HSS Hydra

HSS Hydra 是一个序数记号。

定义

其合法式与极限基本列与 PSS Hydra 相同。

若表达式的最后一项为 $p_{0}$ ，处理方法与 PSS Hydra 一致；

若表达式的最后一项为 $p_{n + 1}$ ，那么从这一项开始，从里向外找到所有包含它的 $p_{n}$ ，将这些 $p_{n}$ 称为“根”；按字典序比较所有根内部的表达式，小于最内侧根的表达式叫做“小根”；位于最外侧的、自身不是“小根”、内部没有“小根”的根是最后一项复制时所要找的参考对象。把这个根内部的表达式不断复制在最后一项的位置，完成展开。

强度分析

HSS Hydra 的极限为 $ψ (M_{ω})$ 。该分析来自梅天狸的知乎文章，使用 BMS 与之对照。^[1]

p0=(0)

p0(p0)=(0)(1)

p0(p0(p0))=(0)(1)(2)

p0(p1)=(0,0)(1,1)

p0(p1+p0)=(0,0)(1,1)(1,0)

p0(p1+p0(p0))=(0,0)(1,1)(1,0)(2,0)

p0(p1+p0(p0(p1)))=(0,0)(1,1)(1,0)(2,1)

p0(p1+p0(p0(p1))+p0(p0(p1)))=(0,0)(1,1)(1,0)(2,1)(1,0)(2,1)

p0(p1+p0(p0(p1)+p0))=(0,0)(1,1)(1,0)(2,1)(2,0)

p0(p1+p0(p0(p1)+p0(p0(p1))))=(0,0)(1,1)(1,0)(2,1)(2,0)(3,1)

p0(p1+p0(p1))=(0,0)(1,1)(1,1)

p0(p1+p0(p1)+p0(p0(p1)+p0(p1)))=(0,0)(1,1)(1,1)(1,0)(2,1)(2,1)

p0(p1+p0(p1)+p0(p1))=(0,0)(1,1)(1,1)(1,1)

p0(p1+p0(p1+p0))=(0,0)(1,1)(2,0)

p0(p1+p0(p1+p0(p0)))=(0,0)(1,1)(2,0)(3,0)

p0(p1+p0(p1+p0(p0(p1))))=(0,0)(1,1)(2,0)(3,1)

p0(p1+p0(p1+p0(p0(p1)+p0(p1))))=(0,0)(1,1)(2,0)(3,1)(3,1)

p0(p1+p0(p1+p0(p1)))=(0,0)(1,1)(2,1)

p0(p1+p0(p1+p0(p1))+p0(p0(p1+p0(p1+p0(p1)))))=(0,0)(1,1)(2,1)(1,0)(2,1)(3,1)

p0(p1+p0(p1+p0(p1))+p0(p1))=(0,0)(1,1)(2,1)(1,1)

p0(p1+p0(p1+p0(p1))+p0(p1+p0(p0(p1+p0(p1+p0(p1))))))=(0,0)(1,1)(2,1)(1,1)(2,0)(3,1)(4,1)

p0(p1+p0(p1+p0(p1))+p0(p1+p0(p1)))=(0,0)(1,1)(2,1)(1,1)(2,1)

p0(p1+p0(p1+p0(p1)+p0))=(0,0)(1,1)(2,1)(2,0)

p0(p1+p0(p1+p0(p1)+p0(p0(p1+p0(p1+p0(p1))))))=(0,0)(1,1)(2,1)(2,0)(3,1)(4,1)

p0(p1+p0(p1+p0(p1)+p0(p1)))=(0,0)(1,1)(2,1)(2,1)

p0(p1+p0(p1+p0(p1+p0)))=(0,0)(1,1)(2,1)(3,0)

p0(p1+p0(p1+p0(p1+p0(p1))))=(0,0)(1,1)(2,1)(3,1)

