  We study the dynamic critical behavior of a Swendsen--Wang--type algorithm
for the Ashkin--Teller model. We find that the Li--Sokal bound on the
autocorrelation time ($\tau_{{\rm int},{\cal E}} \ge {\rm const} \times C_H$)
holds along the self-dual curve of the symmetric Ashkin--Teller model, but this
bound is apparently not sharp. The ratio $\tau_{{\rm int},{\cal E}}/C_H$
appears to tend to infinity either as a logarithm or as a small power ($0.05
\ltapprox p \ltapprox 0.12$).
