The realization space is
  [1   0   1   0   1    0   x1 - x2 - 1                   x2                                     x1*x2 - x2^2 - x2                                                   x2                                                   x2]
  [0   1   1   0   0    1   x1 - x2 - 1   -x1^2 + x1*x2 + x1   -x1^3 + 2*x1^2*x2 + 2*x1^2 - x1*x2^2 - 2*x1*x2 - x1   x1^3 - 2*x1^2*x2 - 2*x1^2 + x1*x2^2 + 2*x1*x2 + x1   x1^3 - 2*x1^2*x2 - 2*x1^2 + x1*x2^2 + 2*x1*x2 + x1]
  [0   0   0   1   1   -1           -x2                x1*x2                                                 -x2^2                                                x1*x2                                                 x2^2]
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 - x2 - 1, x1, x1 - x2, x1^2 - x1*x2 - 2*x1 + 1, x1^3 - 2*x1^2*x2 - 2*x1^2 + x1*x2^2 + 2*x1*x2 + x1 + x2^2, x1 - 1, x1^3 - x1^2*x2 - 2*x1^2 + x1*x2 + x1 - x2, x1 - 2, x1^2 - x1*x2 - x1 - x2, x1^2 - 2*x1 - x2 + 1, x1^3 - 2*x1^2*x2 - 3*x1^2 + x1*x2^2 + 3*x1*x2 + 3*x1 + x2^2 - x2 - 1, x1^3 - 2*x1^2*x2 - 2*x1^2 + x1*x2^2 + 2*x1*x2 + x1 + x2^2 - x2, x2 - 1, x2, x1^3 - 2*x1^2*x2 - 2*x1^2 + x1*x2^2 + 3*x1*x2 + x1 - x2, x1^3 - 2*x1^2*x2 - 3*x1^2 + x1*x2^2 + 4*x1*x2 + 3*x1 - 2*x2 - 1, x1^2 - 2*x1*x2 - 2*x1 + x2^2 + 3*x2 + 1, x1 - 2*x2 - 1, x1^2 - 2*x1*x2 - x1 + x2]