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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 2231 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(a(b(x1))) -> c(c(c(x1)))
   c(x1) -> b(a(x1))
   c(b(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 a b a b a b -> b b a a b a b a b"
a a b a b a b -> b b a a b a b a b
by OverlapClosure OC 3"a a b a b a b -> b b a a c b a b
by OverlapClosure OC 2"a a b a b -> b b a a a
by OverlapClosure OC 3"a a b a b -> c a b a
by OverlapClosure OC 2"a a b -> c a
by OverlapClosure OC 3"a a b -> c c b a
by OverlapClosure OC 2"a a b -> c c c
by original rule (OC 1)""c -> b a
by original rule (OC 1)"""c b -> 
by original rule (OC 1)"""a a b -> a b a
by OverlapClosure OC 3"a a b -> c b a b a
by OverlapClosure OC 3"a a b -> c c b a
by OverlapClosure OC 2"a a b -> c c c
by original rule (OC 1)""c -> b a
by original rule (OC 1)"""c -> b a
by original rule (OC 1)"""c b -> 
by original rule (OC 1)""""c a b -> b b a a
by OverlapClosure OC 3"c a b -> b b a c b a
by OverlapClosure OC 2"c -> b a
by original rule (OC 1)""a a b -> b a c b a
by OverlapClosure OC 3"a a b -> c c b a
by OverlapClosure OC 2"a a b -> c c c
by original rule (OC 1)""c -> b a
by original rule (OC 1)"""c -> b a
by original rule (OC 1)""""c b -> 
by original rule (OC 1)""""a a b -> c b a b
by OverlapClosure OC 2"a a b -> c b a c
by OverlapClosure OC 3"a a b -> c c c
by original rule (OC 1)""c -> b a
by original rule (OC 1)"""c -> b
by OverlapClosure OC 2"c -> b a
by original rule (OC 1)""a -> 
by original rule (OC 1)"""""c -> b a
by original rule (OC 1)"

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(2)
NO