Conway chained arrow notation

Conway chained arrow notation, created by mathematician John Horton Conway, is a means of expressing certain extremely large numbers. It is simply a finite sequence of positive integers separated by rightward arrows, e.g. 2 → 3 → 4 → 5 → 6.

As with most combinatorial notations, the definition is recursive. In this case the notation eventually resolves to being the leftmost number raised to some (usually enormous) integer power.

A Conway chain (or chain for short) is defined as follows:

Any chain represents an integer, according to the four rules below. Two chains are said to be equivalent if they represent the same integer.

If ${\displaystyle p}$ and ${\displaystyle q}$ are positive integers, and ${\displaystyle X}$ is a subchain, then:

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