The realization space is
  [1   0   1         1   1   0              1   1         1        0         1]
  [0   1   1   -x1 + 2   0   0              0   1   -x1 + 1   x1 - 1   -x1 + 2]
  [0   0   0         0   1   1   -x1^2 + 2*x1   1        x1      -x1        x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^7 + 5*x1^6 - 11*x1^5 + 15*x1^4 - 12*x1^3 + 4*x1^2)
avoiding the zero loci of the polynomials
RingElem[x1, x1^2 - 3*x1 + 3, x1 - 1, 2, x1^2 - 2*x1 + 2, x1 - 2, 2*x1 - 1, x1 + 1, x1^3 - 3*x1^2 + 4*x1 - 1, x1^2 - x1 - 1, x1^2 - x1 + 1]