The realization space is
  [1   1   0       x3 - 1   0   1   1    0       x3 - 1         1    1]
  [0   1   1   x2*x3 - x3   0   0   1    1   x2*x3 - x3   -x2 + 1   x3]
  [0   0   0            0   1   1   1   x1   x2*x3 - x2        x2   x3]
in the multivariate polynomial ring in 3 variables over ZZ
within the vanishing set of the ideal
Ideal (x2^2 - 3*x2*x3 + x2 + 2*x3 - 1)
avoiding the zero loci of the polynomials
RingElem[x3, 2*x2 - 1, x2, 2*x3 - 1, x2 - x3, x2 + x3 - 1, x2 - 1, x3 - 1, x1*x2 + x1*x3 - x1 + x2 - x3, x1*x3 - x3 + 1, x1 - 1, x1*x3 - x1 - x3, x1, x1*x2 - x1*x3 + x3 - 1, x2*x3 - 2*x3 + 1, x1*x2 - x1 + x2, x1 + 1, 2*x1*x2*x3 - x1*x2 - 2*x1*x3 + x1 + x2*x3 - x2, x1*x2 + x2 - 1, x2^2*x3 - 4*x2*x3 + 2*x2 + 2*x3 - 1, x1*x2*x3 - x1*x3 - x2*x3 + x2, x1*x2*x3 - 2*x1*x3 + x1 - x2*x3 + x2, x1*x2*x3 - 2*x1*x3 + x1 - x2*x3 + x2 + x3 - 1, x1*x2*x3 - 2*x1*x3 + x1 + x3 - 1, x1*x2*x3 - x1*x3 + x3 - 1]