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