The realization space is
  [1   1   0   0        1        1   0            x1 - 1        x1 - 1            x1 - 1      x1^2 - 2*x1 + 1]
  [0   1   1   1   x1 - 1       x1   0                 0        x1 - 1   x1^2 - 2*x1 + 1   x1^3 - 2*x1^2 + x1]
  [0   0   0   1   x1 - 1   x1 - 1   1   x1^2 - 3*x1 + 1   x1^2 - 2*x1       x1^2 - 2*x1        x1^3 - 2*x1^2]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-x1^10 + 8*x1^9 - 23*x1^8 + 20*x1^7 + 37*x1^6 - 113*x1^5 + 124*x1^4 - 69*x1^3 + 19*x1^2 - 2*x1)
avoiding the zero loci of the polynomials
RingElem[x1 - 2, x1, x1^2 - 3*x1 + 1, x1 - 1, x1^3 - 4*x1^2 + 5*x1 - 1, x1^3 - 5*x1^2 + 6*x1 - 1, x1^4 - 4*x1^3 + 6*x1^2 - 5*x1 + 1, 2*x1^2 - 4*x1 + 1, x1^2 - 4*x1 + 1, x1^3 - 3*x1^2 + 2*x1 - 1]