The realization space is
  [1   x1   1   0                   x2                   x1   1   0                   x2    1                   x1]
  [1   x2   0   1   -x1^2 + x1*x2 + x2   -x1^2 + x1*x2 + x2   1   0   -x1^2 + x1*x2 + x2    0   -x1^2 + x1*x2 + x2]
  [1   x2   0   0                   x2                   x2   0   1                x1*x2   x1                x1*x2]
in the multivariate polynomial ring in 2 variables over ZZ
avoiding the zero loci of the polynomials
RingElem[x1^3 - x1^2*x2 - x1*x2 + x2, x1^4 - x1^3*x2 - x1^2*x2 + x2^2, x1, x1^2 - x1*x2 - x2, x1 - x2, x1^2 - 2*x1*x2 + x2, x2, x1 - 1, x1^2 - x1*x2 + x1 - 2*x2, x1^2 - x2, x1 + 1, x1^2 - x1 - 1, x2 - 1, x1^3 - 2*x1^2 + x2, x1^3 - x1^2*x2 - x2, x1^3 - x1^2*x2 + x1^2 - x1*x2 - x2, x1^2 - 2*x2, x1^2*x2 + x1^2 - x1*x2 - x2]