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