sentences:  Levi's lemma can be applied repeatedly in order to solve word equations; in this context it is sometimes called the Nielsen transformation by analogy with the Nielsen transformation for groups.For example, starting with an equation "xα" = "yβ" where "x" and "y" are the unknowns, we can transform it (assuming "|x| ≥ |y|", so there exists "t" such that "x"="yt") to "ytα" = "yβ", thus to "tα" = "β".This approach results in a graph of substitutions generated by repeatedly applying Levi's lemma.