Let A be the free algebra K< x1, ..., xn > of rank n over a field K. A word in the underlying monoid of A is simply an associative product of the letters (or variables) of A. For consistency with the commutative case, we will call these monoid words monomials. Elements of A, called noncommutative polynomials, are finite sums of terms, where a term is the product of a coefficient from K and a monomial. The terms are sorted with respect to an admissible order <, which satisfies, for monomials p, q, r, the following conditions: