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