Football or Cupcake

A machine prints a string made of $17$ words, each chosen independently and uniformly at random from the vocabulary {cup, cake, foot, ball}, and joins them without spaces. Adjacent words that form a compound word are merged into a single word: "foot" followed by "ball" becomes the single word "football", and "cup" followed by "cake" becomes the single word "cupcake". No other pair forms a compound.

What is the expected number of words in the final string?