False positive when incrementing unsigned integer

[nc]

I have encountered a false positive in Cppcheck 2.13.0

Severity: style
Summary: Condition '++counter==0' is always false

Example code that triggers the false positive:

#include <iostream>
#include <limits>

void incr(unsigned & counter)
{
    std::cout << "Incrementing counter. Curr value: " << counter << '\n';

    if (++counter == 0)
    {
        std::cout << "Condition '++counter == 0' is true\n";
    }

    std::cout << "Value after increment: " << counter << '\n';
}

int main()
{
    unsigned counter {};
    incr(counter);

    counter = std::numeric_limits<unsigned>::max();
    incr(counter);
}

[CHR]

Looks like an instance of this issue: https://trac.cppcheck.net/ticket/10616