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