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