The realization space is
  [1   1   0                                 1   0   1   1                                 0                                 1         1    1]
  [0   1   1   -x1^2 - 2*x1*x2 + 3*x1 + x2 - 1   0   0   1                            x2 - 1   -x1^2 - 2*x1*x2 + 3*x1 + x2 - 1        x1   x1]
  [0   0   0                                 0   1   1   1   -x1^2 - 2*x1*x2 + 3*x1 + x2 - 2                                x2   -x1 + 1   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (x1^3 + 2*x1^2*x2 - 3*x1^2 - 2*x1*x2 + 3*x1 + x2 - 1)
avoiding the zero loci of the polynomials
RingElem[x1 + x2 - 1, x1, x1 - 1, x1^2 + 2*x1*x2 - 2*x1 - x2 + 1, x2, x2 - 1, x1^2 + 2*x1*x2 - 3*x1 - x2 + 2, x1^3 + 2*x1^2*x2 - 3*x1^2 - x1*x2 + 2*x1 + x2^2 - x2, x1^3 + 2*x1^2*x2 - 4*x1^2 - 3*x1*x2 + 5*x1 + x2^2 - 2, x1^3 + 2*x1^2*x2 - 3*x1^2 - x1*x2 + 2*x1 + x2^2 - 2*x2 + 1, x1^3 + 2*x1^2*x2 - 4*x1^2 - 3*x1*x2 + 5*x1 + x2^2 - x2 - 1, x1 - x2, x1^2*x2 - x1^2 + 2*x1*x2^2 - 5*x1*x2 + 2*x1 - x2^2 + 3*x2 - 1, x1^2*x2 - x1^2 + 2*x1*x2^2 - 5*x1*x2 + 2*x1 - x2^2 + 2*x2 - 1, x1^2 + 2*x1*x2 - 3*x1 - x2 + 1, x1^3 + 2*x1^2*x2 - 4*x1^2 - 4*x1*x2 + 4*x1 + x2 - 1, x1 + 2*x2 - 2, x1^4 + 4*x1^3*x2 - 5*x1^3 + 4*x1^2*x2^2 - 12*x1^2*x2 + 9*x1^2 - 4*x1*x2^2 + 10*x1*x2 - 6*x1 - x2 + 1, x1^2 + 2*x1*x2 - 3*x1 - 2*x2 + 3, x1^4 + 4*x1^3*x2 - 5*x1^3 + 4*x1^2*x2^2 - 12*x1^2*x2 + 9*x1^2 - 4*x1*x2^2 + 10*x1*x2 - 6*x1 + x2^2 - 2*x2 + 1, x1^3 + 2*x1^2*x2 - 4*x1^2 - 4*x1*x2 + 6*x1 + x2 - 2, 2*x1 - 1, x1^3 + 2*x1^2*x2 - 3*x1^2 - x1*x2 + 3*x1 - 1, x1^2 + 2*x1*x2 - 3*x1 + 1, x1^4 + 4*x1^3*x2 - 6*x1^3 + 4*x1^2*x2^2 - 14*x1^2*x2 + 13*x1^2 - 4*x1*x2^2 + 14*x1*x2 - 12*x1 - 3*x2 + 4, x1^4 + 4*x1^3*x2 - 6*x1^3 + 4*x1^2*x2^2 - 14*x1^2*x2 + 12*x1^2 - 4*x1*x2^2 + 12*x1*x2 - 9*x1 - x2 + 1, x1^4 + 4*x1^3*x2 - 6*x1^3 + 4*x1^2*x2^2 - 14*x1^2*x2 + 13*x1^2 - 4*x1*x2^2 + 14*x1*x2 - 12*x1 + x2^2 - 3*x2 + 3, x1^4 + 4*x1^3*x2 - 6*x1^3 + 4*x1^2*x2^2 - 14*x1^2*x2 + 12*x1^2 - 4*x1*x2^2 + 12*x1*x2 - 9*x1 + x2^2 - 2*x2 + 1]