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

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

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

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

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

b a → c b
by original rule (OC 1)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

b a a a → c c
by OverlapClosure OC 2

b a → c b
by original rule (OC 1)

b a a → c
by OverlapClosure OC 2

b a → c b
by original rule (OC 1)

b a →
by original rule (OC 1)

c a → a a a b
by original rule (OC 1)

c a → a a a b
by original rule (OC 1)

b a → c b
by original rule (OC 1)

b a → c b
by original rule (OC 1)

b a a → c
by OverlapClosure OC 2

b a → c b
by original rule (OC 1)

b a →
by original rule (OC 1)

c a → a a a b
by original rule (OC 1)

b a → c b
by original rule (OC 1)

b a →
by original rule (OC 1)

c a → a a a b
by original rule (OC 1)

c a → a a a b
by original rule (OC 1)

b a →
by original rule (OC 1)

c a → a a a b
by original rule (OC 1)

b a → c b
by original rule (OC 1)

b a →
by original rule (OC 1)

c a → a a a b
by original rule (OC 1)

c a → a a a b
by original rule (OC 1)

(4) NO