The realization space is
  [1   1   0   0   1   1        0                       x1*x2 - x1 + x2^2 - 3*x2 + 2                                x1*x2 - x1 - x2 + 1    1                       x1*x2 - x1 + x2^2 - 3*x2 + 2]
  [0   1   1   0   0   1   x1 - 1   x1^2*x2 + x1*x2^2 - 2*x1*x2 - x1 - x2^2 + x2 + 1   x1^2*x2 + x1*x2^2 - 2*x1*x2 - x1 - x2^2 + x2 + 1   x1   x1^2*x2 + x1*x2^2 - 2*x1*x2 - x1 - x2^2 + x2 + 1]
  [0   0   0   1   1   1   x2 - 1                x1*x2^2 - x1*x2 + x2^3 - 2*x2^2 + 1             x1*x2^2 - x1*x2 + x2^3 - 3*x2^2 + 2*x2   x2             x1*x2^2 - x1*x2 + x2^3 - 3*x2^2 + 2*x2]
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 + x1*x2 - 3*x1 - x2^2 + x2 + 1, x2, x2 - 1, x1 + x2 - 2, x1*x2 + x2^2 - x2 - 1, x1 - 1, x1^2*x2 - x1*x2 - x1 - x2^3 + 2*x2^2 - x2 + 1, x1^2*x2 + x1*x2^2 - 3*x1*x2 - 2*x2^2 + 4*x2 - 1, x1 + 2*x2 - 3, x1^2*x2 + 2*x1*x2^2 - 4*x1*x2 + x2^3 - 5*x2^2 + 6*x2 - 1, x1 + x2^2 - x2 - 1, x1^2 - 2*x1 - x2^2 + x2 + 1, x1 - x2, x1, x1 + x2 - 1]