We've talked about simple sentences in which we divide verbs into intransitive verbs (comprising intransitive verbs with one dependent--verbs of movement and change-of-state verbs, and with two dependents) and transitive verbs (comprising transitive verbs with two dependents and 'ditransitive verbs', which take three dependents).

Now, we are ready to move on to sentences considered 'subordinate sentences' according to DG approach. Do you remember that 'dependent' we were talking about in simple sentences is essentially an NP? What about the following sentences?
a. Suda loves travelling.
b. John wants to finish his paper before friday.
c. Anita told her parents that she got accepted to Harvard.

DG considers the above sentences subordinate sentences. Again, the verb is the factor that determines if a sentence is a simple one or a subordinate one. When the verb takes a dependent in a verb form (either bare infinitive--i.e. work, to infinitive--i.e. to work, Ving--i.e. working) as in a. and b., or when the sentence takes a dependent that consists another verb as in c., the sentence is considered a subordinate sentence.

A subordinate sentence is a sentence that consists of at least two simple sentences, one being embedded within a larger unit or the main sentence. There are two types of dependents in subordinate sentences: the subordinate sentences with complements and with adjuncts.

When its dependent is required, the sentence is considered a subordinate sentence with complement. For example,

d. John said that he would arrive late.
e. John quitted smoking when he was in college.

Obviously, without 'that he ...' and 'smoking (when...), the sentences do not make any sense.

Now let's see what subordinate sentences with adjuncts look like;
f. Jane wants to talk to Mary to tell her about her grades.
g. Jane spotted Jim walking down the street nervously.

You may notice that 'to tell her... and 'walking down ...' are optional. The sentences make sense with or without those additional phrases.

h. John wants to be a lawyer to please his parents.
Can you list the dependents in the above sentence and identify how many dependents there are?
1. 'to be a lawyer': 1st dependent: complement
2. 'to please his parents': 2nd dependent (optional): adjunct

From the example in h. we can conclude that a complement tend to be closer to the head than an adjunct.