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