I want a famous application of comprehensive grobner basis w.r.t. lex order and w.r.t. some conditions on parametric coefficients.

Question

Let $I$ be an parametric polynomial ideal in $K[a_1,\cdots,a_m][x_1,\cdots,x_n]$ where $a_1,\cdots,a_m$ is a sequence of parameters and $x_1,\cdots,x_n$ is a sequence of variables. Is there any famous example or application which in it we must compute the reduced Groebner basis of $I$ w.r.t. lex ordering and w.r.t. some conditions on parameters?