  We describe several technical tools that prove to be efficient for
investigating the rewrite systems associated with a family of algebraic laws,
and might be useful for more general rewrite systems. These tools consist in
introducing a monoid of partial operators, listing the monoid relations
expressing the possible local confluence of the rewrite system, then
introducing the group presented by these relations, and finally replacing the
initial rewrite system with a internal process entirely sitting in the latter
group. When the approach can be completed, one typically obtains a practical
method for constructing algebras satisfying prescribed laws and for solving the
associated word problem.
