std::string class inheritance and tedious c++ overload resolution #2, C++ (gcc)

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#include <string>

template <class t_elem, class t_traits, class t_alloc>
class path_basic_string : public std::basic_string<t_elem, t_traits, t_alloc>
{
public:
    using base_type = std::basic_string<t_elem, t_traits, t_alloc>;

path_basic_string() = default;
    path_basic_string(const path_basic_string & ) = default;
    path_basic_string(path_basic_string &&) = default;

path_basic_string & operator =(path_basic_string path_str)
    {
        this->base_type::operator=(std::move(path_str));
        return *this;
    }

path_basic_string(base_type r) :
        base_type(std::move(r))
    {
    }

path_basic_string(const t_elem * p) :
        base_type(p)
    {
    }

base_type & str()
    {
        return *this;
    }

const base_type & str() const
    {
        return *this;
    }

using base_type::base_type;
    using base_type::operator=;

// ... all over operators are removed as not related to the issue ...

// (1)
    friend path_basic_string operator+ (const t_elem * p, const base_type & r)
    {
        path_basic_string l_path = p;
        l_path += "xxx";
        return std::move(l_path);
    }

friend path_basic_string operator+ (const t_elem * p, base_type && r)
    {
        if (!r.empty()) {
            return "111" + ("/" + r); // call base operator instead in case if it is specialized for this
        }

return "111";
    }

// (2)
    friend path_basic_string operator+ (const t_elem * p, path_basic_string && r)
    {
        base_type && r_path = std::move(std::forward<base_type>(r));
        if (!r_path.empty()) {
            return "222" + ("/" + r_path); // call base operator instead in case if it is specialized for this
        }

return "222";
    }

// (3) required here to intercept the second argument
    template <typename T>
    friend path_basic_string operator+ (const t_elem * p, T && r)
    {
        base_type && r_path = std::move(std::forward<base_type>(r));
        if (!r_path.empty()) {
            return "333" + ("/" + r_path); // call base operator instead in case if it is specialized for this
        }

return "333";
    }
};

using path_string = path_basic_string<char, std::char_traits<char>, std::allocator<char> >;

std::string test_path_string_operator_plus_right_xref(path_string && right_path_str)
{
    return "aaa" + right_path_str;
}

int main()
{
    const path_string test =
        test_path_string_operator_plus_right_xref(std::move(path_string{ "bbb" }));
    printf("-%s-\n", test.str().c_str());

return 0;
}

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Compilation time: 0.33 sec, absolute running time: 0.2 sec, cpu time: 0.11 sec, memory peak: 3 Mb, absolute service time: 0,54 sec