The realization space is
  [1   1   0              x1   0   1   1        0              x1         1        2*x1 - 1]
  [0   1   1   x1^2 + x1 - 1   0   0   1   x1 - 1   x1^2 + x1 - 1   -x1 + 1   x1^2 + x1 - 1]
  [0   0   0               0   1   1   1      -x1            x1^2        x1   x1^2 + x1 - 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-4*x1^9 + 14*x1^8 - 16*x1^7 + 3*x1^6 + 7*x1^5 - 5*x1^4 + x1^3)
avoiding the zero loci of the polynomials
RingElem[x1^2 + x1 - 1, 2*x1 - 1, x1, 2*x1^2 - 1, x1 - 1, 3*x1 - 2, x1 + 1, x1^3 - 2*x1^2 - x1 + 1, 2*x1 + 1, 2]