The realization space is
  [1   0   1   1   -x1 + 2    1   0        1         0            -x1 + 2              1]
  [0   1   1   1         1   x1   0        0         1                  1             x1]
  [0   0   0   1         1    1   1   x1 - 1   -x1 + 2   -x1^2 + 3*x1 - 2   -x1^2 + 2*x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^6 + 6*x1^5 - 16*x1^4 + 24*x1^3 - 20*x1^2 + 8*x1 - 1)
avoiding the zero loci of the polynomials
RingElem[x1 - 2, x1, x1^2 - x1 - 1, x1 - 1, 2*x1 - 3, x1^2 - 3*x1 + 3, x1^2 - x1 + 1, x1^2 - 3*x1 + 1, x1^3 - 3*x1^2 + 2*x1 + 1, x1^2 - 2*x1 + 2]