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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) RFCMatchBoundsTRSProof [EQUIVALENT, 4 ms]
(4) YES


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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116

Node 83 is start node and node 84 is final node.

Those nodes are connected through the following edges:

* 83 to 85 labelled b_1(0)* 84 to 84 labelled #_1(0)* 85 to 86 labelled a_1(0)* 86 to 87 labelled a_1(0)* 87 to 88 labelled a_1(0)* 88 to 89 labelled b_1(0)* 89 to 90 labelled b_1(0)* 90 to 91 labelled a_1(0)* 90 to 101 labelled b_1(1)* 91 to 92 labelled a_1(0)* 91 to 93 labelled b_1(1)* 92 to 84 labelled a_1(0)* 92 to 93 labelled b_1(1)* 93 to 94 labelled a_1(1)* 94 to 95 labelled a_1(1)* 95 to 96 labelled a_1(1)* 96 to 97 labelled b_1(1)* 97 to 98 labelled b_1(1)* 98 to 99 labelled a_1(1)* 98 to 109 labelled b_1(2)* 99 to 100 labelled a_1(1)* 99 to 93 labelled b_1(1)* 100 to 84 labelled a_1(1)* 100 to 93 labelled b_1(1)* 101 to 102 labelled a_1(1)* 102 to 103 labelled a_1(1)* 103 to 104 labelled a_1(1)* 104 to 105 labelled b_1(1)* 105 to 106 labelled b_1(1)* 106 to 107 labelled a_1(1)* 107 to 108 labelled a_1(1)* 107 to 93 labelled b_1(1)* 108 to 97 labelled a_1(1)* 109 to 110 labelled a_1(2)* 110 to 111 labelled a_1(2)* 111 to 112 labelled a_1(2)* 112 to 113 labelled b_1(2)* 113 to 114 labelled b_1(2)* 114 to 115 labelled a_1(2)* 115 to 116 labelled a_1(2)* 115 to 93 labelled b_1(1)* 116 to 97 labelled a_1(2)


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(4)
YES