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