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