The realization space is
  [1   0   1   0   1    0             1                                         x2                            x2    1                                         x2]
  [0   1   1   0   0    1             1   x1*x2^2 + 2*x1*x2 + x1 + x2^3 - 2*x2 - 1   -x1*x2 - x1 - x2^2 + x2 + 2   x1   x1*x2^2 + 2*x1*x2 + x1 + x2^3 - 2*x2 - 1]
  [0   0   0   1   1   -1   x1 + x2 - 1      -x1*x2^2 - x1*x2 - x2^3 + x2^2 + 2*x2             x1*x2 + x2^2 - x2   x2                                       x2^2]
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*x2 + x1 + x2^2 - 2, x2, x2 - 1, x1^2*x2 + x1^2 + 2*x1*x2^2 - x1*x2 - 3*x1 + x2^3 - 2*x2^2 - 2*x2 + 2, x1^2*x2 + x1^2 + x1*x2^2 - 2*x1*x2 - 3*x1 - x2^2 + 2, x2 + 1, x1 + x2 - 1, x1 - 2, x1 + x2 - 2, x1^2*x2 + x1^2 + 2*x1*x2^2 - 2*x1*x2 - 4*x1 + x2^3 - 3*x2^2 - x2 + 4, x1^2*x2 + x1^2 + x1*x2^2 - 2*x1*x2 - 3*x1 - 2*x2^2 + x2 + 2, x1*x2 + x1 + x2^2 + x2 - 1, x1^2*x2 + x1^2 + 2*x1*x2^2 - x1*x2 - 3*x1 + x2^3 - x2^2 - 2*x2 + 2, x1^2*x2^2 - x1^2 + 2*x1*x2^3 - 2*x1*x2^2 - 2*x1*x2 + 3*x1 + x2^4 - 2*x2^3 - x2^2 + 4*x2 - 2, x1^4*x2^2 + 2*x1^4*x2 + x1^4 + 4*x1^3*x2^3 + 2*x1^3*x2^2 - 8*x1^3*x2 - 6*x1^3 + 6*x1^2*x2^4 - 5*x1^2*x2^3 - 18*x1^2*x2^2 + 6*x1^2*x2 + 13*x1^2 + 4*x1*x2^5 - 8*x1*x2^4 - 10*x1*x2^3 + 22*x1*x2^2 + 8*x1*x2 - 12*x1 + x2^6 - 3*x2^5 - x2^4 + 10*x2^3 - 4*x2^2 - 8*x2 + 4, x1 + x2, x1^3*x2 + x1^3 + 2*x1^2*x2^2 - x1^2*x2 - 3*x1^2 + x1*x2^3 - 3*x1*x2^2 - 2*x1*x2 + 3*x1 - x2^3 + x2^2 + 2*x2 - 2, x1, x1^4*x2^2 + 2*x1^4*x2 + x1^4 + 3*x1^3*x2^3 - 9*x1^3*x2 - 6*x1^3 + 3*x1^2*x2^4 - 7*x1^2*x2^3 - 12*x1^2*x2^2 + 11*x1^2*x2 + 13*x1^2 + x1*x2^5 - 6*x1*x2^4 + x1*x2^3 + 20*x1*x2^2 - 12*x1 - x2^5 + 3*x2^4 + 3*x2^3 - 8*x2^2 - 4*x2 + 4, x1^2*x2^2 - x1^2 + 2*x1*x2^3 - 2*x1*x2^2 - x1*x2 + 3*x1 + x2^4 - 2*x2^3 + 2*x2 - 2, x1^3*x2 + x1^3 + 2*x1^2*x2^2 - 2*x1^2*x2 - 4*x1^2 + x1*x2^3 - 5*x1*x2^2 - x1*x2 + 5*x1 - 2*x2^3 + 3*x2^2 + 2*x2 - 2, x1^3*x2 + x1^3 + 2*x1^2*x2^2 - x1^2*x2 - 3*x1^2 + x1*x2^3 - 3*x1*x2^2 - 3*x1*x2 + 2*x1 - x2^3 + 3*x2, x1^2*x2 + x1^2 + x1*x2^2 - x1*x2 - 2*x1 - x2^2 - x2 + 1]