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