Conjugacy problem for residually nilpotent one-relator groups

Determine whether the conjugacy problem is decidable in the subclass of residually nilpotent one-relator groups.

Background

Residually nilpotent groups retain substantial control via their lower central series, yet the difficulty of the conjugacy problem can persist. Understanding this subclass could bridge algorithmic results between general one-relator groups and well-behaved residually nilpotent cases.