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(b(c(a(a(x1)))))
a(c(x1)) → a(a(x1))

Q is empty.

(1) NonTerminationProof (EQUIVALENT transformation)

We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.

Found the self-embedding DerivationStructure:

a a b c a b b c b b → b b c b b c b b c a b b c a a b c a b b c b b c a a

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

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

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

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

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

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

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

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

a c → a a
by original rule (OC 1)

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

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

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

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

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

a c → a a
by original rule (OC 1)

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

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

a c → a a
by original rule (OC 1)

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

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

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

(2) NO