Can the subsequences overlap?

If not, what should

aaaaaaaaaaa*aa*aaaaaaaaaaaaaaa*aa*aaaaaaaaaaa
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return? The following all match some interpretation of your spec:

aaaaaaaaaaa*aa*aaaaaaaa     2
aaaaaaa*aa*aaaaaaaaaaa      2
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or

aaaaaaaaaaa*aa*aaaaaaaaaa   2
aaaaa*aa*aaaaaaaaaaa        2
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or

aaaaaaaaaa                  0
a*aa*aaaaaaaaaaaaaaa*aa*a   4
aaaaaaaaaa                  0
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or

aaaaaaaaaaa                 0
*aa*aaaaaaaaaaaaaaa*aa*     4
aaaaaaaaaaa                 0
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