The realization space is
  [1   0   1    1   1   0                        1   1                     1    0                  1]
  [0   1   1   x1   0   0                        0   1      -x1*x3 + x1 + x3    1   -x1*x3 + x1 + x3]
  [0   0   0    0   1   1   -x1*x3 + x1 + 2*x3 - 1   1   x1*x3 - x1 - x3 + 1   x2                 x3]
in the multivariate polynomial ring in 3 variables over ZZ
within the vanishing set of the ideal
Ideal (x1*x2 - x1*x3 - x2*x3 + x3, x2*x3^2 - 2*x2*x3 + x3^2 - x3 + 1, x1*x3^2 - x1 - 2*x3^2 + x3)
avoiding the zero loci of the polynomials
RingElem[x1*x2*x3 - x1*x2 - x2*x3 + x3, x2, x1*x2*x3 - x1*x2 - x2*x3 + x2 + x3, x1*x2 - x2 + 1, x3, x1*x2*x3 - x1*x2 - x2*x3 + x3 - 1, x3 - 1, x1*x3 - x1 - 2*x3 + 1, x1*x3 - x1 - x3, x1 - 1, x1, x1^2*x3 - x1^2 - 3*x1*x3 + 3*x1 + 2*x3 - 1, x1^2*x3^2 - 2*x1^2*x3 + x1^2 - 3*x1*x3^2 + 5*x1*x3 - 2*x1 + 2*x3^2 - 2*x3 + 1, x1 - 2, x2 + 1, x2*x3 + x3 - 1, x1*x2*x3 - x1*x2 + 2*x1*x3 - 2*x1 - x2*x3 - 3*x3 + 2, x1*x2*x3 - x1*x2 + x1*x3 - x1 - x2*x3 + x2 - x3, x2 - 1, x1*x3 - x1 - x2 - 2*x3 + 2, x1*x3 - x1 - x2 - 2*x3 + 1, x1*x2 - x1*x3 + x1 + 2*x3 - 1, x1*x2 + 1, 2*x1*x3 - 2*x1 - 2*x3 + 1, x1^2*x3^2 - 2*x1^2*x3 + x1^2 - 3*x1*x3^2 + 7*x1*x3 - 4*x1 + 2*x3^2 - 5*x3 + 2, 2*x1*x3 - 2*x1 - 3*x3 + 2]