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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 416 ms]
(2) NO


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

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

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(2)
NO