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

c a a a a a → b b b c a a a a a c

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

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

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

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

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

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

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

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

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

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

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

c a a → b c c
by OverlapClosure OC 3

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

c a → b c b c
by original rule (OC 1)

c a → a c
by OverlapClosure OC 3

c a → b a a c
by OverlapClosure OC 3

c a → b c b c
by original rule (OC 1)

c b → a a
by original rule (OC 1)

b a →
by original rule (OC 1)

b a →
by original rule (OC 1)

c a → a c
by OverlapClosure OC 3

c a → b a a c
by OverlapClosure OC 3

c a → b c b c
by original rule (OC 1)

c b → a a
by original rule (OC 1)

b a →
by original rule (OC 1)

c a → b c b c
by original rule (OC 1)

c a → b c b c
by original rule (OC 1)

c b → a a
by original rule (OC 1)

b a →
by original rule (OC 1)

c b → a a
by original rule (OC 1)

c a a → b c c
by OverlapClosure OC 3

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

c a → b c b c
by original rule (OC 1)

c a → a c
by OverlapClosure OC 3

c a → b a a c
by OverlapClosure OC 3

c a → b c b c
by original rule (OC 1)

c b → a a
by original rule (OC 1)

b a →
by original rule (OC 1)

b a →
by original rule (OC 1)

c a → a c
by OverlapClosure OC 3

c a → b a a c
by OverlapClosure OC 3

c a → b c b c
by original rule (OC 1)

c b → a a
by original rule (OC 1)

b a →
by original rule (OC 1)

c a → b c b c
by original rule (OC 1)

c b → a a
by original rule (OC 1)

c b → a a
by original rule (OC 1)

(4) NO