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