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