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

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

(2) NO