Regular expressions with numeric occurrence indicators are an extension of traditional
regular expressions, which let the required minimum and the allowed maximum number of
iterations of subexpressions be described with numeric parameters. We consider the problem of
testing whether a given regular expression E with numeric occurrence indicators is
1-unambiguous or not. This condition means, informally, that any prefix of any word accepted
by expression E determines a unique path of matching symbol positions in E. The main
contribution of this paper is a polynomial-time method for solving this problem, and a formal
proof of its correctness.