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it is almost 6 years old so I think it is time to lay it down to rest. can't hurt trying that piece of software though. I reinstalled the OS completely clean a year ago and she only uses it for a bit of word processing and netflix. plenty of storage space left. spotify seems to make it drop to its knees though
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4GB of RAM is barely anything these days but that shouldn't mean the computer isn't capable of running as smoothly as it did before unless there's some hardware fault.
If you've re-installed the OS, that's one thing. Is there a possibility some malware got on there? Try that Dr. Cleaner thing or a trial of Cocktail (maintain.se) and if that doesn't improve matters, download Black Magic Disk Speed Test. Totally legit disk benchmarking tool. That should indicate if the SSD is wearing out.
Is the Air slow in a particular way? A lot of these "cleaning" apps are full of Adware but some of them are legit.