  Suppose $A=\{a_1,\ldots,a_{n+2}\}\subset\mathbb{Z}^n$ has cardinality $n+2$,
with all the coordinates of the $a_j$ having absolute value at most $d$, and
the $a_j$ do not all lie in the same affine hyperplane. Suppose
$F=(f_1,\ldots,f_n)$ is an $n\times n$ polynomial system with generic integer
coefficients at most $H$ in absolute value, and $A$ the union of the sets of
exponent vectors of the $f_i$. We give the first algorithm that, for any fixed
$n$, counts exactly the number of real roots of $F$ in in time polynomial in
$\log(dH)$.
