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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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

(0) QTRS
(1) NonTerminationProof [COMPLETE, 21.8 s]
(2) NO


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

   a(a(a(x1))) -> a(b(c(c(c(x1)))))
   c(b(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 a a b a a b b a b -> a b b a b b a b c b a b b a a a b a a b b a b c c c"
a a a b a a b b a b -> a b b a b b a b c b a b b a a a b a a b b a b c c c
by OverlapClosure OC 2"a a a b a a b b a b -> a b b a b b a b c b a b b a a a b a a b b a a a
by OverlapClosure OC 2"a a a b a a b b -> a b b a b b a b c b a b b a a a b a a a
by OverlapClosure OC 3"a a a b a a b b -> a b b a b b a b c b a b b a a a c b a a
by OverlapClosure OC 3"a a a b a a b b -> a b b a b b a b c b a b b a a a c c b a
by OverlapClosure OC 2"a a a b a a b -> a b b a b b a b c b a b b a a a c c c
by OverlapClosure OC 3"a a a b a a b -> a b b a b b a b c b a b c b a a c c c
by OverlapClosure OC 3"a a a b a a b -> a b b a b b a b c b a b c c b a c c c
by OverlapClosure OC 3"a a a b a a b -> a b b a b b a b c b a b c c c b c c c
by OverlapClosure OC 3"a a a b a a b -> a b b a b b a b c b a a a b c c c
by OverlapClosure OC 2"a a a b a a b -> a b b a b b a b c b a a a a a
by OverlapClosure OC 3"a a a b a a b -> a b b a b b a b c c b a a a a
by OverlapClosure OC 3"a a a b a a b -> a b b a b b a b c c c b a a a
by OverlapClosure OC 3"a a a b a a b -> a b b a b b a a a b a a a
by OverlapClosure OC 3"a a a b a a b -> a b b a b b a a a c b a a
by OverlapClosure OC 3"a a a b a a b -> a b b a b b a a a c c b a
by OverlapClosure OC 2"a a a b a a -> a b b a b b a a a c c c
by OverlapClosure OC 3"a a a b a a -> a b b a b c b a a c c c
by OverlapClosure OC 3"a a a b a a -> a b b a b c c b a c c c
by OverlapClosure OC 3"a a a b a a -> a b b a b c c c b c c c
by OverlapClosure OC 3"a a a b a a -> a b b a a a b c c c
by OverlapClosure OC 2"a a a b -> a b b a a a
by OverlapClosure OC 3"a a a b -> a b c b a a
by OverlapClosure OC 3"a a a b -> a b c c b a
by OverlapClosure OC 2"a a a -> a b c c c
by original rule (OC 1)""c b -> b a
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""a a a -> a b c c c
by original rule (OC 1)"""a a a -> a b c c c
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""a a a -> a b c c c
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""a a a -> a b c c c
by original rule (OC 1)"""a a a -> a b c c c
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""a a a b -> a b b a a a
by OverlapClosure OC 3"a a a b -> a b c b a a
by OverlapClosure OC 3"a a a b -> a b c c b a
by OverlapClosure OC 2"a a a -> a b c c c
by original rule (OC 1)""c b -> b a
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)"""c b -> b a
by original rule (OC 1)""""a a a -> a b c c c
by original rule (OC 1)"

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(2)
NO