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