p0(p1+p0(p1+p0(p1+p0(p1)))+p0(p1+p0(p1+p0(p1))))=(0,0)(1,1)(2,1)(3,1)(1,1)(2,1)(3,1)

p0(p1+p0(p1+p0(p1+p0(p1))+p0(p1+p0(p1))))=(0,0)(1,1)(2,1)(3,1)(2,1)(3,1)

p0(p1+p0(p1+p0(p1+p0(p1)+p0(p1))))=(0,0)(1,1)(2,1)(3,1)(3,1)

p0(p1+p0(p1+p0(p1+p0(p1+p0))))=(0,0)(1,1)(2,1)(3,1)(4,0)

p0(p1+p0(p1+p0(p1+p0(p1+p0(p1)))))=(0,0)(1,1)(2,1)(3,1)(4,1)

p0(p1+p1)=(0,0)(1,1)(2,2)

p0(p1+p1+p0(p0(p1+p1)))=(0,0)(1,1)(2,2)(1,0)(2,1)(3,2)

p0(p1+p1+p0(p1))=(0,0)(1,1)(2,2)(1,1)

p0(p1+p1+p0(p1+p0(p1)))=(0,0)(1,1)(2,2)(1,1)(2,1)

p0(p1+p1+p0(p1+p0(p1+p1)))=(0,0)(1,1)(2,2)(1,1)(2,2)

p0(p1+p1+p0(p1+p0(p1+p1)+p0))=(0,0)(1,1)(2,2)(2,0)

p0(p1+p1+p0(p1+p0(p1+p1)+p0(p1)))=(0,0)(1,1)(2,2)(2,1)

p0(p1+p1+p0(p1+p0(p1+p1)+p0(p1+p0(p1+p1))))=(0,0)(1,1)(2,2)(2,1)(3,2)

p0(p1+p1+p0(p1+p1))=(0,0)(1,1)(2,2)(2,2)

p0(p1+p1+p0(p1+p1+p0))=(0,0)(1,1)(2,2)(3,0)

p0(p1+p1+p0(p1+p1+p0(p1)))=(0,0)(1,1)(2,2)(3,1)

p0(p1+p1+p0(p1+p1+p0(p1+p0(p1+p1+p0(p1+p1)))))=(0,0)(1,1)(2,2)(3,1)(4,2)(4,2)

p0(p1+p1+p0(p1+p1+p0(p1+p1)))=(0,0)(1,1)(2,2)(3,2)

p0(p1+p1+p0(p1+p1+p0(p1+p1+p0(p1+p1))))=(0,0)(1,1)(2,2)(3,2)(4,2)

p0(p1+p1+p1)=(0,0)(1,1)(2,2)(3,3)

p0(p1+p1+p1+p0(p1+p0(p1+p1+p1)))=(0,0)(1,1)(2,2)(3,3)(1,1)(2,2)(3,3)

p0(p1+p1+p1+p0(p1+p1+p0(p1+p1+p1)))=(0,0)(1,1)(2,2)(3,3)(2,2)(3,3)

p0(p1+p1+p1+p0(p1+p1+p1))=(0,0)(1,1)(2,2)(3,3)(3,3)

p0(p1+p1+p1+p1)=(0,0)(1,1)(2,2)(3,3)(4,4)

p0(p1(p0))=(0,0,0)(1,1,1)

p0(p1(p0)+p0(p0(p1(p0))))=(0,0,0)(1,1,1)(1,0,0)(2,1,1)

p0(p1(p0)+p0(p1))=(0,0,0)(1,1,1)(1,1,0)

p0(p1(p0)+p0(p1+p0(p1(p0))))=(0,0,0)(1,1,1)(1,1,0)(2,2,1)

p0(p1(p0)+p0(p1+p1))=(0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)

p0(p1(p0)+p0(p1+p1+p0(p1(p0))))=(0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,3,1)

p0(p1(p0)+p0(p1+p1+p1))=(0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,3,1)(3,3,0)

p0(p1(p0)+p0(p1(p0))))=(0,0,0)(1,1,1)(1,1,1)

