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The phrase "ascending order of complexity" is correct and usable in written English.
It can be used when discussing a sequence or arrangement that increases in complexity from the simplest to the most complex.
Example: "The tasks were arranged in ascending order of complexity, starting with the easiest and progressing to the most challenging."
Alternatives: "increasing complexity" or "gradually more complex".
Exact(4)
Fitch's experiments were based on the so-called Chomsky hierarchy, a system for classifying types of grammar, ranked in ascending order of complexity.
The toys, which he called gifts, consisted of six sets, or groups, arranged in ascending order of complexity, beginning with coloured worsted balls and progressing to such objects as blocks, squares, and cubes.
We used criteria taken from the 'cognitive dimensions' literature and an exercise of typical geometric operations in ascending order of complexity.
Next, the concept-evaluation framework, proposed in an earlier work, is used to organize the topologies obtained in an ascending order of complexity, hence completing the conceptual design phase of the subject motion generators.
Similar(56)
The strategies are presented in ascending order of implementation complexity.
Thermal models of 3-D circuits include analytic expressions, compact thermal resistive networks, and 3-D grids for finite element analysis, in ascending order of increasing computational complexity and accuracy.
We have ignored the complexity of sorting the open stack according to ascending order of their f-function values.
Perhaps in ascending order of intelligence?
Here they are, in ascending order of importance.
I list them in ascending order of plausibility: 1.
That's in ascending order of horror, presumably.
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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