TimeConstraint is an option for Simplify and FullSimplify which gives the maximum number of seconds for which to try any particular transformation on any subpart of an expression.
The default setting for TimeConstraint is 300 (corresponding to 5 minutes) in Simplify and Infinity in FullSimplify.
Settings for TimeConstraint give only the maximum time to be spent in doing a particular transformation on a particular subpart; the total time spent in processing the whole expression may be considerably larger.
Changing the setting for TimeConstraint will never affect the validity of a result obtained from Simplify or FullSimplify, but smaller settings may prevent the simplest possible form from being found.
Since different computer systems run at different speeds, the same setting for TimeConstraint can lead to different results on different systems.
See The Mathematica Book: Section 3.3.9.
See also: ExcludedForms, TimeConstrained.