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