I think you're right w.r.t re-usability, though I've found semi-Thue systems more useful for formulating Turing Machines in order to avoid shifting things aroun

I think you're right w.r.t re-usability, though I've found semi-Thue systems more useful for formulating Turing Machines in order to avoid shifting things around. The string can just expand as needed, though the complexity probably changes.