the negative of rinne me is ní dhearna mé.
Makes perfect sense......
My understanding is that rinne came from ro-ghní and ní dhearna came from ní do ro-ghní. (In Dinneen’s dictionary, the headword for déan was still do-ghním.)
Coincidentally, I just did an exercise with "activity" - gníomhaíocht, which I presume is the same root.
Indeed it is.