  The join of two varieties is the smallest variety containing both. In finite
semigroup theory, the varieties of R-trivial and L-trivial monoids are two of
the most prominent classes of finite monoids. Their join is known to be
decidable due to a result of Almeida and Azevedo. In this paper, we give a new
proof for Almeida and Azevedo's effective characterization of the join of
R-trivial and L-trivial monoids. This characterization is a single identity of
omega-terms using three variables.
