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