Consider using a regex that captures sets of two digits (or 'empties') separated by a comma, as tuples:

use strict;
use warnings;

while ( my $line = <DATA> ) {
    print +( join ',', map "($_)", $line =~ /(\d*,\d*),?/g ), "\n";
}

__DATA__
1,1,,,,
1,2,,,,
3,4,1,1,,
1,1,1,1,,
5,6,3,4,1,2
1,1,1,1,1,1
,,,,1,1
,,1,2,,
,,1,1,1,2
,,,,,
5,6,3,4,2,2
[download]

Output:

(1,1),(,),(,)
(1,2),(,),(,)
(3,4),(1,1),(,)
(1,1),(1,1),(,)
(5,6),(3,4),(1,2)
(1,1),(1,1),(1,1)
(,),(,),(1,1)
(,),(1,2),(,)
(,),(1,1),(1,2)
(,),(,),(,)
(5,6),(3,4),(2,2)
[download]

And then testing for '1,1' and '1,2' in each line:

use strict;
use warnings;

my ( $i, $success, $fail );

while ( my $line = <DATA> ) {
    $i++;
    my %tuples = map { $_ => 1 } $line =~ /(\d*,\d*),?/g;
    $success++ if exists $tuples{'1,1'};
    $fail++    if exists $tuples{'1,2'};
}

print "Total Lines: $i\nSuccess: $success\nFail: $fail\n";

__DATA__
1,1,,,,
1,2,,,,
3,4,1,1,,
1,1,1,1,,
5,6,3,4,1,2
1,1,1,1,1,1
,,,,1,1
,,1,2,,
,,1,1,1,2
,,,,,
5,6,3,4,2,2
[download]

Output:

Total Lines: 11
Success: 6
Fail: 4
[download]

BTW - You were off by one in all of your array indices. You had:

if((($f[1]==1)&&($f[2]==1))|| ...
[download]

when you meant:

if((($f[0]==1)&&($f[1]==1))|| ...
[download]

Hope this helps!

Edit: Updated to reflect the '1,2' "Fail" condition, which I failed to notice. Thank you, Jim.