In this work we investigate the Weihrauch degree of the problem $\mathsf{DS}$ of finding an infinite descending sequence through a given ill-founded linear order, which is shared by the problem $\mathsf{BS}$ of finding a bad sequence through a given non-well quasi-order. We show that $\mathsf{DS}$, despite being hard to solve (it has computable inputs with no hyperarithmetic solution), is rather weak in terms of uniform computational strength. To make the latter precise, we introduce the notion of the deterministic part of a Weihrauch degree. We then generalize $\mathsf{DS}$ and $\mathsf{BS}$ by considering $\boldsymbol{\Gamma}$-presented orders, where $\boldsymbol{\Gamma}$ is a Borel pointclass or $\boldsymbol{\Delta}^1_1$, $\boldsymbol{\Sigma}^1_1$, $\boldsymbol{\Pi}^1_1$. We study the obtained $\mathsf{DS}$-hierarchy and $\mathsf{BS}$-hierarchy of problems in comparison with the (effective) Baire hierarchy and show that they do not collapse at any finite level.

翻译：在这项工作中,我们调查了在某个没有根据的线性顺序中找到无限递减序列的Weishrauch 问题的程度 $\ mathsfsf{DS} 。 在这项工作中,我们调查了通过给定的非高级准顺序找到坏序列的$\ mathsfsf{BS} 美元。 我们显示,$\ mathsf{DS} 尽管很难解决( 它有可计算的投入,没有超度溶液),但在统一计算强度方面相当薄弱。 要精确地说明后一点,我们引入了Weishrauch 等级中确定性部分的概念。 然后我们通过考虑 $\ boldsymsbol_Gamma} $ 和 $\ bassy_Basy_Basy_Basy_r_Basy_Basy_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_ $ $的任何问题, 在任何BAR_BAR_BAR_BAR_BAR_BAR_BAR_BAR_$BAR________$的比较, $ $ $和BAR_BAR_BAR_BAR_BAR_BAR_BAR______$的 $的比较。