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It still takes a few seconds to identify the word since this is not how Arabic is usually written but yes the word "Al-Khawarizmi" is legible.

In fact, the logo contains text both in black and navy blue, the navy blue part is "Al-Khawarizmi" or in Arabic "الخوارزمي". Then the navy blue script is rotated at 90 degrees 3 additional times.

no, it's very readable because it's a well known calligraphy called kufi as others have pointed out.

Yes, it is readable, it's called kuffi,

See http://www.kufic.info

thank you!