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