The realization space is
  [1   1    1   0   1   0   x1*x2 - x2 + 1    1   x1*x2 - x2 + 1    1    0]
  [1   0   x1   1   1   0   x1*x2 - x2 + 1   x1               x1    0    1]
  [0   0    0   0   1   1            x1*x2   x1            x1*x2   x1   x2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1 + x2, x1, x2 + 1, x2, x1 + x2 - 1, x1^2*x2 + x1*x2^2 - 2*x1*x2 + x1 - x2^2 + x2, x2 - 1, x1 - 1, x1*x2 - x1 - x2, x1^2*x2 - 2*x1*x2 + x1 + x2, x1^2*x2 - 2*x1*x2 + 2*x1 + x2 - 1, x1*x2 - x2 + 1, x1*x2 - x1 - 2*x2 + 1, x1 - 2, x1*x2 - 2*x2 + 1, x1^2*x2 - 3*x1*x2 + x1 + x2 - 1, 2*x2 - 1]