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