The realization space is
  [1   1   0             1   0   1   1        0                         x2 - 1                           x2 - 1    1]
  [0   1   1   x1 + x2 - 1   0   0   1   x1 - 1   x1*x2 - x1 + x2^2 - 2*x2 + 1   2*x1*x2 - x1 + x2^2 - 3*x2 + 1   x1]
  [0   0   0             0   1   1   1   x2 - 1       -x1*x2 - x2^2 + 3*x2 - 1                        x2^2 - x2   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[x2, x1*x2 + x2^2 - 3*x2 + 1, x2 - 1, x1*x2 + 2*x2^2 - 4*x2 + 1, x1^2*x2 + 2*x1*x2^2 - 4*x1*x2 + x1 + x2^3 - 2*x2^2 + x2, x1^2*x2 + 2*x1*x2^2 - 4*x1*x2 + x1 + x2^3 - 3*x2^2 + 3*x2 - 1, x1 + x2 - 2, x1 - x2, x1 - 1, x1, x1 + x2 - 1, x1*x2 + x2^2 - 2*x2 + 1, 2*x1^2*x2^2 - x1^2*x2 + 4*x1*x2^3 - 13*x1*x2^2 + 8*x1*x2 - x1 + 2*x2^4 - 11*x2^3 + 20*x2^2 - 12*x2 + 2, 2*x1^2*x2^2 - x1^2*x2 + 4*x1*x2^3 - 11*x1*x2^2 + 6*x1*x2 - x1 + 2*x2^4 - 9*x2^3 + 13*x2^2 - 6*x2 + 1, 2*x2 - 1, 2*x1*x2 - x1 + x2^2 - 4*x2 + 2, 2*x1*x2 - x1 + x2^2 - 3*x2 + 1, x1^2*x2 + 2*x1*x2^2 - 6*x1*x2 + 2*x1 + x2^3 - 4*x2^2 + 6*x2 - 2, x1^2*x2 + 2*x1*x2^2 - 6*x1*x2 + 2*x1 + x2^3 - 5*x2^2 + 8*x2 - 3]