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