Only 2 values get printed in String Sort Question

#1

When I run the sample input through my code, the output is:
apple
bat
But, the output should be
apple
batman
bat
I made the complex comparator myself.
Here is it’s code.
bool myCompare(string a, string b){
int m = a.length();
int n = b.length();

int x;

if (m<n)
	x=m;
else
	x=n;

int check=0;

for (int i=0; i<x; i++)
{
	if (a[i]==b[i])
	check++;
}
if (check==x)
	return a>b;
else 
	return a<b;

}
Can you suggest where I am going wrong.