The pumping lemma states that formula_3 can be split into five substrings, formula_7, where formula_21 is non-empty and the length of formula_22 is at most formula_5, such that repeating formula_24 and formula_25 the same number of times (formula_26) in formula_3 produces a string that is still in the language. It is often useful to repeat zero times, which removes formula_24 and formula_25 from the string. This process of "pumping up" additional copies of formula_24 and formula_25 is what gives the pumping lemma its name.