Overload resolution of template functions

Consider this code:

//Number1
template<typename T1, typename T2>
auto max (T1 a, T2 b)
{
    std::cout << "auto max(T1 a, T2 b)" <<std::endl;
    return  b < a ? a : b;
}

//Number2
template<typename RT, typename T1, typename T2>
RT max (T1 a, T2 b)
{
    std::cout << "RT max(T1 a, T2 b)" << std::endl;
    return  b < a ? a : b;
}


int main()
{
    auto a = ::max(4, 7.2);         //Select Number1

    auto b = ::max<double>(4, 7.4); //Select Number2

    auto c = ::max<int>(7, 4.);     //Compile-time error overload ambiguous

        auto c = ::max<double>(7, 4.); //Select Number2

}

auto c = ::max<int>(7, 4.); : This line fails to compile because of overload ambiguity with the following message:

maxdefault4.cpp:9:27: error: call of overloaded 'max(int, double)' is ambiguous
  auto c = ::max<int>(7, 4.);
                           ^
maxdefault4.cpp:9:27: note: candidates are:
In file included from maxdefault4.cpp:1:0:
maxdefault4.hpp:4:6: note: auto max(T1, T2) [with T1 = int; T2 = double]
 auto max (T1 a, T2 b)
      ^
maxdefault4.hpp:11:4: note: RT max(T1, T2) [with RT = int; T1 = int; T2 = double]
 RT max (T1 a, T2 b)
    ^

while the following code: àuto c = ::max<double>(7, 4.) succeed, why don't we have the same error message saying the call is amgiguous for max<double> the same the way max<int> failed ?

Why for double there's no problem ?

I've read in "C++ templates, the completes Guide" book that the template argument deduction does not take the return type into account, so why max<int> is ambiguous and not max<double>?

Does the return type of a template function really not taken into account in argument dedcution ?

Thank you!