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