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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 22.3 s]
(2) NO


----------------------------------------

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

   a(a(b(x1))) -> a(b(c(a(a(x1)))))
   a(c(x1)) -> b(a(x1))

Q is empty.

----------------------------------------

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

----------------------------------------

(2)
NO