Solution
= Solution
For the <wave equation>[wave operator] $\partial_x^2-\partial_y^2$, use the symbol
$$
P(\xi,\eta)=\eta^2-\xi^2
$$
and complexify $\eta$. Its roots $\eta=\pm\xi$ are real for every real $\xi$, so the single horizontal step
$$
\boxed{\operatorname{Im}\eta=1}
$$
never meets a root and is an explicit <Hörmander staircase>.