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