Quick question about finding the PID of long-running processes

The end result that I'd like is to terminate any process on my ps -u username list that extends beyond 20 minutes. I know for a fact that this process will be named l[0-999].exe, but I don't know the number in between and I won't know the PID. Is there a way to use grep or pidof to do this task every 20 minutes or so?

Thanks!

The proper way to do this, instead of grepping ps and hoping nothing goes wrong or false matches don't turn up, would be to save the PID in the first place so you can look it up later, usually in a PID file. How is this process being launched?

The problem is that the PID and the process name is always being changed. The only thing that is relatively constant is the time iteration. I myself don't know the way this is being done because it was coded by someone else, but I do know that I occasionally have to kill anything that the system gets caught up on. The arbitrary value that the group I'm working in has set the system caught time to 20 minutes.