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

(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.

(1) NonTerminationProof (EQUIVALENT 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