C++言語ベースルーチンによる両目演算子の再ロード

#include<iostream>
#include<cstring>
using namespace std;
class String
{
public:
    String( ){p=NULL;}
    String(char *str);
    friend bool operator>(String &s1, String &s2);
    friend bool operator<(String &s1, String &s2);
    friend bool operator==(String &s1, String &s2);
        friend bool operator>=(String &s1, String &s2);
    friend bool operator<=(String &s1, String &s2);
    friend bool operator!=(String &s1, String &s2);
    void display( );
private:
    char *p;
};
String::String(char *str)
{
    p = new char[strlen(str)+1];
    strcpy(p, str);
}
 
void String::display( )
{
    cout << p;
}
 
bool operator>(String &s1,String &s2)
{
    if(strcmp(s1.p,s2.p)>0)
        return true;
    else
        return false;
}
 
bool operator<(String &s1,String &s2)
{
    if(strcmp(s1.p,s2.p)<0)
        return true;
    else
        return false;
}
 
bool operator==(String &s1,String &s2)
{
    return !((s1>s2)||(s1<s2));
}
 
bool operator>=(String &s1,String &s2)
{
    return !(s1<s2);
}
 
bool operator<=(String &s1,String &s2)
{
    return !(s1>s2);
}
 
bool operator!=(String &s1,String &s2)
{
    return ((s1>s2)||(s1<s2));
}
 
void compare(String &s1,String &s2)
{
    if(s1>s2)
    {
        s1.display( );
        cout<<" > ";
        s2.display( );
    }
    else if(s1<s2)
    {
        s1.display( );
        cout<<" < ";
        s2.display( );
    }
    else if(s1==s2)
    {
        s1.display( );
        cout<<" = ";
        s2.display( );
    }
    cout<<endl;
}
 
int main( )
{
    String s1("Hello"),s2("Money"),s3("Girl"),s4("Hello");
    compare(s1,s2);
    compare(s2,s3);
    compare(s1,s4);
    return 0;
}