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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

a → b
by original rule (OC 1)

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

a → b
by original rule (OC 1)

a → b
by original rule (OC 1)

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

a → b
by original rule (OC 1)

a → b
by original rule (OC 1)

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

a → b
by original rule (OC 1)

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

a → b
by original rule (OC 1)

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

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

a → b
by original rule (OC 1)

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

(4) NO