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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 19 ms]
(2) YES


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(0)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   a(a(b(x1))) -> b(b(a(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 3. This implies Q-termination of R.
The following rules were used to construct the certificate:

   a(a(b(x1))) -> b(b(a(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, 15, 16, 19, 20, 21, 25, 26, 31, 32, 35, 36, 40, 41, 42, 43, 44, 45, 46, 47

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 6 labelled a_1(0)* 1 to 31 labelled a_1(1)* 2 to 2 labelled #_1(0)* 3 to 4 labelled b_1(0)* 3 to 15 labelled a_1(1)* 4 to 5 labelled a_1(0)* 4 to 19 labelled b_1(1)* 4 to 40 labelled a_1(2)* 5 to 2 labelled a_1(0)* 5 to 19 labelled b_1(1)* 5 to 40 labelled a_1(2)* 6 to 7 labelled c_1(0)* 7 to 2 labelled b_1(0)* 7 to 25 labelled a_1(1)* 15 to 16 labelled c_1(1)* 16 to 5 labelled b_1(1)* 16 to 25 labelled a_1(1)* 16 to 40 labelled b_1(1)* 16 to 44 labelled a_1(2)* 19 to 20 labelled b_1(1)* 19 to 35 labelled a_1(2)* 19 to 44 labelled a_1(2)* 20 to 21 labelled a_1(1)* 20 to 19 labelled b_1(1)* 20 to 40 labelled a_1(2)* 21 to 2 labelled a_1(1)* 21 to 19 labelled b_1(1)* 21 to 40 labelled a_1(2)* 25 to 26 labelled c_1(1)* 26 to 2 labelled b_1(1)* 26 to 25 labelled a_1(1)* 31 to 32 labelled c_1(1)* 32 to 15 labelled b_1(1)* 35 to 36 labelled c_1(2)* 36 to 21 labelled b_1(2)* 36 to 42 labelled a_1(2)* 36 to 46 labelled a_1(3)* 40 to 41 labelled c_1(2)* 41 to 35 labelled b_1(2)* 41 to 44 labelled b_1(2)* 42 to 43 labelled c_1(2)* 43 to 2 labelled b_1(2)* 43 to 25 labelled a_1(1)* 44 to 45 labelled c_1(2)* 45 to 40 labelled b_1(2)* 46 to 47 labelled c_1(3)* 47 to 40 labelled b_1(3)


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(2)
YES