The realization space is
  [1   0   1   0   1   0   x1^3 - x1^2     x1^2 - x1   x1^3 - x1^2        x1*x2 - x2         x1^2 - x1]
  [0   1   1   1   1   0     x1^3 - x2     x1^3 - x2     x1^3 - x2         x1^3 - x2         x1^3 - x2]
  [0   1   1   0   0   1   x1^3 - x1^2   x1^3 - x1^2    x1*x2 - x2   x1^2*x2 - x1*x2   x1^2*x2 - x1*x2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1 - x2, x1^3 - x1^2*x2 + x1*x2 - x2, x1^3 - x2, x2, x1 - 1, x1^2 + x2, x1^2 - x2, x1 + 1, x1^3 - x1^2 + x1 - x2, x1^3 - x1^2*x2 + x1^2 - x2, x2 - 1, x1^4 - x1^3 - x1^2*x2 + x1^2 - x1*x2 + x2^2, x1^2 - x1 + 1, x1, x1^5 - x1^4*x2 + x1^3*x2 - 2*x1^2*x2 + x2^2, x1^3 - 2*x1^2 + x2]