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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 19.1 s]
(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)) -> b(b(c(a(c(x1)))))
   c(c(x1)) -> 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 c b b c -> b b c b b b b b b b b b b b b b b b a b c b b c a c"
a b c b b c -> b b c b b b b b b b b b b b b b b b a b c b b c a c
by OverlapClosure OC 2"a b c b b c -> b b c b b b b b b b b b b b b b b b a b c a b
by OverlapClosure OC 3"a b c b b c -> b b c b b b b b b b b b b b b b b c c b c a b
by OverlapClosure OC 2"a b c b b -> b b c b b b b b b b b b b b b b b c c b c a c
by OverlapClosure OC 3"a b c b b -> b b c b b b b b b b b b b b b b b c a c b c a c
by OverlapClosure OC 3"a b c b b -> b b c b b b b b b b b b b b b a b b c a c
by OverlapClosure OC 2"a b c b -> b b c b b b b b b b b b b b b a a
by OverlapClosure OC 3"a b c b -> b b c b b b b b b b b b a b a
by OverlapClosure OC 3"a b c b -> b b c b b b b b b a b b a
by OverlapClosure OC 3"a b c b -> b b c b b b a b b b a
by OverlapClosure OC 3"a b c b -> b b c b b c c b b b a
by OverlapClosure OC 2"a b c b -> b b c b b c c b b c c
by OverlapClosure OC 2"a b c -> b b c b b c c a
by OverlapClosure OC 3"a b c -> b b c b b c a c a
by OverlapClosure OC 3"a b c -> b b c a b a
by OverlapClosure OC 2"a b -> b b c a c
by original rule (OC 1)""c c -> b a
by original rule (OC 1)"""a b -> b b c a c
by original rule (OC 1)"""a -> 
by original rule (OC 1)"""a b -> b b c c
by OverlapClosure OC 3"a b -> b b c a c
by original rule (OC 1)""a -> 
by original rule (OC 1)""""c c -> b a
by original rule (OC 1)"""c c -> b a
by original rule (OC 1)"""a b -> b b b a
by OverlapClosure OC 2"a b -> b b c c
by OverlapClosure OC 3"a b -> b b c a c
by original rule (OC 1)""a -> 
by original rule (OC 1)"""c c -> b a
by original rule (OC 1)""""a b -> b b b a
by OverlapClosure OC 2"a b -> b b c c
by OverlapClosure OC 3"a b -> b b c a c
by original rule (OC 1)""a -> 
by original rule (OC 1)"""c c -> b a
by original rule (OC 1)""""a b -> b b b a
by OverlapClosure OC 2"a b -> b b c c
by OverlapClosure OC 3"a b -> b b c a c
by original rule (OC 1)""a -> 
by original rule (OC 1)"""c c -> b a
by original rule (OC 1)""""a b -> b b c a c
by original rule (OC 1)"""a b -> b b c a c
by original rule (OC 1)"""a -> 
by original rule (OC 1)"""c c -> b
by OverlapClosure OC 2"c c -> b a
by original rule (OC 1)""a -> 
by original rule (OC 1)""""c c -> b a
by original rule (OC 1)"""a b -> b b c a c
by original rule (OC 1)"

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(2)
NO