TimeConstraint->t specifies that a maximum of t seconds of CPU time should be spent trying a particular transformation or part of an algorithm.
TimeConstraint->Infinity specifies that there should be no limit on the CPU time allowed.
In functions such as Simplify and 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 functions like 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.