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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 4766 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))) -> a(c(c(a(a(a(x1))))))
   a(c(x1)) -> b(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 b a b c b c -> b c b c b c a b c a a b a b c b c a a a"
a a b a b c b c -> b c b c b c a b c a a b a b c b c a a a
by OverlapClosure OC 3"a a b a b c b c -> b c b c b c a b c a a b a b c a c c a a a
by OverlapClosure OC 2"a a b a b c -> b c b c b c a b c a a b a a a
by OverlapClosure OC 3"a a b a b c -> b c b c b c a a a b c a a a
by OverlapClosure OC 3"a a b a b c -> b c b c a a b b c a a a
by OverlapClosure OC 2"a a b a b c -> b c b c a a b a a b
by OverlapClosure OC 3"a a b a b c -> b c a a b c a a b
by OverlapClosure OC 2"a a b -> b c a a a
by OverlapClosure OC 3"a a b -> a c c a a a
by original rule (OC 1)""a c -> b
by original rule (OC 1)"""a a b c -> b c a a b
by OverlapClosure OC 3"a a b c -> a c c a a b
by OverlapClosure OC 2"a a b -> a c c a a a
by original rule (OC 1)""a c -> b
by original rule (OC 1)"""a c -> b
by original rule (OC 1)""""a a b c -> b c a a b
by OverlapClosure OC 3"a a b c -> a c c a a b
by OverlapClosure OC 2"a a b -> a c c a a a
by original rule (OC 1)""a c -> b
by original rule (OC 1)"""a c -> b
by original rule (OC 1)""""a a b -> b c a a a
by OverlapClosure OC 3"a a b -> a c c a a a
by original rule (OC 1)""a c -> b
by original rule (OC 1)""""a a b -> b c a a a
by OverlapClosure OC 3"a a b -> a c c a a a
by original rule (OC 1)""a c -> b
by original rule (OC 1)""""a a b c -> b c a a b
by OverlapClosure OC 3"a a b c -> a c c a a b
by OverlapClosure OC 2"a a b -> a c c a a a
by original rule (OC 1)""a c -> b
by original rule (OC 1)"""a c -> b
by original rule (OC 1)""""a a b c -> b c a c c a a a
by OverlapClosure OC 2"a a b c -> b c a a b
by OverlapClosure OC 3"a a b c -> a c c a a b
by OverlapClosure OC 2"a a b -> a c c a a a
by original rule (OC 1)""a c -> b
by original rule (OC 1)"""a c -> b
by original rule (OC 1)"""a a b -> a c c a a a
by original rule (OC 1)""""a c -> b
by original rule (OC 1)"

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(2)
NO