The realization space is
  [1   1   0   0   1   1             0              1                      x2        1    1]
  [1   0   1   0   1   0            x2        -x2 + 1                   x1*x2   x1 + 1   x1]
  [0   0   0   1   1   1   x1 + x2 - 1   -x1 - x2 + 1   -x1 + x2^2 - 2*x2 + 1       x2   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (x1^2 + x1*x2 - x2^2 + 2*x2 - 1, -x1^3*x2 + x1^2*x2^2 + 2*x1*x2^3 - 3*x1*x2^2 + x1*x2 - x2^4 + x2^3)
avoiding the zero loci of the polynomials
RingElem[x2, x2 - 1, x1 + x2 - 1, x1 + 2*x2 - 1, x1 - 1, x1, x1^2 + x1*x2 - 2*x1 - x2^2 - x2 + 1, x1^2 + x1*x2 - x1 - x2^2 + x2, x1^2 + x1*x2 - x1 - x2^2, x1^2 + x1*x2 - 2*x1 - x2^2 + 1, x1 - x2, x1^2 + 2*x1*x2 - x1 - x2^2, x1^2 + 2*x1*x2 - x2^2 + 2*x2 - 1, x1^2 + 2*x1*x2 - x1 - x2^2 + x2, x1^2 + 2*x1*x2 - x2^2 + 3*x2 - 1, x1 + x2, x1^2 + x1*x2 - x2^2 + x2, x1^2 + x1*x2 + x1 - x2^2 + 3*x2 - 1, x1^2 + x1*x2 - x2^2 + x2 - 1, x1 + 1, x1 - x2 + 1, x1^2*x2 + x1*x2^2 - x1 - x2^3 + 3*x2^2 - 3*x2 + 1, x1^2*x2 + x1*x2^2 + x1*x2 - x1 - x2^3 + 4*x2^2 - 4*x2 + 1, x1^2 + x1*x2 - x1 - x2^2 + 2*x2, x1^2 + x1*x2 - x2^2 + 3*x2 - 1, x1*x2 - x1 + x2^2 - 3*x2 + 1, x1 - x2^2 + 3*x2 - 1, x1*x2 + x1 - x2^2 + 2*x2 - 1, x1 - x2^2 + 2*x2 - 1]