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

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

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

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

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

c a → b c
by OverlapClosure OC 3

c a → a b c
by OverlapClosure OC 3

c a → a a b c
by original rule (OC 1)

a →
by original rule (OC 1)

a →
by original rule (OC 1)

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

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

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

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

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

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

c a → a a b c
by original rule (OC 1)

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

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

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

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

c a → a a b c
by original rule (OC 1)

c a → a a b c
by original rule (OC 1)

b a a → a c
by original rule (OC 1)

c a → a a b c
by original rule (OC 1)

b a a → a c
by original rule (OC 1)

c a → a a b c
by original rule (OC 1)

b a a → a c
by original rule (OC 1)

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

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

c a → a b c
by OverlapClosure OC 3

c a → a a b c
by original rule (OC 1)

a →
by original rule (OC 1)

c a → a a b c
by original rule (OC 1)

b a a → a c
by original rule (OC 1)

c a → a a b c
by original rule (OC 1)

b a a → a c
by original rule (OC 1)

c a → a a b c
by original rule (OC 1)

b a a → a c
by original rule (OC 1)

(4) NO