Regenerate Strings from Run-Length Digit Encoding

Inverse of an RLE-style decoding: given a digits-only string like `'2345'`, enumerate strings that decode to the same multiset when interpreted as run-length-encoded segments. For `'2345'` the decoded base is two of 3 followed by four of 5 (`'335555'`); equivalent encodings include `'2 of 345555'` shape variants. Requirements The forward operation reads digit pairs as (count, digit): '2345' becomes two 3s followed by four 5s, or '335555'. Given a decoded digits string, return every valid encoding, including different partitions of one repeated run such as four 5s encoded once as '45' or split as '15' + '35'. Notes Backtrack from left to right. At the start of a maximal equal-digit run of length k, choose a positive prefix length, emit (length, digit), and recurse on the unconsumed suffix. Define whether counts may contain multiple digits and whether adjacent segments with the same digit are allowed; these choices determine the result set. Disallow zero-count segments unless the contract explicitly permits them. Generate segments in a canonical order and use a set only as a defensive deduplication check. Preparation Implement the forward decoder first to make the contract executable. Enumerate '333' and '335555' by hand, then compare the backtracking output with the expected set. Test a single digit, all-distinct digits, a run longer than nine, and the chosen same-digit-adjacency rule.