Clarification of Termination

My lease states:
Either can release each other at the end of 30 days written notice or at any time or 3 days notice of breach.
So question is they have not paid rent and I am trying to get them out quicker than eviction which gives them 30 plus if I win but 10 days to be served by court, court date to be set blah blah… etc).
On the non- renewal after 3 day notice I get a writ of possession and wait for the sheriff.
Is this about the way it goes?

The laws are state specific and in TX may be judge specific (they don’t always know or follow the law). However, the 3 day notice for breach is similar to a 30 day notice. After the 3 days is up and the breach is not cured, you then have to go to court to file for eviction (same as going to court if the tenant did not move out after the 30 day notice). True, you may have saved 27 days, but the judge is likely to give them time to cure the breach.

You will not be able to get a writ of possession or have the sheriff move them out until you go through the entire legal proceeding. If the breach is for a dangerous situation (not non-payment of rent), you might be able to get a court hearing sooner. Good luck, and when you go to court make sure you have all the paperwork you need (ask the clerk).