The realization space is
  [1   0   1                           1   0   1    0             1                           1                               1    1]
  [0   1   1   -x1*x2 + x1 - x2^2 + 2*x2   0   0    1             1   -x1*x2 + x1 - x2^2 + 2*x2   -x1*x2 + x1 - x2^2 + 3*x2 - 1   x1]
  [0   0   0                           0   1   1   -1   x1 + x2 - 1                          x2                               1   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (x1*x2^2 - x1*x2 + x1 + x2^3 - 3*x2^2 + x2)
avoiding the zero loci of the polynomials
RingElem[x2 - 1, x1*x2^2 - x1*x2 + x1 + x2^3 - 3*x2^2 + 2*x2 - 1, x2, x1 - 1, x1*x2 + x2^2 - 3*x2 + 1, x1*x2 - x1 + x2^2 - 3*x2 + 1, x1 + x2 - 2, x1 + x2, x1 + x2 - 1, x1, x2 - 2, x1*x2 - x1 + x2^2 - 2*x2, x1*x2 - x1 + x2^2 - 3*x2, x1^2*x2 - x1^2 + 2*x1*x2^2 - 4*x1*x2 + x1 + x2^3 - 3*x2^2 + 3*x2, x1^2*x2 - x1^2 + 2*x1*x2^2 - 5*x1*x2 + 2*x1 + x2^3 - 4*x2^2 + 5*x2 - 1]