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