The realization space is
  [1   1   0    1   0   1   1                                0        x1 - x2                   x2 - 1                          x1 - x2]
  [1   0   1   x1   0   1   0           x1*x2 - x1 - x2^2 + x2   x1^2 - x1*x2   x1^2 - x1*x2 - x1 + x2   -x1^2*x2 + x1^2 + x1*x2 - x2^2]
  [0   0   0    0   1   1   1   -x1^2*x2 + 3*x1*x2 - x1 - x2^2     x1*x2 - x2               x1*x2 - x1                     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[x1^2 - x1 + x2, x2 - 1, x1 - x2, x1, x2, x1^4*x2 + x1^3*x2^2 - 5*x1^3*x2 + x1^3 - x1^2*x2^2 + 6*x1^2*x2 - x1^2 + 2*x1*x2^3 - 5*x1*x2^2 + x2^2, x1^4*x2 - 5*x1^3*x2 + x1^3 + 2*x1^2*x2^2 + 5*x1^2*x2 - x1^2 - 4*x1*x2^2 + x2^2, x1^5*x2^2 - x1^5*x2 - 5*x1^4*x2^2 + 6*x1^4*x2 - x1^4 + 2*x1^3*x2^3 + 2*x1^3*x2^2 - 6*x1^3*x2 + x1^3 - 3*x1^2*x2^3 + 6*x1^2*x2^2 - 2*x1*x2^3 - x1*x2^2 + x2^4, x1^3*x2 - 4*x1^2*x2 + x1^2 + 2*x1*x2^2 + x1*x2 - x2^3, x1^2*x2 - 4*x1*x2 + x1 + x2^2 + x2, x1^2 - 2*x1 + x2, x1^5*x2^2 - x1^5*x2 - 5*x1^4*x2^2 + 5*x1^4*x2 - x1^4 + 2*x1^3*x2^3 + 4*x1^3*x2^2 - 2*x1^3*x2 - 4*x1^2*x2^3 - 2*x1^2*x2^2 + 4*x1*x2^3 - x2^4, x1^2*x2 + x1*x2^2 - 4*x1*x2 + x1 + x2, x1^2*x2 - 3*x1*x2 + x1 + 2*x2^2 - x2, x1^5*x2 + x1^4*x2^2 - 5*x1^4*x2 + x1^4 - x1^3*x2^2 + 6*x1^3*x2 - x1^3 + 2*x1^2*x2^3 - 5*x1^2*x2^2 - x1^2*x2 + 3*x1*x2^2 - x2^3, x1^4*x2^2 - x1^4*x2 + x1^3*x2^3 - 6*x1^3*x2^2 + 5*x1^3*x2 - x1^3 - x1^2*x2^3 + 7*x1^2*x2^2 - 3*x1^2*x2 + 2*x1*x2^4 - 6*x1*x2^3 + x1*x2^2 + x2^3, x1^3*x2 + x1^2*x2^2 - 4*x1^2*x2 + x1^2 - x1*x2^2 + 2*x1*x2 + x2^3 - x2^2, x1^5*x2^2 - x1^5*x2 + x1^4*x2^3 - 6*x1^4*x2^2 + 5*x1^4*x2 - x1^4 - x1^3*x2^3 + 7*x1^3*x2^2 - 3*x1^3*x2 + 2*x1^2*x2^4 - 6*x1^2*x2^3 + 2*x1^2*x2^2 - x1^2*x2 - x1*x2^3 + 2*x1*x2^2 + x2^4 - x2^3, x1^2*x2 - x1^2 - 2*x1*x2 + x1 + 2*x2^2 - x2, x1^2*x2 - x1^2 - x1*x2 + x2^2, x1*x2 - 2*x1 + x2, x1 - 1, x1^3*x2 - 4*x1^2*x2 + x1^2 + 2*x1*x2^2 - x2^2, x1^4*x2 - 6*x1^3*x2 + x1^3 + 2*x1^2*x2^2 + 8*x1^2*x2 - 2*x1^2 - 4*x1*x2^2 - x1*x2 + x2^2, x1^2*x2 - 3*x1*x2 + x1 + x2, x1^5*x2 + x1^4*x2^2 - 5*x1^4*x2 + x1^4 - 3*x1^3*x2^2 + 7*x1^3*x2 - x1^3 + 2*x1^2*x2^3 + 2*x1^2*x2^2 - 6*x1^2*x2 + x1^2 - 4*x1*x2^3 + 4*x1*x2^2 + x2^3 - x2^2, x1^6*x2 + x1^5*x2^2 - 6*x1^5*x2 + x1^5 - 2*x1^4*x2^2 + 11*x1^4*x2 - 2*x1^4 + 2*x1^3*x2^3 - 4*x1^3*x2^2 - 6*x1^3*x2 + x1^3 - 2*x1^2*x2^3 + 5*x1^2*x2^2 + x1^2*x2 + 2*x1*x2^3 - 3*x1*x2^2 - x2^4 + x2^3, x1^5*x2 + x1^4*x2^2 - 5*x1^4*x2 + x1^4 - 2*x1^3*x2^2 + 6*x1^3*x2 - x1^3 + x1^2*x2^3 - x1^2*x2^2 - x1^2*x2 + x1*x2^3 - x1*x2^2 - x2^4 + x2^3, x1^6*x2 + x1^5*x2^2 - 6*x1^5*x2 + x1^5 - 2*x1^4*x2^2 + 10*x1^4*x2 - 2*x1^4 + 2*x1^3*x2^3 - 4*x1^3*x2^2 - 2*x1^3*x2 - x1^2*x2^3 + 3*x1^2*x2^2 - x1^2*x2 - 2*x1*x2^3 + 2*x1*x2^2 + x2^4 - x2^3, x1^3 - 3*x1^2 + 2*x1*x2 + x1 - x2, x1^4*x2 - 4*x1^3*x2 + x1^3 + 2*x1^2*x2^2 + x1^2*x2 - x1*x2 - x2^3 + x2^2, x1^3*x2 - 3*x1^2*x2 + x1^2 + 3*x1*x2^2 - 3*x1*x2 + x1 - x2^2 + x2, x1^4*x2 - 3*x1^3*x2 + x1^3 + 3*x1^2*x2^2 - 3*x1^2*x2 + x1^2 - 2*x1*x2^2 + 2*x1*x2 + x2^3 - x2^2, x1^3*x2 - 5*x1^2*x2 + x1^2 + 2*x1*x2^2 + 2*x1*x2 - x2^2, x1^3*x2 - 4*x1^2*x2 + x1^2 + x1*x2^2 + 2*x1*x2 - x2^2, x1^3*x2 + x1^2*x2^2 - 4*x1^2*x2 + x1^2 - 2*x1*x2^2 + 3*x1*x2 + 2*x2^3 - 2*x2^2, x1^4*x2 + x1^3*x2^2 - 4*x1^3*x2 + x1^3 - x1^2*x2^2 + 2*x1^2*x2 + x1*x2^3 - 2*x1*x2^2 + x1*x2 + x2^3 - x2^2, x1^3*x2 + x1^2*x2^2 - 5*x1^2*x2 + x1^2 - 2*x1*x2^2 + 6*x1*x2 - x1 + x2^3 - x2^2 - x2]