  We consider nonsymmetric operads with two binary operations satisfying
relations in arity 3; hence these operads are quadratic, and so we can
investigate Koszul duality. We first consider operations which are
nonassociative (not necessarily associative) and then specialize to the
associative case. We obtain a complete classification of self-dual quadratic
nonsymmetric operads with two (associative or nonassociative) binary
operations. These operads generalize associativity for one operation to the
setting of two operations.
