@Article{ KufleitnerLauser12dmtcs, author = "Manfred Kufleitner and Alexander Lauser", title = "The Join of the Varieties of {R}-trivial and {L}-trivial Monoids via Combinatorics on Words", journal = "Discrete Mathematics {\&} Theoretical Computer Science", volume = "14", number = "1", year = "2012", pages = "141--146", abstract = "The join of two varieties is the smallest variety containing both. In finite semigroup theory, the varieties of $\mathcal{R}$-trivial and $\mathcal{L}$-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 $\mathcal{R}$-trivial and $\mathcal{L}$-trivial monoids. This characterization is a single identity of $\omega$-terms using three variables." }