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