The realization space is
  [1                           x1*x2        1   1   0        1   0   x1                           x1*x2                               0    1]
  [1   x1^3 - x1^2*x2 + 2*x1*x2 - x2        0   0   1       x1   0   x1   x1^3 - x1^2*x2 + 2*x1*x2 - x2                               1   x1]
  [0                           x1*x2   x1 + 1   0   0   x1 + 1   1   x2                            x2^2   -x1^2 + x1*x2 - 2*x1 + x2 - 1   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[x1^3 - x1^2*x2 + x1^2 - x1 + 2*x2 - 1, x1^5 - 3*x1^4*x2 + 2*x1^4 + 2*x1^3*x2^2 - 3*x1^3*x2 + x1^3 + x1^2*x2 - 2*x1*x2^2 + x1*x2 + x2^2 - x2, x1 - x2 + 1, x1^2 + x1 - 1, x1^3 - x1^2*x2 + 2*x1^2 - x1*x2 + x1 + x2, x1 + 1, x1 - 1, x1, x1 - x2, x1^3 - 2*x1^2*x2 + 2*x1*x2 - x2, x1^4 - 3*x1^3*x2 + x1^3 + x1^2*x2^2 - x1*x2^2 + x1*x2 + x2^2 - x2, x1^3 - x1^2*x2 + x1*x2 - x2, x2, x1^2 - x1*x2 + x2, x2 - 1, x1^2 + x2 - 1, x1^4 - 3*x1^3*x2 + x1^3 + x1^2*x2^2 + x1^2*x2 - 2*x1*x2^2 + x1*x2 + x2^2 - x2, x1^2 - x1 + 1, x1^5 - 2*x1^4*x2 + 2*x1^4 + x1^3*x2^2 - 2*x1^3*x2 + x1^3 - x1*x2 + 2*x2^2 - x2, x1^5 - 2*x1^4*x2 + 2*x1^4 + x1^3*x2^2 - x1^3*x2 + x1^3 - x1^2*x2^2 + x1^2*x2 - x1*x2^2 - x1*x2 + 2*x2^2 - x2, x1^5 - 2*x1^4*x2 + 2*x1^4 + x1^3*x2^2 - x1^3*x2 + x1^3 - x1^2*x2^2 + 2*x1^2*x2 - x1*x2^2 + 2*x2^2 - x2, x1^5 - 3*x1^4*x2 + 2*x1^4 + 2*x1^3*x2^2 - 3*x1^3*x2 + x1^3 - x1*x2^2 - x1*x2 + 2*x2^2 - x2, x1^5 - 2*x1^4*x2 + 2*x1^4 + x1^3*x2^2 - 2*x1^3*x2 + x1^3 - x2, x1^3 - x1^2*x2 + x1^2 - x1*x2 + x2, x1^5 - 3*x1^4*x2 + 2*x1^4 + 2*x1^3*x2^2 - 3*x1^3*x2 + x1^3 - x1*x2^2 + x2^2 - x2, x1^2 - x1*x2 + x1 + 1, x1^5 - 2*x1^4*x2 + 2*x1^4 + x1^3*x2^2 - x1^3*x2 + x1^3 - x1^2*x2^2 + 2*x1^2*x2 - x1*x2^2 + x1*x2 + x2^2 - x2, x1^5 - 2*x1^4*x2 + 2*x1^4 + x1^3*x2^2 - x1^3*x2 + x1^3 - x1^2*x2^2 + x1^2*x2 - x1*x2^2 + x2^2 - x2, x1^5 - 2*x1^4*x2 + 2*x1^4 + x1^3*x2^2 - 2*x1^3*x2 + x1^3 + x2^2 - x2, x1^2 + x1 - x2, x1^3 - x1^2*x2 + 2*x1*x2 - x2, x1^4 - x1^3*x2 + x1^3 - x1*x2^2 + x2^2 - x2, x1^4 - x1^3*x2 + x1^3 + x1^2*x2 - x1*x2^2 + x1*x2 - x2, x1^4 - x1^3*x2 + x1^3 + x2^2 - x2, x1^5 - x1^4*x2 + x1^4 - 2*x1^3*x2 + 2*x1^2*x2^2 + x1^2*x2 - 2*x1*x2^2 - x1*x2 + x2^2, x1^5 - x1^4*x2 + x1^4 - x1^3*x2 + x1^2*x2^2 + x1^2*x2 - 2*x1*x2^2 - x1*x2 + x2^2, x1^4 - x1^3*x2 + x1^3 - x1^2*x2 + x1*x2 - x2]