would like to join indentical sub-trees

It kind of depends what you mean by "identical subtrees".

If by identical, you mean that any substructure references below the top level are references to the same hash or array , then simply stringifying both hashes (or both arrays) and comparing the string for equality will tell you if they are identical or not. And it will be considerably faster than full tree traversal methods.

AFAIK (and my ability to quickly verify), any hash that contains the same keys and values will stringify(*) to the same string, regardless of either the order in which the hash was constructed or whether it has at anytime contains other keys subsequently removed. So there should be no need to sort the keys.

If you would consider two different arrays or hashes that contains the same data as "identical", then it would be necessary to recursively stringify contained references bottom up. It might well still be quicker than an element by element recursive comparison if all you need is a boolean yes/no rather than a blow-by-blow differences found.

(*using suitable delimiters.)