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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

Q is empty.

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

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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26

Node 2 is start node and node 4 is final node.

Those nodes are connected through the following edges:

* 2 to 5 labelled a_1(0)* 4 to 4 labelled #_1(0)* 5 to 6 labelled a_1(0)* 6 to 7 labelled b_1(0)* 7 to 8 labelled a_1(0)* 8 to 9 labelled a_1(0)* 9 to 10 labelled a_1(0)* 10 to 11 labelled b_1(0)* 10 to 16 labelled a_1(1)* 11 to 12 labelled a_1(0)* 12 to 13 labelled b_1(0)* 12 to 16 labelled a_1(1)* 13 to 14 labelled a_1(0)* 14 to 15 labelled b_1(0)* 14 to 16 labelled a_1(1)* 15 to 4 labelled a_1(0)* 16 to 17 labelled a_1(1)* 17 to 18 labelled b_1(1)* 18 to 19 labelled a_1(1)* 19 to 20 labelled a_1(1)* 20 to 21 labelled a_1(1)* 21 to 22 labelled b_1(1)* 21 to 16 labelled a_1(1)* 22 to 23 labelled a_1(1)* 23 to 24 labelled b_1(1)* 23 to 16 labelled a_1(1)* 24 to 25 labelled a_1(1)* 25 to 26 labelled b_1(1)* 25 to 16 labelled a_1(1)* 26 to 4 labelled a_1(1)


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(4)
YES