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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(b(a(a(b(x1)))))))) -> a(a(b(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(b(a(a(b(x1)))))))) -> a(a(b(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(b(a(a(x))))))) -> a(a(b(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(b(a(a(x))))))) -> a(a(b(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(b(a(a(x))))))) -> a(a(b(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:
13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 34, 35, 36, 37, 38, 39, 40, 41, 42

Node 13 is start node and node 14 is final node.

Those nodes are connected through the following edges:

* 13 to 15 labelled a_1(0)* 14 to 14 labelled #_1(0)* 15 to 16 labelled a_1(0)* 16 to 17 labelled b_1(0)* 17 to 18 labelled b_1(0)* 18 to 19 labelled a_1(0)* 19 to 20 labelled a_1(0)* 20 to 21 labelled b_1(0)* 20 to 34 labelled a_1(1)* 21 to 22 labelled a_1(0)* 22 to 23 labelled a_1(0)* 23 to 14 labelled b_1(0)* 23 to 34 labelled a_1(1)* 34 to 35 labelled a_1(1)* 35 to 36 labelled b_1(1)* 36 to 37 labelled b_1(1)* 37 to 38 labelled a_1(1)* 38 to 39 labelled a_1(1)* 39 to 40 labelled b_1(1)* 39 to 34 labelled a_1(1)* 40 to 41 labelled a_1(1)* 41 to 42 labelled a_1(1)* 42 to 14 labelled b_1(1)* 42 to 34 labelled a_1(1)


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(4)
YES