The realization space is
  [1   x1^2 + x1        1   1   0        1   0   x1^2 + x1 - 1     x1^4 + 2*x1^3 - x1                 0      x1^2 + x1 - 1]
  [1        x1^2        0   0   1       x1   0   x1^2 + x1 - 1     x1^4 + x1^3 - x1^2     x1^2 + x1 - 1   x1^3 + x1^2 - x1]
  [0   x1^2 + x1   x1 + 1   0   0   x1 + 1   1       x1^2 + x1   x1^4 + 2*x1^3 + x1^2   x1^2 + 2*x1 + 1        x1^3 + x1^2]
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 + 1, x1, x1^2 + 2*x1 - 1, x1 - 1, x1^2 + x1 - 1, x1 + 2, x1^3 - x1 + 1, x1^3 + x1^2 - 2*x1 + 1, x1^3 + x1^2 - 1]