The aim is to study the set of subsets of grids of the Waterloo language from the point of view of abstract algebra and graph theory. The study was conducted using the library for working with transition graphs of nondeterministic finite automata NFALib implemented by one of the authors in C#, as well as statistical methods for analyzing algorithms. The results are regularities obtained when considering semilattices on a set of subsets of grids of the Waterloo language. It follows from the results obtained that the minimum covering automaton equivalent to the Waterloo automaton can be obtained by adding one additional to the minimum covering set of grids.