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