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