We can notice that we will stay in state zero as long as the output is identical to the input.
we can move from state zero, which corresponds to edit distance zero, to state one, which corresponds to edit distance one, with three different ways: • input is mapped to a different output (input is consumed and a different symbol is emitted) which corresponds to a substitution, • input is mapped to an epsilon (input is consumed and no output emitted) which corresponds to a deletion, and • an epsilon is mapped to an output (output is emitted without consuming any input) which corresponds to an insertion.