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functions, one can set .

The function then becomes a sequence of unary functions, defined from iteration:

Computation

Computation by LOOP program

The functions fit into the (finite-level) fast-growing hierarchy (FGH) of functions
:

The following inequality holds:

For fixed , the function can be computed by a LOOP program of nesting depth :
:
# INPUT (n)LOOP n: # nesting depth: 1 LOOP n: # nesting depth: 2 ... # ... LOOP n: # nesting depth: k n += 1 #
# OUTPUT (n)

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