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The phrase "appears to be declining" is grammatically correct and can be used in written English.
It describes a decrease in something, either temporary or lasting. For example, "Recent surveys indicate that public interest in the matter appears to be declining."
Exact(60)
Filmmaking appears to be declining.
But it appears to be declining.
Support for other jihadist groups also appears to be declining.
It's not necessarily making people richer, since household income appears to be declining.
All agree it is good that food waste appears to be declining, but terrible that it is still so high.
The Guardian's opening salvo was pretty depressing as well: "Support for gender equality appears to be declining".
Yet as science fair season kicks into high gear, participation among high school students appears to be declining.
On Monday, the WHO said "the number of new cases occurring each day… appears to be declining".
The population appears to be declining due to habitat destruction, but it is considered not yet to have crossed a threshold to list it as threatened.
But now their leverage appears to be declining as tensions rise with Iraqi Arabs, raising the specter of another fissure alongside the sectarian divide between Sunnis and Shiites.
Deforestation for the past half century has been a major source of greenhouse gas emissions, although that too now appears to be declining.
More suggestions(18)
appears to be shrinking
appears to be lowering
appears to be indulging
appears to be advancing
appears to be reconsidering
appears to be decaying
appears to be increasing
appears to be diminishing
appears to be undermining
seems to be declining
appears to be losing
appears to be descending
appears to be deepening
appears to show declining
appears to be decreasing
appears to be yielding
appears to be receding
appears to be sliding
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com