  Let $U$ be an arbitrary word in letters $x_1^{\pm 1}, ..., x_m^{\pm 1}$ and
$m \ge 2$. We prove that the group presentation $<x_1, ..., x_m \|\
  U x_i U^{-1} = x_{i+1}, i=1,..., m-1>$ is aspherical. The proof is based upon
prior partial results of A. Klyachko and the author on the asphericity of such
presentations.
