NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Waldmann_06_SRS/uni-2.srs

Termination w.r.t. Q of the given QTRS could be disproven:

0 QTRS
↳1 NonTerminationProof (⇒, 64 ms)
↳2 NO

(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

a(a(a(a(x)))) → a(c(a(c(c(x)))))
c(c(c(x))) → a(a(a(x)))

Q is empty.

(1) NonTerminationProof (COMPLETE transformation)

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)

(2) NO