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