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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 3033 ms]
(2) NO


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

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

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(2)
NO