Are "Creep up" and "Climb up" phrasal verb?

Solution 1:

The test to distinguish a

[Verb + [Prepositional Phrase]]

constituent from a

[[Phrasal Verb] + Object]

constituent uses the syntactic rule of Particle Shift, which applies only to phrasal verbs.

The test works like this: true transitive phrasal verbs like look up in its 'research' sense govern the syntactic alternation that produces these two synonymous grammatical sentences:

• I looked up the word in a dictionary.
• I looked the word up in a dictionary.

The "particle" (which is a question-begging term for the "preposition part" of a phrasal verb) may appear either before or after the direct object noun phrase, at the speaker's choice. There is no difference except pronunciation between these two variants. Further examples:

• They burned up/down the barn. ~ They burned the barn up/down.
• She drank up/down her coffee. ~ She drank her coffee up/down.

By comparison, real prepositional phrases do not allow the object to appear before the preposition:

• He looked up the staircase, but not *He looked the staircase up.

Applying this test to the original example phrases, we find that

• The ivy is creeping up the backstairs, but not *The ivy is creeping the backstairs up.
• The ivy is climbing up the wall, but not *The ivy is climbing the wall up.

So the syntax lab results show that these are not phrasal verbs (because they fail the test),
but rather verbs modified by prepositional phrases.

The situation is even more definitive with a pronoun object; phrasal verbs require Particle Shift with pronoun objects, so we get very clear contrasts like

• That's the dictionary I looked it up in
  ~
  *That's the dictionary I looked up it in.
  but
• *The back wall, the ivy is climbing it up
  ~
  The back wall, the ivy is climbing up it.