The realization space is
  [1   1   0                 x2   1   0         1         1    1    0]
  [0   1   1   -x1*x2 - x1 + x2   0   0   -x1 + 1   -x1 + 1    1    1]
  [0   0   0                  0   1   1        x1         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, x2, x1 - x2 - 1, x1*x2 - x1 + 1, x1*x2 - x2 + 1, x1*x2 + 1, x1 - 1, x1*x2 + x1 - x2, x2 + 1, x1*x2 + x1 - 2*x2 - 1]