The realization space is
  [1   0   1   0   1   0   x2                   x2      x2                        x2^2                        x2^2]
  [1   1   0   1   0   0   x1   -x1*x2 + x1 + x2^2      x1   -x1^2*x2 + x1^2 + x1*x2^2   -x1^2*x2 + x1^2 + x1*x2^2]
  [1   1   0   0   1   1    0                 x2^2   x1*x2                     x1*x2^2                        x2^3]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1*x2 - x1 - x2, x1 - x2, x1, x1*x2 - x1 - x2^2, x2 - 1, x1^2*x2 - x1^2 - 2*x1*x2 + x1 + x2^2, x1*x2 - x1 - 2*x2 + 1, x2, x1^2*x2 - x1^2 - x1*x2^2 + x1*x2 + x2^3, x1*x2 - x1 - 2*x2^2 + x2, x1^2*x2 - x1^2 - x1*x2^2 + x2^3 - x2^2, x1^2*x2 - x1^2 - x1*x2^2 + x2^3, x1 - 1, x1*x2 - x1 + x2, x1 + x2^2 - x2, x1^2*x2 - x1^2 - x2^2, x1 + x2]