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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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:

   a(b(x1)) -> b(a(x1))
   b(a(x1)) -> a(c(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 2. This implies Q-termination of R.
The following rules were used to construct the certificate:

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

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

Those nodes are connected through the following edges:

* 1 to 3 labelled b_1(0)* 1 to 4 labelled a_1(0)* 1 to 6 labelled a_1(1)* 2 to 2 labelled #_1(0)* 3 to 2 labelled a_1(0)* 3 to 8 labelled b_1(1)* 3 to 9 labelled a_1(2)* 4 to 5 labelled c_1(0)* 5 to 2 labelled b_1(0)* 5 to 6 labelled a_1(1)* 6 to 7 labelled c_1(1)* 7 to 2 labelled b_1(1)* 7 to 6 labelled a_1(1)* 7 to 9 labelled b_1(1)* 8 to 2 labelled a_1(1)* 8 to 8 labelled b_1(1)* 8 to 9 labelled a_1(2)* 9 to 10 labelled c_1(2)* 10 to 2 labelled b_1(2)* 10 to 6 labelled a_1(1)* 10 to 9 labelled b_1(2)


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(2)
YES