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