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