Can I evict for this rule being broken in the lease?

[Tim Callahan]

Hi, we have a lease that allows dogs as long as they are on a leash at all times when the dog is outside and on the property.  This is specifically stated in the lease.  It's a safely issue for us, as we live in another unit in the house.  Now I have a tenant who has broken this rule several times, letting their small dog run free everywhere. It ran after a car coming up the driveway the other day and was barking at our guests. 

We have posted warning letters on their door twice now about this.

How would we fare if we started eviction proceedings because the tenant refuses to obey this rule?  

[Nathan Gesner]

Quote from @Tim Callahan:

Yes, you can remove a tenant for lease violations. It's technically a termination of their lease, not an eviction, which would be a court action. You would only evict if they refuse to leave.

I issue a written warning the first time. The second time, I issue a written warning and notify them that another violation will result in termination of their lease. The third time, I give them a 30-day notice of termination and get them out.