Sequence of tenses: past simple + present perfect

Question

I'm having a problem with reporting the following sentence in a simple-past context:

Person X: Since they arrived, he's been very happy.

The person X said that since they had arrived, he (???) very happy.

Thank you very much!

Answer 1

Here is our original sentence, in direct speech:

Person X: Since they arrived, he's been very happy.

To report that sentence, which was said in the past, in indirect speech, there are a few ways to change the tenses:

(a) Person X said that since they had arrived, he had been very happy.
(b) Person X said that since they arrived, he was very happy.
(c) Person X said that since they arrived, he has been very happy.

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The typical tense changes after past reporting verb (said in our sentence) are discussed in Practical English Usage by Michael Swan under 275.2. Here is the summary:

will → would
simple present → simple past
present progressive → past progressive
present perfect → past perfect
past → past perfect
can → could
may → might
past perfect tenses do not change

So, if we applied these rules to our sentence, "past → past perfect" would change arrived into had arrived, and "present perfect → past perfect" would change he's been into he had been (or he'd been). This is how we get sentence (a).

(a) Person X said that since they had arrived, he had been very happy.

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However, as Swan noted in 278.1 indirect speech (5): advanced points: reporting past tenses,

However, past perfect tenses are not always used, especially if the time relationships are clear without a change from past to past perfect.
    This man on TV said that dinosaurs were around for 250 million years.
    (NOT *... that dinosaurs had been around ...)
    I told you John (had) phoned this morning, didn't I?
    We were glad to hear you (had) enjoyed your trip to Denmark.

Because in your sentence it is clear that the arrival was the reason of his being happy, thus the backshift from arrived to had arrived is optional. And since we chose not to backshift the since-clause, we must change the tense in the main clause to match it. This is how we get sentence (b).

(b) Person X said that since they arrived, he was very happy.

Note that, though the sentence is possible, the usage of the tenses is a little different from the original.

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Here is another possibility, which reports what person X said more faithfully. If that person X said the sentence recently, and we can safely assume that what X said is still true, then the backshift is entirely optional. This is how we get sentence (c).

(c) Person X said that since they arrived, he has been very happy.

Answer 2

With reported speech, both the simple past and the present perfect tenses usually both shift to the past perfect, provided that there is no relevance to the present.

That would suggest:

Person X: Since they arrived, he's been very happy.

Person X said that since they'd arrived, he'd been very happy.

With that said, this source, however, notes:

You do not need to change the tense if the reporting verb is in the present, or if the original statement was about something that is still true.

While the statement is not in the present tense, it could potentially still be true/applicable.

So, in other words, if the person whom Person X is speaking about is, in fact, still happy and the situation is unchanged, then you don't need to shift the tense backward.

For example:

Person X: My neighbor was very happy after the new tenants initially moved in; that is, of course until they began stealing his mail.

Per Person X, since the new tenants had moved in, his neighbor had initially been very happy; that was, however, he said, before they'd begun stealing his neighbor's mail.

Side note: If this is something that you've written yourself (as opposed to an example you're directly quoting from a grammar book), I think that the entire sentence (i.e. the direct speech) should be in the present perfect.

E.g.:

Person X: Since the couple has arrived, the gentleman has been very happy.

Person X said that since the couple had arrived, the gentleman had been very happy. (or, if this is still applicable According to Person X, the gentleman has been very happy since the couple has arrived.)

Answer 3

It's quite simple actually once you use the rules for reported speech. Since you are using the simple past context, every tense must shift to its respective past form.

So, the simple past tense should become the past perfect tense and the present perfect tense should become the past perfect tense.

Your answer should be:

The person X said that since they had arrived, he had been very happy.

There are no two ways about this one; this is the only way to do it.