No descansaron, por eso deben haber terminado el proyecto temprano.

Questions & Answers about No descansaron, por eso deben haber terminado el proyecto temprano.

Why is deben in the present tense if they finished the project in the past?
We use the present tense deben because the speaker is making a deduction right now. The perfect infinitive (haber terminado) is what places the actual action (finishing the project) in the past. If you used the past tense and said debieron haber terminado, the meaning would change completely to an unfulfilled obligation: "they should have finished."
Since this sentence expresses a probability ("they must have"), shouldn't it be deben de haber terminado?
Strictly speaking, traditional grammar rules state that deber + infinitive expresses obligation, while deber de + infinitive expresses probability. So, deben de haber terminado is the classic way to say this. However, in everyday Latin American Spanish, native speakers frequently drop the de and use deber for both obligation and probability. The context here (using a perfect infinitive) makes it obvious that it's a deduction, not an obligation.
Could I just say por eso terminaron instead of using the perfect infinitive haber terminado?
You could, but it changes the meaning from a deduction to a stated fact. Por eso terminaron simply means "that's why they finished." By using the modal verb deben followed by the perfect infinitive haber terminado, you express an assumption based on evidence: "that's why they must have finished."
Can I use así que instead of por eso here?
Yes, you can. They are very similar and both work perfectly in this sentence. Por eso translates more directly to "for that reason" or "that's why," emphasizing that their lack of rest is the specific cause. Así que just means "so," which is slightly broader but completely natural here.

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