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