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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

   b(a(b(b(a(b(a(x1))))))) -> a(b(a(a(b(b(a(b(b(a(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, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

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 b_1(0)* 4 to 5 labelled a_1(0)* 5 to 6 labelled a_1(0)* 6 to 7 labelled b_1(0)* 7 to 8 labelled b_1(0)* 7 to 12 labelled a_1(1)* 8 to 9 labelled a_1(0)* 9 to 10 labelled b_1(0)* 10 to 11 labelled b_1(0)* 10 to 12 labelled a_1(1)* 11 to 2 labelled a_1(0)* 12 to 13 labelled b_1(1)* 13 to 14 labelled a_1(1)* 14 to 15 labelled a_1(1)* 15 to 16 labelled b_1(1)* 16 to 17 labelled b_1(1)* 16 to 12 labelled a_1(1)* 17 to 18 labelled a_1(1)* 18 to 19 labelled b_1(1)* 19 to 20 labelled b_1(1)* 19 to 12 labelled a_1(1)* 20 to 2 labelled a_1(1)


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(2)
YES