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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

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

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, 17, 19, 21, 24, 26, 27

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

Those nodes are connected through the following edges:

* 2 to 5 labelled c_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 b_1(0)* 7 to 17 labelled c_1(1)* 8 to 9 labelled b_1(0)* 9 to 10 labelled c_1(0)* 10 to 4 labelled a_1(0)* 17 to 19 labelled a_1(1)* 19 to 21 labelled b_1(1)* 21 to 24 labelled b_1(1)* 21 to 17 labelled c_1(1)* 24 to 26 labelled b_1(1)* 26 to 27 labelled c_1(1)* 27 to 4 labelled a_1(1)


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(4)
YES