This is independent,
    !HPF$ INDEPENDENT
    DO i = 1, n
     b(i) = b(i) + b(i)
    END DO
this is not, (dependence on order of execution),
    DO i = 1, n
     b(i) = b(i+1) + b(i)
    END DO
nor is this,
    DO i = 1, n
     b(i) = b(i-1) + b(i)
    END DO
however, this is
!HPF$ INDEPENDENT
    DO i = 1, n
     a(i) = b(i-1) + b(i)
    END DO
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