The realization space is
  [1                 x1   1   1   0    1   0   x1                 x1            0    1]
  [1   -x1^2 + 2*x1 - 1   0   0   1   x1   0   x1   -x1^2 + 2*x1 - 1            1   x1]
  [1   -x1^2 + 2*x1 - 1   0   1   0    0   1   x2                 x2   x1*x2 + x2   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal (x1^3 - x1 + 1)
avoiding the zero loci of the polynomials
RingElem[x1^2*x2 - 2*x2 + 1, 2*x1^3*x2 - x1^2 - 2*x1*x2 + 2*x1 + x2 - 1, x2, x1^2 + x1 - 1, x1^2*x2 + x1*x2 - x2 + 1, x1 + 1, x1 - 1, x1^2*x2 - 2*x1^2 + 2*x1 - 1, x1^2 - 2*x1 + x2 + 1, 2*x1^2 - 2*x1 + 1, x1^2 - x1 + 1, x1^2*x2 - 2*x1^2 - x1*x2 + 2*x1 + x2 - 1, x1 - x2, x1, x2 - 1, x1^2 + x1*x2 - 2*x1 + 1, x1^3 - x1^2*x2 + 2*x1*x2 - x1 - x2 + 1, x1^3*x2 - x1 + 2*x2, x1^3 - x1^2 - x1 + 2, x1^3*x2 - x1^2*x2 - x1*x2 - x1 + 2*x2, 2*x1^3 - x1 + 2, x1^3*x2 - x1^2 + 2*x1 - 1, x1^2*x2 + x1*x2 + x1 - x2, x1^2*x2 - x2 + 1, 2*x1^3*x2 - x1^2 - x1*x2 + 2*x1 + x2 - 1, x1^2*x2 + x1*x2 + 1, x1^3*x2 - x1^2*x2 - x1^2 - x1*x2 + x1 + x2 - 1, x1*x2 + x2 - 1, 2*x1^2 - x1*x2 - 2*x1 + x2 + 1, 2*x1^2 - x1*x2 - 2*x1 + 1, x1^4 - 3*x1^3 + 2*x1^2*x2 + 3*x1^2 - 2*x1*x2 - x1 + x2, x1 - x2 - 1, 2*x1^3 - x1^2*x2 - 3*x1^2 + 2*x1*x2 + 2*x1 - x2]