p0(p1(p0)+p0(p1(p0)+p0(p1)))=(0,0,0)(1,1,1)(2,1,0)

p0(p1(p0)+p0(p1(p0)+p0(p1))+p0(p1+p0(p1(p0)+p0(p1(p0)+p0(p1)))))=(0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)

p0(p1(p0)+p0(p1(p0)+p0(p1))+p0(p1+p1+p0(p1(p0)+p0(p1(p0)+p0(p1)))))=(0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,0)(3,3,1)(4,1,0)

p0(p1(p0)+p0(p1(p0)+p0(p1))+p0(p1(p0)))=(0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,1)

p0(p1(p0)+p0(p1(p0)+p0(p1)+p0(p1)))=(0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(3,1,0)

p0(p1(p0)+p0(p1(p0)+p0(p1+p1)))=(0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,2,0)

p0(p1(p0)+p0(p1(p0)+p0(p1+p1+p1)))=(0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,2,0)(2,2,0)(3,3,1)(3,3,0)

p0(p1(p0)+p0(p1(p0)+p0(p1(p0))))=(0,0,0)(1,1,1)(2,1,0)(1,1,1)

p0(p1(p0)+p0(p1(p0)+p0(p1(p0)))+p0(p1(p0)+p0(p1(p0))))=(0,0,0)(1,1,1)(2,1,0)(1,1,1)(2,1,0)(1,1,1)

p0(p1(p0)+p0(p1(p0)+p0(p1(p0))+p0(p1)))=(0,0,0)(1,1,1)(2,1,0)(1,1,1)(2,1,0)(2,1,0)

p0(p1(p0)+p0(p1(p0)+p0(p1(p0))+p0(p1(p0))))=(0,0,0)(1,1,1)(2,1,0)(2,1,0)(1,1,1)

p0(p1(p0)+p0(p1(p0)+p0(p1(p0)+p0(p1(p0)))))=(0,0,0)(1,1,1)(2,1,0)(3,1,0)(1,1,1)

p0(p1(p0)+p1)=(0,0,0)(1,1,1)(2,1,0)(3,2,0)

p0(p1(p0)+p1+p0(p1(p0)+p1))=(0,0,0)(1,1,1)(2,1,0)(3,2,0)(3,2,0)

p0(p1(p0)+p1+p1)=(0,0,0)(1,1,1)(2,1,0)(3,2,0)(4,3,0)

p0(p1(p0)+p1(p0))=(0,0,0)(1,1,1)(2,1,0)(3,2,1)

p0(p1(p0)+p1(p0)+p1)=(0,0,0)(1,1,1)(2,1,0)(3,2,1)(4,2,0)(5,3,0)

p0(p1(p0)+p1(p0)+p1(p0))=(0,0,0)(1,1,1)(2,1,0)(3,2,1)(4,2,0)(5,3,1)

p0(p1(p0+p0))=(0,0,0)(1,1,1)(2,1,1)

p0(p1(p0+p0)+p0(p1(p0+p0)))=(0,0,0)(1,1,1)(2,1,1)(1,1,1)(2,1,1)

p0(p1(p0+p0)+p0(p1(p0+p0)+p0(p1)))=(0,0,0)(1,1,1)(2,1,1)(2,1,0)

p0(p1(p0+p0)+p0(p1(p0+p0)+p0(p1(p0))))=(0,0,0)(1,1,1)(2,1,1)(2,1,0)(1,1,1)

p0(p1(p0+p0)+p0(p1(p0+p0)+p0(p1(p0+p0))))=(0,0,0)(1,1,1)(2,1,1)(2,1,0)(1,1,1)(2,1,1)

p0(p1(p0+p0)+p1)=(0,0,0)(1,1,1)(2,1,1)(2,1,0)(3,2,0)

p0(p1(p0+p0)+p1(p0+p0))=(0,0,0)(1,1,1)(2,1,1)(2,1,0)(3,2,1)(4,2,1)

