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

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

(2) NO