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