p0(p1(p0+p0+p0))=(0,0,0)(1,1,1)(2,1,1)(2,1,1)

p0(p1(p0(p0)))=(0,0,0)(1,1,1)(2,1,1)(3,0,0)

p0(p1(p0(p0(p1))))=(0,0,0)(1,1,1)(2,1,1)(3,0,0)(4,1,0)

p0(p1(p0(p0(p1(p0)))))=(0,0,0)(1,1,1)(2,1,1)(3,0,0)(4,1,1)

p0(p1(p0(p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)

p0(p1(p0(p1))+p0(p1+p0(p1(p0(p1)))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)

p0(p1(p0(p1))+p0(p1(p0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)

p0(p1(p0(p1))+p0(p1(p0(p1))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(2,2,1)(3,2,1)(4,1,0)

p0(p1(p0(p1))+p1)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(3,2,0)(4,3,0)

p0(p1(p0(p1))+p1(p0(p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(3,2,0)(4,3,1)(5,3,1)(6,1,0)

p0(p1(p0(p1)+p0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(3,2,1)

p0(p1(p0(p1)+p0(p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,1,0)(3,2,1)(4,1,0)

p0(p1(p0(p1+p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,0)(2,2,1)(3,2,1)(4,2,0)

p0(p1(p0(p1(p0))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)

p0(p1(p0(p1(p0+p0))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)

p0(p1(p0(p1(p0(p1)))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)

p0(p1(p1))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)

p0(p1(p1)+p0(p1))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)(1,1,0)

p0(p1(p1)+p0(p1(p0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)(1,1,1)

p0(p1(p1)+p0(p1(p0(p1(p1)))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)

p0(p1(p1)+p0(p1(p0(p1(p1)))+p0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)(2,0,0)

p0(p1(p1)+p0(p1(p0(p1(p1)))+p0(p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)

p0(p1(p1)+p0(p1(p0(p1(p1)))+p0(p1(p1))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)

p0(p1(p1)+p0(p1(p0(p1(p1)))+p1))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,0)

p0(p1(p1)+p0(p1(p0(p1(p1)))+p1(p0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)

p0(p1(p1)+p0(p1(p0(p1(p1)))+p1(p0(p1(p1)))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,1,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)

p0(p1(p1)+p0(p1(p0(p1(p1))+p0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,1,0)(4,2,1)

p0(p1(p1)+p0(p1(p0(p1(p1))+p0(p1(p1)))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,1,0)(4,2,1)(5,1,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)

p0(p1(p1)+p0(p1(p0(p1(p1)+p0))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,1,0)(5,0,0)

p0(p1(p1)+p0(p1(p0(p1(p1)+p0(p1(p0(p1(p1))))))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,1,0)(5,1,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)

p0(p1(p1)+p0(p1(p0(p1(p1)+p0(p1(p0(p1(p1)))+p0(p1(p0(p1(p1)))+p1))))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,1,0)(6,2,0)

p0(p1(p1)+p0(p1(p0(p1(p1)+p0(p1(p0(p1(p1)))+p1))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,0)(3,2,1)(4,2,1)(5,2,0)

p0(p1(p1)+p0(p1(p0(p1(p1)+p0(p1(p0(p1(p1)))+p1(p0(p1(p1)))))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,0)(3,2,1)(4,2,1)(5,1,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)

p0(p1(p1)+p0(p1(p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,0)(4,0,0)

p0(p1(p1)+p0(p1(p1))+p0(p1(p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,0)(4,2,0)(5,3,1)(6,3,1)(7,3,0)(6,0,0)

p0(p1(p1)+p0(p1(p1)+p0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)

p0(p1(p1)+p0(p1(p1)+p0+p0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(2,1,1)

p0(p1(p1)+p0(p1(p1)+p0(p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)

p0(p1(p1)+p0(p1(p1)+p0(p1(p0(p1(p1))))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)

