  We construct new examples of non-nil algebras with any number of generators,
which are direct sums of two locally nilpotent subalgebras. As all previously
known examples, our examples are contracted semigroup algebras and the
underlying semigroups are unions of locally nilpotent subsemigroups. In our
constructions we make more transparent than in the past the close relationship
between the considered problem and combinatorics of words.
