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