  Bracketed words are basic structures both in mathematics (such as Rota-Baxter
algebras) and mathematical physics (such as rooted trees) where the locations
of the substructures are important. In this paper we give the classification of
the relative locations of two bracketed subwords of a bracketed word in an
operated semigroup into the separated, nested and intersecting cases. We
achieve this by establishing a correspondence between relative locations of
bracketed words and those of words by applying the concept of Motzkin words
which are the algebraic forms of Motzkin paths.
