73 labelled b_1(1)* 72 to 71 labelled a_1(1)* 73 to 74 labelled b_1(1)* 74 to 75 labelled b_1(1)* 75 to 76 labelled b_1(1)* 76 to 64 labelled a_1(1)


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(4)
YES