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