The realization space is
  [1   1   0                                        x2   0   1   1        0                                        x2         1    1]
  [0   1   1   x1*x2^2 + x1 + x2^3 - 3*x2^2 + 2*x2 - 1   0   0   1   x2 - 1   x1*x2^2 + x1 + x2^3 - 3*x2^2 + 2*x2 - 1   -x2 + 1   x1]
  [0   0   0                                         0   1   1   1      -x2                               x1 + x2 - 1        x2   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal with 2 generators
avoiding the zero loci of the polynomials
RingElem[x2, x1 + x2 - 1, x2 - 1, x1 - x2^2 + x2 - 1, x1^2 - x1*x2^3 - x1 - x2^4 + 3*x2^3 - 2*x2^2 + x2, x1^2 - x1*x2^3 - 2*x1 - x2^4 + 3*x2^3 - x2^2 + 1, x1*x2^2 - x1*x2 + x1 + x2^3 - 3*x2^2 + 2*x2 - 1, x1^2 - x1*x2^3 + x1*x2^2 - x1*x2 - x2^4 + 4*x2^3 - 5*x2^2 + 3*x2 - 1, x1^2 - x1*x2^3 + x1*x2^2 - x1*x2 - x1 - x2^4 + 4*x2^3 - 4*x2^2 + 2*x2, x1 + x2 - 2, x1*x2^2 - x1*x2 + x1 + x2^3 - 4*x2^2 + 3*x2 - 1, x1*x2 + x2^2 - 2*x2 + 1, x1*x2 + x2^2 - 3*x2 + 1, x1 - x2, x1 - 1, x1, x1*x2^3 - x1*x2^2 + 2*x1*x2 - x1 + x2^4 - 4*x2^3 + 5*x2^2 - 3*x2 + 1, x1*x2^2 + x1 + x2^3 - 3*x2^2 + 2*x2 - 1, x1*x2^2 + x1 + x2^3 - 3*x2^2 + x2 - 1, x1*x2^3 + 2*x1*x2 - x1 + x2^4 - 3*x2^3 + 3*x2^2 - 3*x2 + 1, x1*x2^2 + 2*x1 + x2^3 - 3*x2^2 + 2*x2 - 2, x1*x2^2 + x1 + x2^3 - 2*x2^2 + x2 - 1, 2*x2 - 1, x1*x2^3 - x1*x2^2 + x1*x2 - x1 + x2^4 - 4*x2^3 + 3*x2^2 - 2*x2 + 1, x1*x2^3 + 2*x1*x2 - x1 + x2^4 - 3*x2^3 + 2*x2^2 - 3*x2 + 1, x1*x2^3 + 2*x1*x2 - x1 + x2^4 - 3*x2^3 + 2*x2^2 - 2*x2 + 1, x1*x2^3 + 2*x1*x2 - x1 + x2^4 - 3*x2^3 + x2^2 - 2*x2 + 1, x1*x2^2 + x1 + x2^3 - 3*x2^2, x1*x2^2 + x1 + x2^3 - 3*x2^2 + x2]