The class of very simple grammars is known to be polynomialtime identifiable in the limit from positive data. This paper introduces an extension of very simple grammars called right-unique simple grammars, and presents an algorithm that identifies right-unique simple grammars in the limit from positive data. The learning algorithm possesses the following three properties. It computes a conjecture in polynomial time in the size of the input data if we regard the cardinality of the alphabet as a constant. It always outputs a grammar which is consistent with the input data. It never changes the conjecture unless the newly provided example contradicts the previous conjecture. The algorithm has a sub-algorithm that solves the inclusion problem for a superclass of right-unique simple grammars, which is also presented in this paper.