Constructing an unrestricted grammar for a^n b^m c^n d^m
How about the following:
$$
\begin{align*}
&amp;S \to XY \\
&amp;X \to aXC | aC \\
&amp;Y \to BYd | Bd \\
&amp;CB \to BC \\
&amp;aB \to ab \\
&amp;bB \to bb \\
&amp;Cd \to cd \\
&amp;Cc \to cc \\
\end{align*}
$$
In this grammar you need to apply $O(nm)$ rules to get $a^nb^mc^nd^m$.