I have used Compiz 0.8.4 for a three years and upgraded it to 0.9.13 just after it appeared in official Debian Stretch repo. 0.9.13 worked almost fine though it needed reconfiguration. But after reboot I frequently get freezes on animations; not only Compiz ones but also GTK+3 (ripple effect), Firefox tab animations, probably on any active screen refreshes. The input is still processed, even the mouse cursor is moved but all the screen image keeps static and continues repainting only after I go to tty1 and back. I did not notice such issue if running another WM instead, f.e., Openbox. Checking and unchecking options of OpenGL plugin does not help. Looks similar to the old bug #353514.
System: Linux localhost 4.8.0-2-amd64 #1 SMP Debian 4.8.11-1 (2016-12-02) x86_64 GNU/Linux
Compiz version: 0.9.13.0+16.10.20160818.2-4
Seems like this is not directly a Compiz issue, but rather a X.Org or Radeon driver one. Firstly I disabled the animations plugin but still was getting freezes on animations in applications. So I temporarily replaced Compiz with Marco and during this couple of days did not get X.Org completely frozen but browser windows themselves (Firefox and Chromium) are still sometimes getting frozen. Switching to TTY and back resolves the freeze just like with the full freeze when running Compiz. So I move this issue to X.Org bugtracker.