p0(p1(p1)+p0(p1(p1)+p0(p1(p0(p1(p1)+p0(p1(p1)+p0))))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)

p0(p1(p1)+p0(p1(p1)+p0(p1(p1))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)

p0(p1(p1)+p0(p1(p1)+p0(p1(p1))+p0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)

p0(p1(p1)+p0(p1(p1)+p0(p1(p1))+p0(p1(p1))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)

p0(p1(p1)+p0(p1(p1)+p0(p1(p1)+p0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(3,0,0)

p0(p1(p1)+p0(p1(p1)+p0(p1(p1)+p0(p1(p1)))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(3,1,0)(2,0,0)

p0(p1(p1)+p1)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)

p0(p1(p1)+p1+p1)=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)(5,3,0)

p0(p1(p1)+p1(p0))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)

p0(p1(p1)+p1(p0(p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)

p0(p1(p1)+p1(p0(p1(p1))))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)(2,0,0)

p0(p1(p1)+p1(p0(p1(p1))+p1))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)

p0(p1(p1)+p1(p1))=(0,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,0,0)

p0(p1(p1+p0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)

p0(p1(p1+p0+p0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)

p0(p1(p1+p0(p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)

p0(p1(p1+p0(p1(p0(p1(p1))))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(2,0,0)

p0(p1(p1+p0(p1(p0(p1(p1+p0))))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)

p0(p1(p1+p0(p1(p0(p1(p1+p0(p1)))))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1,0)

p0(p1(p1+p0(p1(p1))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1,0)(2,0,0)

p0(p1(p1+p0(p1(p1+p0))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)

p0(p1(p1+p1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)

p0(p1(p1+p1)+p0(p1(p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,0)(4,0,0)

p0(p1(p1+p1)+p0(p1(p1+p0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,1)

p0(p1(p1+p1)+p0(p1(p1+p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,1)(4,2,1)(5,2,0)(4,0,0)

p0(p1(p1+p1)+p0(p1(p1+p1)+p0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,1,1)

p0(p1(p1+p1)+p1)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,0)

p0(p1(p1+p1)+p1(p1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,0,0)

p0(p1(p1+p1)+p1(p1+p0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)

p0(p1(p1+p1)+p1(p1+p1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(5,0,0)

p0(p1(p1+p1+p0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)

p0(p1(p1+p1+p1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)

p0(p1(p1(p0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,0,0)

p0(p1(p1(p0(p1))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)

p0(p1(p1(p0(p1(p1(p0))))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,1)(3,0,0)

p0(p1(p1(p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)

p0(p1(p1(p1))+p0(p1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)(1,1,0)

p0(p1(p1(p1))+p0(p1(p0(p1(p1(p1))))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)

p0(p1(p1(p1))+p0(p1(p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,1,0)(2,0,0)

p0(p1(p1(p1))+p0(p1(p1+p0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,1)

p0(p1(p1(p1))+p0(p1(p1(p0))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,1)(3,0,0)

p0(p1(p1(p1))+p0(p1(p1(p0(p1)))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)

p0(p1(p1(p1))+p0(p1(p1(p0(p1(p1(p1)))))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,0,0)

p0(p1(p1(p1))+p0(p1(p1(p0(p1(p1(p1)))))+p1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,0)(3,2,0)

p0(p1(p1(p1))+p0(p1(p1(p1))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,0)(3,2,1)(4,2,1)(5,2,1)(5,2,0)(4,0,0)

p0(p1(p1(p1))+p0(p1(p1(p1))+p0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)

p0(p1(p1(p1))+p0(p1(p1(p1))+p0(p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)

p0(p1(p1(p1))+p0(p1(p1(p1))+p0(p1(p1(p1)))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(2,0,0)

p0(p1(p1(p1))+p1)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,0)

p0(p1(p1(p1))+p1(p1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,0,0)

p0(p1(p1(p1))+p1(p1(p0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,0,0)

