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