An Automated Approach to the Collatz Conjecture

Abstract We explore the Collatz conjecture and its variants through lens of termination string rewriting. construct a rewriting system that simulates iterated application function on strings corresponding to mixed binary–ternary representations positive integers. prove this is equivalent conjecture. also previously studied using unary does not admit proofs via natural matrix interpretations, even when used in conjunction with dependency pairs. To show feasibility our approach proving mathematically interesting statements, we implement minimal prover uses natural/arctic interpretations find automated nontrivial weakenings Although do succeed conjecture, believe ideas here represent an new approach.