The realization space is
  [1   0   1   1   x1 - 2    1   0                  1               0         x1 - 2    1]
  [0   1   1   1       -1   x1   0                  0               1             -1   x1]
  [0   0   0   1       -1    1   1   x1*x2 - 2*x2 + 1   -x1*x2 + 2*x2   x1*x2 - 2*x2   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (x1^3*x2 - 4*x1^2*x2 + x1^2 + 5*x1*x2 - x1 - 3*x2 + 1)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x2, x2 - 1, x1*x2 - 2*x2 + 1, x1*x2 - 3*x2 + 1, x1 - 2, x1^2 - 3*x1 + 3, x1^2*x2 - 3*x1*x2 + 3*x2 - 1, x1^3*x2 - 4*x1^2*x2 + 6*x1*x2 - 4*x2 + 1, x1, x1^2*x2 - 3*x1*x2 + x1 + 3*x2 - 1, x1 - x2, x1^2*x2 - 2*x1*x2 + 1, x1^2*x2 - 4*x1*x2 + x1 + 4*x2 - 1, x1^2*x2 - 3*x1*x2 + x1 + x2, x1^2*x2 - 3*x1*x2 + 2*x2 + 1, x1^2*x2 - 3*x1*x2 + x1 + 2*x2]