The realization space is
  [1   1   0   0   x1 - 1     x1 - 1   0            x1^2 - 3*x1 + 1         x1^3 - 3*x1^2 + x1            x1^2 - 3*x1 + 1    1]
  [0   1   1   1       x1   2*x1 - 1   0                          0         x1^3 - 3*x1^2 + x1         x1^3 - 3*x1^2 + x1   x1]
  [0   1   1   0        0     x1 - 1   1   x1^2 - 2*x1*x2 - x1 + x2   x1^2 - 2*x1*x2 - x1 + x2   x1^2 - 2*x1*x2 - x1 + x2   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal with 2 generators
avoiding the zero loci of the polynomials
RingElem[x1, x1 - 1, x2 - 1, x1 - 2, x1^2 - 3*x1 + 1, x1^3 - 4*x1^2 + 2*x1*x2 + 2*x1 - x2, x1^2 - x1*x2 - 2*x1 + x2, x1^2*x2 - 2*x1*x2 - x1 + x2, x1^2 - 2*x1*x2 - x1 + x2, x2, x1^2 - 2*x1 + x2, x1 - x2, x1^4 - 6*x1^3 + 4*x1^2*x2 + 7*x1^2 - 4*x1*x2 - 2*x1 + x2, 2*x1 - 1, x1^4 - 6*x1^3 + 2*x1^2*x2 + 9*x1^2 - 3*x1*x2 - 3*x1 + x2, x1^4 - 5*x1^3 + 8*x1^2 - 2*x1*x2 - 3*x1 + x2]