  Let $G$ be a random torsion-free nilpotent group generated by two random
words of length $\ell$ in $U_n(\mathbb{Z})$. Letting $\ell$ grow as a function
of $n$, we analyze the step of $G$, which is bounded by the step of
$U_n(\mathbb{Z})$. We prove a conjecture of Delp, Dymarz, and Schafer-Cohen,
that the threshold function for full step is $\ell = n^2$.
