The realization space is
  [1   1   0     x2 - 1   0   1   1        0      x2 - 1   x1 + x2 - 1    1]
  [0   1   1   -x1 + x2   0   0   1       x1    -x1 + x2            x1   x1]
  [0   0   0          0   1   1   1   x2 - 1   x2^2 - x2        x2 - 1   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (x1^2 - x1 + x2^3 - 3*x2^2 + 3*x2 - 1)
avoiding the zero loci of the polynomials
RingElem[x1, x1 + x2 - 1, x2 - 1, x1*x2 + x2^2 - 2*x2 + 1, x2, x1^2 - x1 - x2^2 + 2*x2 - 1, x1 + x2 - 2, x1 - 1, x1 - x2, x1*x2 + x1 - x2, x1 - x2^2 + x2 - 1, x1^2 + x1*x2 - 2*x1 - x2^2 + x2, x1 - x2 + 1, x1*x2 + x1 - 1, x1*x2 - 1, x1 + x2^2 - 2*x2]