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