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