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