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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 7687 ms]
(2) NO


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

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

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(2)
NO