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(x1)) → b(x1)
a(b(c(x1))) → a(c(c(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:

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

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

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

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

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

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

a a → b
by original rule (OC 1)

a a → b
by original rule (OC 1)

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

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

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

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

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

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

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

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

a a → b
by original rule (OC 1)

a a → b
by original rule (OC 1)

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

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

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

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

a a → b
by original rule (OC 1)

a a → b
by original rule (OC 1)

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

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

a a → b
by original rule (OC 1)

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

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

a a → b
by original rule (OC 1)

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

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

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

a a → b
by original rule (OC 1)

a a → b
by original rule (OC 1)

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

(4) NO