The decomposability-or-regularity conjecture for ultrafilters

Let $obreak\break obreak\lambda<\mu$ be cardinals, and let $D$ be a $(\lambda^+,\mu)$-regular ultrafilter. Decomposability-or-regularity conjecture. $D$ is either $obreak\break obreak\lambda$-decomposable, or $(\lambda',\mu)$-regular for some regular $obreak\break obreak\lambda'\leq\lambda$. The source says that this may be true and provides no resolution.