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

0 QTRS
↳1 NonTerminationProof (⇔)
↳2 NO

(0) Obligation:

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

a(x1) → x1
a(b(x1)) → b(c(a(a(a(x1)))))
a(c(c(x1))) → 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 b b c c → b c b c a a b b c c

a b b c c → b c b c a a b b c c
by OverlapClosure OC 3
a b b c c → b c b c a a a c c b c c
by OverlapClosure OC 3
a b b c c → b c a b c c b c c
by OverlapClosure OC 3
a b b c c → b c a a b c b c c
by OverlapClosure OC 2
a b → b c a a a
by original rule (OC 1)
a b c c → b c b c c
by OverlapClosure OC 3
a b c c → b c a b c
by OverlapClosure OC 2
a b c c → b c a a b
by OverlapClosure OC 2
a b → b c a a a
by original rule (OC 1)
a c c → b
by original rule (OC 1)
a b → b c
by OverlapClosure OC 2
a b → b c a
by OverlapClosure OC 2
a b → b c a a
by OverlapClosure OC 2
a b → b c a a a
by original rule (OC 1)
a →
by original rule (OC 1)
a →
by original rule (OC 1)
a →
by original rule (OC 1)
a b → b c
by OverlapClosure OC 2
a b → b c a
by OverlapClosure OC 2
a b → b c a a
by OverlapClosure OC 2
a b → b c a a a
by original rule (OC 1)
a →
by original rule (OC 1)
a →
by original rule (OC 1)
a →
by original rule (OC 1)
a b → b c
by OverlapClosure OC 2
a b → b c a
by OverlapClosure OC 2
a b → b c a a
by OverlapClosure OC 2
a b → b c a a a
by original rule (OC 1)
a →
by original rule (OC 1)
a →
by original rule (OC 1)
a →
by original rule (OC 1)
a b → b c a a a
by original rule (OC 1)
a c c → b
by original rule (OC 1)

(2) NO