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