User blog comment:Mh314159/Alpha numbers (and beyond)/@comment-35470197-20191007022858/@comment-35470197-20191015012254

1) You need to specify the rule applicable to cases to which neighther the new rules and the current rules are not applicable. For example,\(\alpha[0,0,0]\) and \(\alpha[1,0,0]\). Moreover, the zero replacement rule is ambiguous, because it has no specified order to apply to a given expression. For example, there are two disctinct ways to apply it to \(\alpha[0,1,0,1]\).

2) Similarly, you need to add a rule to compute \(f\{1,1,0\}(x)\). The rule should be carefully chosen, because rules including bothe decrementing the initial term and decrementing the final term sometimes cause non-terminating system.