Let \(V\) be finite dimensional vector space over a field \(K\) and denote \(V^{(n)}=V^{\otimes n}\). Fix a totally ordered basis \(X\) of \(V\) and let \(X^{(n)}\) be the corresponding lexicographically ordered basis of \(V^{(n)}\). If \(E\) is a subspace of \(V^{(2)}\) consider the ideal \(I(E)\) generated by \(E\) in the tensor algebra \(\text{Tens}(V)\) of \(V\). The quotient \(\text{Tens}(V)/I(V)\) is a quadratic algebra on \(V\). It inherits the natural grading on \(\text{Tens}(V)\). Call \(E\) the space of relations of \(A\). An \(X\)-reduction operator \(T\in\hom V\) is an idempotent such that for every \(X\)-generator \(a\) either \(T(a)=a\) (and \(a\) is reduced) or \(T(a)