The realization space is
  [0   1   1   0   0   1             x1*x3                                        x1*x3                x1    1    1]
  [1   0   1   1   0   1   x1 + x2*x3 - x3                       x1*x3 + x2*x3^2 - x3^2   x1 + x2*x3 - x3   x2   x2]
  [1   0   1   0   1   0             x1*x3   2*x1*x3 - x1 + x2*x3^2 - x2*x3 - x3^2 + x3             x1*x3   x1   x3]
in the multivariate polynomial ring in 3 variables over ZZ
within the vanishing set of the ideal
Ideal (x1^2*x3 + x1*x2*x3^2 - 2*x1*x2*x3 + x1*x2 - x1*x3^2 - x2^2*x3^2 + x2^2*x3 + x2*x3^2 - x2*x3)
avoiding the zero loci of the polynomials
RingElem[x1 - x3, x2, x2 - 1, x1*x2*x3 - x1 - x2*x3 + x3, x3, x3 - 1, x1*x3 - x1 - x2*x3 + x3, x1*x2*x3 - x1*x3^2 + x1*x3 - x1 - x2*x3 + x3, 2*x1*x2*x3 - x1*x2 - x1*x3^2 + x2^2*x3^2 - x2^2*x3 - x2*x3^3 - x2*x3^2 + x2*x3 + x3^3, x1 + x2*x3 - x3^2 - x3, 2*x1*x3 - x1 + x2*x3^2 - x2*x3 - x3^3 - x3^2 + x3, x1 + x2*x3 - x3, x1*x2 + x1*x3 - 2*x1 - x2*x3 + x3, x2 - x3 - 1, x2 - x3, x1 - x2 + 1, x1^2*x3 - x1*x2*x3 - x1*x3 + x1 + x2*x3 - x3, x1*x3^2 - x1*x3 + x1 - x2*x3^2 + x2*x3 - x3, x1^2*x3 - 2*x1*x3 + x1 - x2*x3^2 + x2*x3 + x3^2 - x3, x1 - 1, x1, x1 - x2, 2*x1*x3 - x1 - x2*x3 + x3, 2*x1*x3 - x1 + x2*x3^2 - x2*x3 - x3^2 + x3]