The realization space is
  [1   0   1   0   1   0   x1 - 1        2            x1^4 - 2*x1^3 + 2*x1 - 1   2*x1 - 2          4]
  [0   1   1   1   1   0     2*x1     2*x1   x1^4 + 2*x1^3 - 4*x1^2 - 2*x1 + 3       4*x1       4*x1]
  [0   0   0   1   1   1   x1 + 1   x1 + 1                   x1^4 - 2*x1^2 + 1   x1^2 - 1   x1^2 - 1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-2*x1^8 + 8*x1^7 + 16*x1^6 - 88*x1^5 + 28*x1^4 + 152*x1^3 - 96*x1^2 - 72*x1 + 54)
avoiding the zero loci of the polynomials
RingElem[x1 + 1, x1 - 1, x1 - 3, x1^2 - 4*x1 - 1, x1, x1^2 + 4*x1 - 1, x1^2 - 5, x1 + 3, 2]