\].  Given an input $(W, 0^n)$, where $W$ is a nonempty word (not necessarily reduced) over the alphabet ${\mathcal{A}}^{\pm 0}$ and $n \ge 0$ is an integer, written in unary notation as $0^n$, we begin with the empty [pseudobracket system]{}  and nondeterministically apply a sequence of [elementary operation]{}s of size 