The realization space is
  [1   x1 + 1   1   1   0    1   0   x1    x1^2 + x1              0    1]
  [1       x1   0   0   1   x1   0   x1         x1^2           x1^3   x1]
  [1       x1   0   1   0    0   1   x2   x1*x2 + x2   x1^2*x2 - x2   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[x1^3 - x1^2*x2 - x1*x2 + x2, x2, x1 - 1, x1^2 - x1*x2 - x2, x1^2 - x2, x1 + 1, x1 - x2, x1, x2 - 1, x1*x2 - x1 + x2, x1^4 - x1^3*x2 - x2, x1^3 - x2, x1^3 - x1 + 1, x1^3*x2 + x1^3 - x1^2*x2 - x1*x2 + x2, x1^2*x2 + x1^2 - x2, x1^3 - x1^2*x2 + x2, x1 - x2 - 1]