Decidability of residual finiteness for one-relator groups

Develop an algorithm that, given a finite one-relator presentation, decides whether the corresponding group is residually finite.

Background

Residual finiteness is a central property with deep implications (e.g., hopficity and algorithmic consequences). Many one-relator groups are known to be residually finite via geometric and profinite techniques, but there is no general decision procedure known for this class.