  Using methods of computer algebra, especially Gr\"obner bases for submodules
of free modules over polynomial rings, we solve a classification problem in
theory of algebraic operads: we show that the only nontrivial (possibly
inhomogeneous) distributive law between the operad of Lie algebras and the
operad of commutative associative algebras is given by the Livernet-Loday
formula deforming the Poisson operad into the associative operad.
