NO
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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 disproven:

(0) QTRS
(1) NonTerminationProof [COMPLETE, 2196 ms]
(2) NO


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

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

Q is empty.

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(1) NonTerminationProof (COMPLETE)
We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.

Found the self-embedding DerivationStructure: 
"a b b b c b b b c -> b b c b c b b c b a b b b c b b b c b"
a b b b c b b b c -> b b c b c b b c b a b b b c b b b c b
by OverlapClosure OC 3"a b b b c b b b c -> b b c b c b b c b a b b b c b a b b c b
by OverlapClosure OC 2"a b b b c -> b b c b c b b c b a b a
by OverlapClosure OC 3"a b b b c -> b b c b c c c b a
by OverlapClosure OC 3"a b b b c -> b b c b c a b c b a
by OverlapClosure OC 3"a b b b c -> b b c b a b b c b a
by OverlapClosure OC 2"a b b -> b b c b a a
by OverlapClosure OC 3"a b b -> c c a
by OverlapClosure OC 2"a b -> c a
by original rule (OC 1)""a b -> c a
by original rule (OC 1)"""c c -> b b c b a
by original rule (OC 1)"""a b c -> b b c b a
by OverlapClosure OC 2"a b -> c
by OverlapClosure OC 2"a b -> c a
by original rule (OC 1)""a -> 
by original rule (OC 1)"""c c -> b b c b a
by original rule (OC 1)""""a b -> c a
by original rule (OC 1)"""a b -> c
by OverlapClosure OC 2"a b -> c a
by original rule (OC 1)""a -> 
by original rule (OC 1)""""c c -> b b c b a
by original rule (OC 1)"""a b b b c -> b b c b a b b c b
by OverlapClosure OC 2"a b b -> b b c b a a
by OverlapClosure OC 3"a b b -> c c a
by OverlapClosure OC 2"a b -> c a
by original rule (OC 1)""a b -> c a
by original rule (OC 1)"""c c -> b b c b a
by original rule (OC 1)"""a b c -> b b c b
by OverlapClosure OC 2"a b -> c
by OverlapClosure OC 2"a b -> c a
by original rule (OC 1)""a -> 
by original rule (OC 1)"""c c -> b b c b
by OverlapClosure OC 2"c c -> b b c b a
by original rule (OC 1)""a -> 
by original rule (OC 1)""""""a -> 
by original rule (OC 1)"

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(2)
NO