Your algorithm can be implemented with tail-call recursion AND your language supports the same.

Just to nitpick but the compiler/interpreter needs to support tail-call recursion, not just the language. For example, tail-call recursion is part of the language spec for JavaScript (ECMAScript 6), but only certain engines actually support it (https://compat-table.github.io/compat-table/es6/ Ctrl+F tail call).