You should be interested in the discussion in
Evans, G.~A. and Wensley, C.~D. {Complete involutive rewriting systems}. {J. Symbolic Comput.} \textbf{42}~(11-12) (2007) 1034--1051.
on the notion of noncommutative involutive systems, which in the commutative case are a well known modification of the Grobner basis theory. Evans' thesis is available at math.RA/0602140.
I can't help on the proposed applications.
Ronnie Brown