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

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

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

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

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

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

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

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

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

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

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

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

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

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

c a →
by original rule (OC 1)

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

c a →
by original rule (OC 1)

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

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

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

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

c a →
by original rule (OC 1)

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

c a →
by original rule (OC 1)

(4) NO