Here is my verification on RA 6.6 in house.
- Role is user without additional options.
- Check "Application Publisher" to an application for the user.
When the permission is disabled, Delete button is disabled.
- Check "Execute Process" permission to process tag to delete.
You can implement with some ways.
Case 1) For all processes on all environments in specified application.
Case 2) For all processes on specified environment in an application.
Selected an environment and Enable "Can Execute All Processes".
Case 3) For specified tagged process.
Disable "Can Execute All Processes" in Case2 and Check target tags.
I think above is minimum requirement.
I hope my info helps you.