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