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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 4676 ms]
(2) NO


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

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

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(2)
NO