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