  There are two subgraphs $X,Y$ of the $2$-dimensional integer grid such that
for any $k<l$ there is an infinite subset $I\subset \mathbb{N}$ such that the
$k$-wiring profile of $X$ into $Y$ grows quadratically on $I$ while the
$l$-wiring profile of $X$ into $Y$ grows linearly on $I$. This resolves
Question 7.8 of Barrett-Hume.
