I'd split it into two matches:

while ( <DATA> ) {
    chomp;
    print "$_: ", 
          /^a.*b$/ && !/.ab./
              ? "yes"
              : "no",
          "\n";
}

__DATA__
a000000000b
a0a0000b00b
a0000ab000b
ab00000000b
a000ab
[download]

Output:

a000000000b: yes
a0a0000b00b: yes
a0000ab000b: no
ab00000000b: yes
a000ab: yes
[download]

update: Added two more tests cases and fixed a bug