Knuth-Bendix looks a lot similar to the Gröbner basis methods of computational commutative algebra. I haven't yet really started looking into non-commutative Gröbner bases (though the Diamond lemma paper is in my "To read"-pile); but reading through that wikipedia page really did sound a lot like what I've seen in commutative algebra/algebraic geometry.

If ever you figure out just what the Thompson groups can do, please tell me, mmkay?