The realization space is
  [1   1            x1*x2   0   0   1            x1*x2    0       x1            x1*x2]
  [0   1   x1*x2 - x1 - 1   1   0   0            x1*x2    1   x1 + 1          x1*x2^2]
  [0   0                0   0   1   1   x1*x2 - x1 - 1   x1       x1   x1*x2 - x1 - 1]
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[x1^2*x2^2 - x1^2*x2 - x1*x2 + x1 + 1, x1^2*x2^3 - x1^2*x2^2 + x1^2 - x1*x2^2 + x1*x2 + 2*x1 + x2 + 1, x1 + 1, x1*x2 - x1 - 1, x2 - 1, x1^2*x2^2 - x1*x2 + x1 + 1, x1, x1^2*x2^2 + x1 + 1, x2, x1*x2^2 - x1 - 1, x1^2*x2^3 - x1^2*x2 + x1^2 - x1*x2 + 2*x1 + 1, x1*x2^2 - x1*x2 + x1 + 1, x1^2 - x1*x2 + 2*x1 + 1, x1^2 - x1*x2^2 + x1*x2 + 2*x1 + x2 + 1, x1 + x2 + 1, x1^2*x2 - x1*x2 + x1 + 1, x1^2*x2 + x1 + 1]