The realization space is
  [1    1   1   0   0   1    1            x1 - 1        0            x1 - 1      x1 - 1]
  [1   x1   0   1   0   1   x1                 0   x1 - 1               -x1         -x1]
  [0    0   0   0   1   1   x1   x1^2 - 3*x1 + 1      -x1   x1^2 - 3*x1 + 1   x1^2 - x1]
in the multivariate polynomial ring in 1 variable over ZZ
within the vanishing set of the ideal
Ideal (x1^3 - 5*x1^2 + 4*x1 - 1, x1^11 - 11*x1^10 + 37*x1^9 - 50*x1^8 + 31*x1^7 - 9*x1^6 + x1^5)
avoiding the zero loci of the polynomials
RingElem[2*x1 - 1, x1^2 - 5*x1 + 2, x1, 2*x1^4 - 10*x1^3 + 9*x1^2 - 4*x1 + 1, x1^4 - 5*x1^3 + 4*x1^2 - 3*x1 + 1, x1^2 - 4*x1 + 1, x1^3 - 5*x1^2 + 3*x1 - 1, 2*x1^3 - 10*x1^2 + 7*x1 - 1, x1 - 1, x1^2 - 3*x1 + 1, 3*x1^4 - 16*x1^3 + 16*x1^2 - 6*x1 + 1, x1^4 - 4*x1^3 - 2*x1^2 + 4*x1 - 1, 3*x1^3 - 16*x1^2 + 15*x1 - 4, x1^4 - 4*x1^3 - 3*x1^2 + 6*x1 - 2, x1^3 - 4*x1^2 + 1, x1 - 2, x1^2 - 4*x1 + 2, 2*x1^3 - 9*x1^2 + 4*x1 - 1, x1^2 - 4*x1 - 1, 2*x1^2 - 9*x1 + 3, x1^3 - 4*x1^2 - 2*x1 + 1, x1^3 - 5*x1^2 + 2*x1 - 1, x1^2 - 5*x1 + 3, x1 - 4]