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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 44 ms]
(2) NO


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

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

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(2)
NO