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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) 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(b(a(b(b(a(b(b(b(b(b(b(a(b(x1)))))))))))))) -> b(b(b(b(b(a(b(b(a(b(b(a(b(b(b(b(b(b(x1))))))))))))))))))

Q is empty.

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

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

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

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

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

   b(a(b(b(a(b(b(b(b(b(b(a(b(x1))))))))))))) -> b(b(b(b(a(b(b(a(b(b(a(b(b(b(b(b(b(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 1. This implies Q-termination of R.
The following rules were used to construct the certificate:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
3, 4, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53

Node 3 is start node and node 4 is final node.

Those nodes are connected through the following edges:

* 3 to 22 labelled b_1(0)* 4 to 4 labelled #_1(0)* 22 to 23 labelled b_1(0)* 23 to 24 labelled b_1(0)* 24 to 25 labelled b_1(0)* 25 to 26 labelled a_1(0)* 26 to 27 labelled b_1(0)* 27 to 28 labelled b_1(0)* 27 to 38 labelled b_1(1)* 28 to 29 labelled a_1(0)* 29 to 30 labelled b_1(0)* 30 to 31 labelled b_1(0)* 31 to 32 labelled a_1(0)* 32 to 33 labelled b_1(0)* 33 to 34 labelled b_1(0)* 34 to 35 labelled b_1(0)* 35 to 36 labelled b_1(0)* 36 to 37 labelled b_1(0)* 37 to 4 labelled b_1(0)* 37 to 38 labelled b_1(1)* 38 to 39 labelled b_1(1)* 39 to 40 labelled b_1(1)* 40 to 41 labelled b_1(1)* 41 to 42 labelled a_1(1)* 42 to 43 labelled b_1(1)* 43 to 44 labelled b_1(1)* 43 to 38 labelled b_1(1)* 44 to 45 labelled a_1(1)* 45 to 46 labelled b_1(1)* 46 to 47 labelled b_1(1)* 47 to 48 labelled a_1(1)* 48 to 49 labelled b_1(1)* 49 to 50 labelled b_1(1)* 50 to 51 labelled b_1(1)* 51 to 52 labelled b_1(1)* 52 to 53 labelled b_1(1)* 53 to 4 labelled b_1(1)* 53 to 38 labelled b_1(1)


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(4)
YES