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