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