Let ⟨x1,…,xn∣r1,…,rn⟩ be a balanced presentation of the trivial group. Can its relators always be transformed to (x1,…,xn) using finitely many of the following moves?
- Invert a relator.
- Multiply one relator by another.
- Conjugate a relator by any word in the generators.
A bounded computational search that finds no sequence does not establish a counterexample. This question concerns the original conjecture; stabilized variants allowing extra generator–relator pairs are distinct.