Overhead For Autoshrink, Autostats

Does anyone have any benchmarks for the amount of overhead caused by autoshrink of the log and having autostats enabled? We have a customer that insists that turning off these options was necessary to eliminate a performance problem they were having (Query timeouts), but we are not convinced that these two options would have generated enough overhead to have been the root cause (they also rebuilt all their indexes and made some other unspecified changes that more likely solved the problem).

We are hestitant to have them continue with these options disabled because then we need to rely on them to keep the log file shrunk and the statistics updated and because of the data changes during the day, would prefer to have stats updated automatically rather than on a fixed schedule that may not be as appropriate.

Anyway, if anyone has any feedback on overhead generated and potential performance implications of having either of these options enabled, it would be greatly appreciated.

Thanks,
Ray Rankins