Processes have limited space available (limited by physical resources and memory-addressing issues), but generally unlimited time. You usually cannot "run out of" time, you can just "take more" time. The only thing I can think of is if the OS imposes a CPU time limit on the process. Exceeding the limit manifests itself by the OS killing the process.

Also, this doc desparately needs to be patched: s/Non-Finite/Nondeterministic Finite/; "Non-finite" just makes me chuckle/cringe.