  We have undertaken an algorithmic search for new integrable
semi-discretizations of physically relevant nonlinear partial differential
equations. The search is performed by using a compatibility condition for the
discrete Lax operators and symbolic computations. We have discovered a new
integrable system of coupled nonlinear Schrodinger equations which combines
elements of the Ablowitz-Ladik lattice and the triangular-lattice ribbon
studied by Vakhnenko. We show that the continuum limit of the new integrable
system is given by uncoupled complex modified Korteweg-de Vries equations and
uncoupled nonlinear Schrodinger equations.
