The realization space is
  [1   0   1   0   1   0   1    2      2              4]
  [0   1   1   1   1   0   2    0   2*x1           4*x1]
  [0   0   0   1   1   1   1   x1     x1   -x1^2 + 4*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (4*x1^3 - 24*x1^2 + 32*x1)
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 2, x1 - 1, 2, x1 + 2, x1 - 4]