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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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


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

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

Q is empty.

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(1) Strip Symbols Proof (SOUND)
We were given the following TRS:

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

By stripping symbols from the only rule of the system, we obtained the following TRS [ENDRULLIS]: 

   b(a(a(b(a(a(b(b(a(a(x)))))))))) -> a(a(b(b(a(a(b(a(a(b(a(a(b(x)))))))))))))

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(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

   b(a(a(b(a(a(b(b(a(a(x)))))))))) -> a(a(b(b(a(a(b(a(a(b(a(a(b(x)))))))))))))

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 1. This implies Q-termination of R.
The following rules were used to construct the certificate:

   b(a(a(b(a(a(b(b(a(a(x)))))))))) -> a(a(b(b(a(a(b(a(a(b(a(a(b(x)))))))))))))

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93

Node 68 is start node and node 69 is final node.

Those nodes are connected through the following edges:

* 68 to 70 labelled a_1(0)* 69 to 69 labelled #_1(0)* 70 to 71 labelled a_1(0)* 71 to 72 labelled b_1(0)* 72 to 73 labelled b_1(0)* 73 to 74 labelled a_1(0)* 74 to 75 labelled a_1(0)* 75 to 76 labelled b_1(0)* 75 to 82 labelled a_1(1)* 76 to 77 labelled a_1(0)* 77 to 78 labelled a_1(0)* 78 to 79 labelled b_1(0)* 78 to 82 labelled a_1(1)* 79 to 80 labelled a_1(0)* 80 to 81 labelled a_1(0)* 81 to 69 labelled b_1(0)* 81 to 82 labelled a_1(1)* 82 to 83 labelled a_1(1)* 83 to 84 labelled b_1(1)* 84 to 85 labelled b_1(1)* 85 to 86 labelled a_1(1)* 86 to 87 labelled a_1(1)* 87 to 88 labelled b_1(1)* 87 to 82 labelled a_1(1)* 88 to 89 labelled a_1(1)* 89 to 90 labelled a_1(1)* 90 to 91 labelled b_1(1)* 90 to 82 labelled a_1(1)* 91 to 92 labelled a_1(1)* 92 to 93 labelled a_1(1)* 93 to 69 labelled b_1(1)* 93 to 82 labelled a_1(1)


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(4)
YES