Clarifying the axioms of Kleene algebra based on the method of indeterminate coefficients

After introducing the method of indeterminate coefficients, by which we can derive all finite models satisfying a given set of axioms, we derive all models of 8 elements of Kleene algebra by using the method, and find out many examples of a set of independent and complete axioms of Kleene algebra by checking whether each axiom in Kleene algebra is independent from others or not based on the method.