The realization space is
  [1   0   1   0   1    0                         x1                         x2                                                    x1*x2                    x2^2 - 2*x2    1]
  [0   1   1   0   0    1                         x1   x1*x2 - x1 + x2^2 - 2*x2   x1^2 - x1*x2^2 + 4*x1*x2 - 2*x1 - x2^3 + 4*x2^2 - 4*x2                             x1   x1]
  [0   0   0   1   1   -1   x1*x2 - x1 + x2^2 - 2*x2                  x1 + 2*x2                          x1*x2^2 - x1*x2 + x2^3 - 2*x2^2   x1*x2 - 2*x1 + 2*x2^2 - 4*x2   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, x1*x2 - 2*x1 + 2*x2^2 - 5*x2, x1 - x2^2 + 2*x2, x2^2 - 2*x2 - 1, x1*x2 - 2*x1 + x2^2 - 3*x2 + 1, x1*x2^2 - 3*x1*x2 + x1 + x2^3 - 4*x2^2 + 4*x2, x1 + x2, x1*x2 - x1 + x2^2 - 3*x2, x1 + x2 - 1, x1^2 - x2^2 + 2*x2, x1 - 1, x1*x2 - x1 + x2^2 - 2*x2, x2 - 1, x2, x1^3*x2^2 - 3*x1^3*x2 + 2*x1^3 + 3*x1^2*x2^3 - 12*x1^2*x2^2 + 11*x1^2*x2 + 3*x1*x2^4 - 14*x1*x2^3 + 16*x1*x2^2 + x2^5 - 4*x2^4 + 4*x2^3, x1^2*x2^2 - 4*x1^2*x2 + 3*x1^2 + 2*x1*x2^3 - 9*x1*x2^2 + 10*x1*x2 + x2^4 - 4*x2^3 + 4*x2^2, x1 + 2*x2, x1*x2 - x1 + 2*x2^2 - 4*x2, x2 - 2, x1^2*x2 - x1^2 + 2*x1*x2^2 - 4*x1*x2 + x2^3 - 2*x2^2, x1 + x2 - 2]