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Example

Let <= be a total order on an alphabet A, let W_n := N_n -> A be the set of all words with n letters, and let

w := such u: exists n in N: w in Wn /\  u in Wn-1 /\  forall i in Nn-1: ui = wi+1

The lexicographic order <= _n subset W_n x W_n defined as

w <= n u : <=> n = 0 \/ w0 < u0 \/ (w0 = u0 /\  w <= n-1 u)

"back" < ₄ "bare" < ₄ "base" < ₄ "bear" < ₄ "bend" < ₄ "care"

Compare letters in the order of their positions.