YES
proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(a(a(x1))))) -> a(a(b(b(a(b(a(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 3. This implies Q-termination of R.
The following rules were used to construct the certificate:

   b(a(b(a(a(x1))))) -> a(a(b(b(a(b(a(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, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75

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 a_1(0)* 4 to 5 labelled b_1(0)* 5 to 6 labelled b_1(0)* 5 to 19 labelled a_1(1)* 6 to 7 labelled a_1(0)* 7 to 8 labelled b_1(0)* 7 to 11 labelled a_1(1)* 8 to 9 labelled a_1(0)* 9 to 10 labelled b_1(0)* 9 to 11 labelled a_1(1)* 10 to 2 labelled a_1(0)* 11 to 12 labelled a_1(1)* 12 to 13 labelled b_1(1)* 13 to 14 labelled b_1(1)* 13 to 27 labelled a_1(2)* 14 to 15 labelled a_1(1)* 15 to 16 labelled b_1(1)* 15 to 11 labelled a_1(1)* 16 to 17 labelled a_1(1)* 17 to 18 labelled b_1(1)* 17 to 11 labelled a_1(1)* 18 to 2 labelled a_1(1)* 19 to 20 labelled a_1(1)* 20 to 21 labelled b_1(1)* 21 to 22 labelled b_1(1)* 22 to 23 labelled a_1(1)* 23 to 24 labelled b_1(1)* 23 to 35 labelled a_1(2)* 24 to 25 labelled a_1(1)* 25 to 26 labelled b_1(1)* 26 to 11 labelled a_1(1)* 27 to 28 labelled a_1(2)* 28 to 29 labelled b_1(2)* 29 to 30 labelled b_1(2)* 30 to 31 labelled a_1(2)* 31 to 32 labelled b_1(2)* 31 to 35 labelled a_1(2)* 32 to 33 labelled a_1(2)* 33 to 34 labelled b_1(2)* 34 to 11 labelled a_1(2)* 35 to 36 labelled a_1(2)* 36 to 37 labelled b_1(2)* 37 to 38 labelled b_1(2)* 37 to 60 labelled a_1(3)* 38 to 39 labelled a_1(2)* 39 to 40 labelled b_1(2)* 40 to 41 labelled a_1(2)* 41 to 42 labelled b_1(2)* 41 to 52 labelled a_1(2)* 42 to 12 labelled a_1(2)* 52 to 53 labelled a_1(2)* 53 to 54 labelled b_1(2)* 54 to 55 labelled b_1(2)* 55 to 56 labelled a_1(2)* 56 to 57 labelled b_1(2)* 57 to 58 labelled a_1(2)* 58 to 59 labelled b_1(2)* 59 to 28 labelled a_1(2)* 60 to 61 labelled a_1(3)* 61 to 62 labelled b_1(3)* 62 to 63 labelled b_1(3)* 63 to 64 labelled a_1(3)* 64 to 65 labelled b_1(3)* 64 to 68 labelled a_1(3)* 65 to 66 labelled a_1(3)* 66 to 67 labelled b_1(3)* 67 to 52 labelled a_1(3)* 68 to 69 labelled a_1(3)* 69 to 70 labelled b_1(3)* 70 to 71 labelled b_1(3)* 71 to 72 labelled a_1(3)* 72 to 73 labelled b_1(3)* 73 to 74 labelled a_1(3)* 74 to 75 labelled b_1(3)* 75 to 53 labelled a_1(3)


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(2)
YES