The realization space is
  [1   1   0                           x1*x2 - x1   0   1   1    0                           x1*x2 - x1            x1       x1]
  [0   1   1   -x1*x2^2 + 2*x1*x2 - 2*x1 + x2 - 1   0   0   1    1   -x1*x2^2 + 2*x1*x2 - 2*x1 + x2 - 1        x2 - 1   x2 - 1]
  [0   0   0                                    0   1   1   1   x1                      x1*x2^2 - x1*x2   x1 - x2 + 1    x1*x2]
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[x1 + 1, x2 - 1, x1 - x2 + 1, x1*x2^2 - 2*x1*x2 + 2*x1 + x2^2 - 3*x2 + 2, x2, x1, x1*x2^2 - 2*x1*x2 + 2*x1 - 2*x2 + 2, x1*x2 - x2 + 1, x1*x2^2 - x1*x2 + 2*x1 - 2*x2 + 2, x1*x2^2 - 2*x1*x2 + 2*x1 - x2 + 1, x1*x2^2 - x1*x2 + x1 - x2 + 1, x1^2*x2 - x1^2 + x1*x2 - x2 + 1, x1^2*x2^2 - 2*x1^2*x2 + 2*x1^2 + 2*x1*x2^2 - 5*x1*x2 + 3*x1 + x2^2 - 2*x2 + 1, x1*x2 - 2*x1 + x2 - 1, x1^2 - x1*x2 + x1 - x2 + 1, x1 - 2*x2 + 2, x1^2 - x1*x2^2 + x2 - 1, x1*x2^2 - 2*x1*x2 + 2*x1 + x2^2 - 2*x2 + 1, x1*x2^2 - x1*x2 + x1 + x2^2 - 2*x2 + 1, x1*x2^2 - x1*x2 + x1 + x2^2 - 3*x2 + 2, 2*x1*x2^2 - 3*x1*x2 + 2*x1 - x2 + 1, x1 - 1, x1*x2^2 - x1*x2 + x1 - 2*x2 + 2]