"She is looking forward to a rest."
Wikipedia explains that this sentence is a case of a particle-prepositional phrasal verb where "forward" is a particle and "to" is a preposition
...but I'm confused about what the actual verb of the sentence is. Is it just "looking"? Or should I say "is looking"? Or, because this is a phrasal verb, I shouldn't try to separate the word "looking" from its full phrasal form "looking forward to"? (And thus if I were asked what the full predicate is, should I reply that it is "is looking forward to"?)