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