The realization space is
  [1   0   1   0   1    0            x1                                            2*x1^3 + x1^2*x2^2 + 3*x1^2*x2 - 3*x1^2 + x1*x2^3 + 2*x1*x2^2 - 6*x1*x2 + 3*x1 + x2^3 - 3*x2^2 + 3*x2 - 1                                                                                  x1^2*x2 + x1*x2^2    1                             x1 + x2 - 1]
  [0   1   1   0   0    1            x1        2*x1^4 + 9*x1^3 + x1^2*x2^3 + 14*x1^2*x2 - 15*x1^2 + x1*x2^4 + 3*x1*x2^3 + 7*x1*x2^2 - 28*x1*x2 + 17*x1 + x2^4 + 2*x2^3 - 13*x2^2 + 16*x2 - 6   2*x1^3 + x1^2*x2^2 + 3*x1^2*x2 - 3*x1^2 + x1*x2^3 + x1*x2^2 - 5*x1*x2 + 3*x1 - 2*x2^2 + 3*x2 - 1   x1   x1^2*x2 + x1*x2^2 - x1*x2 - x2^2 + x2]
  [0   0   0   1   1   -1   x1 + x2 - 1   2*x1^4 + 11*x1^3 + 2*x1^2*x2^3 + 17*x1^2*x2 - 18*x1^2 + 3*x1*x2^4 + 2*x1*x2^3 + 8*x1*x2^2 - 33*x1*x2 + 20*x1 + x2^5 + 2*x2^3 - 15*x2^2 + 19*x2 - 7                                                          x1^2*x2 + 2*x1*x2^2 - x1*x2 + x2^3 - x2^2   x2                       x1*x2 + x2^2 - 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 - 1, x2 - 1, x1 + x2, x2, x1^2 + x1*x2 - x1 - x2 + 1, x1, x1^2*x2 + x1*x2^2 - x1 - x2 + 1, x1^2*x2 + x1*x2^2 + x1*x2 - 2*x1 + x2^2 - 2*x2 + 1, x1*x2 + x2^2 - 1, x1 + x2 - 1, x1^2 - x1 - x2 + 1, x1^3 + x1^2*x2 - 2*x1^2 - 3*x1*x2 + 2*x1 - x2^2 + 2*x2 - 1, x1^3 + x1^2*x2 - x1^2 - 2*x1*x2 + 2*x1 - x2^2 + 2*x2 - 1, x1^3 + x1^2*x2 - x1^2 - x1*x2 + x1 + x2 - 1, x1^3*x2 - x1^3 + x1^2*x2^2 - 2*x1^2*x2 + 2*x1^2 - x1*x2^2 + 3*x1*x2 - 2*x1 + x2^2 - 2*x2 + 1, 2*x1 + x2 - 1]