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Basic (Alemagno12's Hydra)

# is any valid expression.

Start with a number n.

() --> End of game

#() --> #

(#()) --> (#)(#)(#)...(#)(#)(#) n times

Function AH(n) starts with n = 1, increases n by 1 every step, and resolves the hydra (((...((()))...))) with n levels

As you can see, this is the same as Kirby-Paris Hydras.

Multiple types (Extended Alemagno12's Hydra)

()a --> (((...((()a-1)a-1)a-1...)a-1)a-1)a-1 with n levels

(#())a --> (((...(((#)a-1)a-1)a-1...)a-1)a-1)a-1 with n levels

#(#)1 = #(#)

Function EAH(n) starts with n = 1, increases n by 1 every step, and resolves the hydra (((...((()n)n)n...)n)n)n with n levels

Nested types (Nested Alemagno12's Hydra)

()a --> (){()()()...()()()} with a ()'s

Function NAH(n) starts with n = 1, increases n by 1 every step, and resolves the hydra (){(){(){...(){(){(){()()}}}}}} with n levels

NEW SYSTEM (Advanced Alemagno12's Hydra)

()a --> (((...((()a-1)a-1)a-1...)a-1)a-1)a-1 with n levels

(#)a -->  ((#)a)a-1

#()a = #(((...(((#)a-1)a-1)a-1...)a-1)a-1)a-1 with n levels

(#())a = (#)a(#)a(#)a...(#)a(#)a(#)a with n (#)a's

Function AAH(n) starts with n = 1, increases n by 1 every step, and resolves the hydra (((...((()n)n)n...)n)n)n with n levels

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