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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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) QTRS Reverse [EQUIVALENT, 0 ms]
(2) QTRS
(3) Strip Symbols Proof [SOUND, 0 ms]
(4) QTRS
(5) RFCMatchBoundsTRSProof [EQUIVALENT, 5 ms]
(6) YES


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

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

Q is empty.

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(1) QTRS Reverse (EQUIVALENT)
We applied the QTRS Reverse Processor [REVERSE].
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(2)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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

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

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

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

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(4)
Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:

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

Q is empty.

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(5) 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:

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

The certificate found is represented by the following graph.
The certificate consists of the following enumerated nodes:
7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70

Node 7 is start node and node 8 is final node.

Those nodes are connected through the following edges:

* 7 to 9 labelled b_1(0)* 8 to 8 labelled #_1(0)* 9 to 11 labelled b_1(0)* 11 to 13 labelled a_1(0)* 13 to 15 labelled a_1(0)* 15 to 17 labelled b_1(0)* 17 to 19 labelled b_1(0)* 19 to 21 labelled a_1(0)* 19 to 59 labelled b_1(1)* 21 to 23 labelled a_1(0)* 21 to 59 labelled b_1(1)* 23 to 25 labelled a_1(0)* 23 to 59 labelled b_1(1)* 25 to 27 labelled a_1(0)* 25 to 59 labelled b_1(1)* 27 to 29 labelled a_1(0)* 27 to 59 labelled b_1(1)* 29 to 31 labelled a_1(0)* 29 to 59 labelled b_1(1)* 31 to 8 labelled a_1(0)* 31 to 59 labelled b_1(1)* 59 to 60 labelled b_1(1)* 60 to 61 labelled a_1(1)* 61 to 62 labelled a_1(1)* 62 to 63 labelled b_1(1)* 63 to 64 labelled b_1(1)* 64 to 65 labelled a_1(1)* 64 to 59 labelled b_1(1)* 65 to 66 labelled a_1(1)* 65 to 59 labelled b_1(1)* 66 to 67 labelled a_1(1)* 66 to 59 labelled b_1(1)* 67 to 68 labelled a_1(1)* 67 to 59 labelled b_1(1)* 68 to 69 labelled a_1(1)* 68 to 59 labelled b_1(1)* 69 to 70 labelled a_1(1)* 69 to 59 labelled b_1(1)* 70 to 8 labelled a_1(1)* 70 to 59 labelled b_1(1)


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(6)
YES