Is $\lceil\log n\rceil!$ polynomially bounded?
Don't trust plots.

By Stirling's approximation (and dropping the ceilings to avoid notational overload),

$$\begin{align*}
(\log n)! &amp;\sim \sqrt{2\pi \log n}\left(\frac{\log n}{e}\right)^{\log n}\\
  &amp;= \sqrt{2\pi \log n}\, e^{(\log\log n - 1)\log n}\\
  &amp;= \sqrt{2\pi \log n}\, n^{\log\log n - 1}\,,
\end{align*}$$

which grows faster than any polynomial.  But you're not going to see that by plotting versus $n^{100}$ unless you consider values of $n$ big enough that $\log\log n$ is more than about&nbsp;$99$, i.e., roughly $n\geq e^{e^{99}}\approx 10^{10^{42}}$, and you probably didn't consider values of&nbsp;$n$ quite that big, because no plotting software is going to display values like $(10^{10^{42}})^{100}$.