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