  In this paper, we establish the Composition-Diamond lemma for associative
nonunitary Rota-Baxter algebras with weight $\lambda$. As applications, we
obtain a linear basis of a free commutative Rota-Baxter algebra without unity
and show that every countably generated Rota-Baxter algebra with weight 0 can
be embedded into a two-generated Rota-Baxter algebra.
