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