The realization space is
  [1   0   1   0   1    0                   x1*x2 - x1                           x1                                      x1*x2 - x1                                          x1    1]
  [0   1   1   0   0    1                   x1*x2 - x1   x1*x2 - x2^3 + 2*x2^2 - x2   x1*x2^2 - x1*x2 - x2^4 + 3*x2^3 - 3*x2^2 + x2   2*x1*x2 - 2*x1 - x2^3 + 3*x2^2 - 3*x2 + 1   x1]
  [0   0   0   1   1   -1   x1*x2 - x2^3 + 2*x2^2 - x2                        x1*x2                      x1*x2 - x2^3 + 2*x2^2 - x2                      2*x1 - x2^2 + 2*x2 - 1   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 - x2^2 + x2, 2*x1 - x2^2 + 2*x2 - 1, x1*x2 - 2*x1 + x2^2 - 2*x2 + 1, 2*x1 - x2^2 + x2 - 1, x1 - x2^2 + 2*x2 - 1, x1^2 - 2*x1*x2 + 2*x1 + x2^3 - 3*x2^2 + 3*x2 - 1, x1^2 - 3*x1*x2^2 + 6*x1*x2 - 3*x1 + x2^4 - 4*x2^3 + 6*x2^2 - 4*x2 + 1, x1^2 - x1*x2 + x2^3 - 2*x2^2 + x2, x2, x1^2 - 2*x1*x2^2 + 4*x1*x2 - 3*x1 + x2^4 - 3*x2^3 + 4*x2^2 - 3*x2 + 1, x1^2*x2 - x1^2 - x1*x2 + x2^4 - 2*x2^3 + x2^2, x2 - 1, x1 - 1, x1 - x2^3 + x2^2 + x2 - 1, x1^2*x2 - x1^2 + x1*x2^2 - 3*x1*x2 + x1 + x2^3 - 2*x2^2 + x2, x1 + x2, x1 + x2 - 1, x1, 2*x1*x2 - x1 - x2^3 + 2*x2^2 - x2, 2*x1*x2^2 - 4*x1*x2 + x1 - x2^4 + 4*x2^3 - 5*x2^2 + 2*x2, 2*x1*x2 - 3*x1 - x2^3 + 3*x2^2 - 3*x2 + 1, x1 - x2^3 + 2*x2^2 - x2, x1*x2^2 - x1*x2 + x1 - x2^4 + 2*x2^3 - x2^2, x1^2*x2^2 - 3*x1^2*x2 + x1^2 + x1*x2^4 - x1*x2^3 - x1*x2^2 + x1*x2 - x2^6 + 4*x2^5 - 6*x2^4 + 4*x2^3 - x2^2]