The realization space is
  [1   0   1     x1 - 1   1   0     x1^2 - 3*x1 + 1   1         1         0    1]
  [0   1   1   2*x1 - 1   0   0                   0   1        x1        x1   x1]
  [0   0   0          0   1   1   2*x1^2 - 3*x1 + 1   1   -x1 + 1   -x1 + 1   x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (-8*x1^7 + 52*x1^6 - 130*x1^5 + 167*x1^4 - 121*x1^3 + 50*x1^2 - 11*x1 + 1)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1, x1 - 1, 2*x1^2 - 2*x1 + 1, 2, x1^2 - 4*x1 + 2, x1^2 - 3*x1 + 1, x1^3 - 5*x1^2 + 4*x1 - 1, 3*x1^3 - 8*x1^2 + 5*x1 - 1, 3*x1 - 1, x1^2 + 2*x1 - 1]