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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1089 ms]
(2) NO


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

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

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(2)
NO