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