  We provide an algorithm to check whether a given vacuum space-time
$(\mathcal{M},g)$ admits a Killing vector field w.r.t. which the Mars-Simon
tensor vanishes. In particular, we obtain an algorithmic procedure to check
whether $(\mathcal{M},g)$ is locally isometric to a member of the
Kerr-NUT-(A)dS family. A particular emphasis will be devoted to the Kerr-(A)dS
case.
