Inverting square systems algebraically is exponential

In this paper, we prove that the degree of regularity of square systems, a subfamily of the HFE systems, over a prime finite field of odd characteristic q is exactly q   and, therefore, prove that inverting square systems algebraically using Gröbner basis algorithm is exponential, when q=Ω(n)q=Ω(n), where n is the number of variables of the system.