The realization space is
  [1   0   1   0   1    0     x1 + x2 - 1                                           x1*x2 + x2^2 - x2                                           x1*x2 + x2^2 - x2            x2    1]
  [0   1   1   0   0    1     x1 + x2 - 1   -x1*x2^2 + 2*x1*x2 - x1 - x2^4 + x2^3 + 2*x2^2 - 3*x2 + 1   -x1*x2^2 + 2*x1*x2 - x1 - x2^4 + x2^3 + 2*x2^2 - 3*x2 + 1   x1 + x2 - 1   x1]
  [0   0   0   1   1   -1   x1 + x2^2 - 1                              2*x1*x2 - x1 + x2^3 - 2*x2 + 1                                           x1*x2 + x2^3 - x2          x2^2   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, x2 - 1, x2, x1, x1 + x2, x1 + x2^2 - x2, x1 + x2^2 - 1, x1 + 2*x2 - 2, x1 + x2 - 1, x1 + x2^2 - x2 - 1, x1 + x2^2 + x2 - 1, x1^2 + x1*x2^2 - x1 + x2^3 - x2^2, 2*x1*x2 - x1 + x2^3 - 2*x2 + 1, 2*x1 + x2^2 + x2 - 2]