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