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