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