The realization space is
  [1   x1*x2 + x1 - 1   1   0   x1 - 1   x1*x2 + x1 - 1   x1*x2 + x1 - 1   x1 - 1   0    0    1]
  [1       x1*x2 - x2   0   1      -x2            -x2^2       x1*x2 - x2      -x2   0    1    0]
  [1       x1*x2 - x2   0   0   x1 - 1       x1*x2 - x2                0   -x1*x2   1   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, x1^2 + x1*x2 - 1, x1 - 1, 2*x1 + x2 - 2, 2*x1^2 + x1*x2 - 3*x1 + 1, 2*x1 - 1, x1*x2 + x1 - 1, x1^2*x2 - x1^2 + x1*x2^2 - x1*x2 + 2*x1 - 1, x2 - 1, x1*x2 - x1 + 1, x1^3*x2 + x1^2*x2^2 + x1^2 - x1*x2 - 2*x1 + 1, x1^2*x2 + x1 - 1, x2 + 1, x1*x2 + 2*x1 - 2, x1^2*x2 + 2*x1^2 - 3*x1 + 1]