Decision problems for two‑relator groups

Determine the decidability of the word problem, the conjugacy problem, and the isomorphism problem for finitely presented two‑relator groups.

Background

Unlike the one‑relator case (word problem solved by Magnus), the two‑relator setting lacks any general positive results: the core decision problems are unsolved. The authors emphasize that even finiteness classification is open, underscoring the gap between one‑ and two‑relator theories.

A resolution would be a major advance in combinatorial and geometric group theory.