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

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

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

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

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

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

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

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

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

a → b
by original rule (OC 1)

a → b
by original rule (OC 1)

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

a → b
by original rule (OC 1)

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

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

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

b b c → c c a 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)

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

a → b
by original rule (OC 1)

a → b
by original rule (OC 1)

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

(4) NO