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