Subsequently, the existence of the fixed point found within the Einstein – Hilbert truncation has been confirmed in subspaces of successively increasing complexity. The next step in this development was the inclusion of an R 2 -term in the truncation ansatz. This has been extended further by taking into account polynomials of the scalar curvature R (so-called f ( R ) -truncations), and the square of the Weyl curvature tensor. Also, f(R) theories have been investigated in the Local Potential Approximation finding nonperturbative fixed points in support of the Asymptotic Safety scenario, leading to the so-called Benedetti – Caravelli (BC) fixed point. In such BC formulation, the differential equation for the Ricci scalar R is overconstrained, but some of these constraints can be removed via the resolution of movable singularities.