Groebner-Shirshov bases for some one-relator groups

In this paper, we prove that two-generator one-relator groups with depth less than or equal to 3 can be effectively embedded into a tower of HNN-extensions in which each group has the effective standard normal form. We give an example to show how to deal with some general cases for one-relator groups. By using the Magnus method and Composition-Diamond Lemma, we reprove the G. Higman, B. H. Neumann and H. Neumann's embedding theorem.