On intersections of normal subgroups in groups

The paper is a generalization of [2]. For a group $H=\langle A|O\rangle$, conditions for the equality $\bar N_1\cap \bar N_2 = [\bar N_1,\bar N_2]$ are given in terms of pictures, where $\bar N_i$ is the normal closure of a set $\bar R_i\subset H$ for $i=1,2$.