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