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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 738 ms]
(2) NO


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

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

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(2)
NO