We sketch a tentative proof of P-completeness for the $\beta$-convertibility problem on untyped planar (a.k.a. ordered or non-commutative) $\lambda$-terms.

翻译：我们勾勒了无类型平面（也称为有序或非交换）$λ$-项上$\beta$-可转换性问题的P完全性初步证明框架。