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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

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

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

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

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
2, 6, 7, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

Node 2 is start node and node 6 is final node.

Those nodes are connected through the following edges:

* 2 to 7 labelled a_1(0)* 6 to 6 labelled #_1(0)* 7 to 52 labelled b_1(0)* 52 to 53 labelled a_1(0)* 53 to 54 labelled b_1(0)* 54 to 55 labelled a_1(0)* 55 to 56 labelled a_1(0)* 56 to 57 labelled b_1(0)* 56 to 61 labelled a_1(1)* 57 to 58 labelled a_1(0)* 58 to 59 labelled a_1(0)* 59 to 60 labelled b_1(0)* 59 to 61 labelled a_1(1)* 60 to 6 labelled a_1(0)* 61 to 62 labelled b_1(1)* 62 to 63 labelled a_1(1)* 63 to 64 labelled b_1(1)* 64 to 65 labelled a_1(1)* 65 to 66 labelled a_1(1)* 66 to 67 labelled b_1(1)* 66 to 61 labelled a_1(1)* 67 to 68 labelled a_1(1)* 68 to 69 labelled a_1(1)* 69 to 70 labelled b_1(1)* 69 to 61 labelled a_1(1)* 70 to 6 labelled a_1(1)


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(4)
YES