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

0 QTRS
↳1 NonTerminationProof (⇔, 774 ms)
↳2 NO

(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.

(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 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)

(2) NO