p0(p1(p1(p1))+p1(p1(p0(p1(p1(p1))))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,1,0)(2,0,0)

p0(p1(p1(p1))+p1(p1(p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(5,0,0)

p0(p1(p1(p1)+p0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)

p0(p1(p1(p1)+p1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(2,1,1)(3,1,0)(2,0,0)

p0(p1(p1(p1)+p1(p0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(3,0,0)

p0(p1(p1(p1)+p1(p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(2,1,1)(3,1,1)(3,1,0)(2,0,0)

p0(p1(p1(p1+p0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,0,0)

p0(p1(p1(p1+p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(3,1,0)(2,0,0)

p0(p1(p1(p1(p1))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,1,0)(2,0,0)

p0(p1(p2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)

p0(p1(p2)+p0(p1(p2)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)

p0(p1(p2)+p1)=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(2,1,0)(3,2,0)

p0(p1(p2)+p1(p1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(2,1,0)(3,2,1)(4,2,1)(5,2,0)(4,0,0)

p0(p1(p2)+p1(p2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(2,1,0)(3,2,1)(4,2,1)(5,2,1)(5,2,0)(6,3,0)

p0(p1(p2+p0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(2,1,1)

p0(p1(p2+p0(p1(p2))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(2,1,1)(3,1,0)(1,1,1)(2,1,1)(3,1,0)(4,2,0)

p0(p1(p2+p1))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(2,1,1)(3,1,0)(2,0,0)

p0(p1(p2+p1+p0))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(2,1,1)(3,1,1)

p0(p1(p2+p1(p1))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(2,1,1)(3,1,1)(3,1,0)(2,0,0)

p0(p1(p2+p1(p1(p2)))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(2,1,1)(3,1,1)(3,1,0)(4,2,0)

p0(p1(p2+p1(p1(p2)+p1))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(3,1,0)(2,0,0)

p0(p1(p2+p1(p1(p2)+p1(p1(p2))))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(3,1,0)(4,2,0)

p0(p1(p2+p1(p2)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(4,2,0)

p0(p1(p2+p1(p2+p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(5,1,0)(2,0,0)

p0(p1(p2+p1(p2+p1(p1(p2)))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(5,1,0)(6,2,0)

p0(p1(p2+p1(p2+p1(p2))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(5,2,0)

p0(p1(p2+p2))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)(5,3,0)

p0(p1(p2(p0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)

p0(p1(p2(p0(p1(p2)))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,0)

p0(p1(p2(p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)(2,0,0)

p0(p1(p2(p1(p1(p2)))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,1,0)(7,2,0)

p0(p1(p2(p1(p2))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)

p0(p1(p2(p2)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,0)(5,0,0)

p0(p1(p2(p2+p0)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)

p0(p1(p2(p2+p1)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,1,0)(2,0,0)

p0(p1(p2(p2+p2)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(5,2,1)(6,2,0)(5,0,0)

p0(p1(p2(p2(p0))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,0,0)

p0(p1(p2(p2(p2))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(5,0,0)

p0(p1(p2(p3)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(7,3,0)

p0(p1(p2(p3+p3)))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(7,3,0)(8,4,0)

p0(p1(p2(p3(p3))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,0)(8,0,0)

p0(p1(p2(p3(p4))))=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,0)(4,2,1)(5,2,1)(6,2,1)(6,2,0)(7,3,1)(8,3,1)(9,3,1)(9,3,0)(10,4,0)

limit=(0,0,0)(1,1,1)(2,1,1)(3,1,1)(3,1,1)

↑ SuzukaFox (2025). HSS hydra扽西练习 [HSS Hydra Analysus Practice]. (EB/OL), Zhihu. Available at: https://zhuanlan.zhihu.com/p/1930637321335706887

[1] SuzukaFox (2025). HSS hydra扽西练习 [HSS Hydra Analysus Practice]. (EB/OL), Zhihu. Available at: https://zhuanlan.zhihu.com/p/1930637321335706887

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