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