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