In this paper, we prove a closed formula for the degree of regularity of the family of HFE- (HFE Minus) multivariate public key cryptosystems over a finite field of size q. The degree of regularity of the polynomial system derived from an HFE- system is less than or equal to
\begin{eqnarray*}
\frac{(q-1)(\lfloor \log_q(D-1)\rfloor +a)}2 +2 & &
\text{if is even and is odd,} \\
\frac{(q-1)(\lfloor \log_q(D-1)\rfloor+a+1)}2 +2 & &
\text{otherwise.}
\end{eqnarray*}
Here q is the base field size, D the degree of the HFE polynomial, r=\lfloor \log_q(D-1)\rfloor +1 and a is the number of removed equations (Minus number).
This allows us to present an estimate of the complexity of breaking the HFE Challenge 2:
\begin{itemize}
\item the complexity to break the HFE Challenge 2 directly using algebraic solvers is about 2^{96}.
\end{itemize}