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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

c a → a b
by original rule (OC 1)

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

c a → a b
by original rule (OC 1)

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

c a → a b
by original rule (OC 1)

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

c a → a b
by original rule (OC 1)

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

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

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

c a → a b
by original rule (OC 1)

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

c a → a b
by original rule (OC 1)

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

(4) NO