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

Q is empty.

(1) QTRS Reverse (EQUIVALENT transformation)

We applied the QTRS Reverse Processor [REVERSE].

(2) Obligation:

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

a(x) → x
b(a(x)) → a(a(b(b(c(a(x))))))
b(x) → x
c(c(x)) → x

Q is empty.

(3) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.

Found the self-embedding DerivationStructure:

b a c a → b a c a

b a c a → b a c a
by OverlapClosure OC 3

b a c a → b a a c a
by OverlapClosure OC 2

b a c → b b
by OverlapClosure OC 3

b a c → a b b
by OverlapClosure OC 3

b a c → a a b b
by OverlapClosure OC 2

b a → a a b b c
by OverlapClosure OC 2

b a → a a b b c a
by original rule (OC 1)

a →
by original rule (OC 1)

c c →
by original rule (OC 1)

a →
by original rule (OC 1)

a →
by original rule (OC 1)

b a → a a c a
by OverlapClosure OC 3

b a → a a b c a
by OverlapClosure OC 3

b a → a a b b c a
by original rule (OC 1)

b →
by original rule (OC 1)

b →
by original rule (OC 1)

a →
by original rule (OC 1)

(4) NO