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