The realization space is
  [1   0   1   x1^3 - x1^2 + x1   0   1    0    1   x1^3 - x1^2 + x1   x1     x1]
  [0   1   1                  1   0   0    1    1                  1    1      1]
  [0   0   0                  0   1   1   -1   x1               x1^3   x1   x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^13 - 4*x1^12 + 8*x1^11 - 10*x1^10 + 7*x1^9 - x1^8 - 4*x1^7 + 6*x1^6 - 4*x1^5 + x1^4)
avoiding the zero loci of the polynomials
RingElem[x1 - 1, x1, x1^2 + 1, x1^2 - x1 + 1, x1^3 - x1^2 + 2*x1 - 1, x1 + 1, x1^4 + x1 - 1]