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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 510 ms]
(2) NO


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

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

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(2)
NO