An OO style solution: (It prints out all the bad calling chains it found, for each function.)

package func;

use strict;

sub new {
    my $self = {};
    shift;
    $self->{CALLED} = [];
    $self->{MARK} = 0;
    $self->{NAME} = shift;
    bless $self;
    return $self;
}

sub call {
    my ($self, $called) = @_;
    push @{$self->{CALLED}}, $called;
}

sub mark {
    my $result = 0;
    my ($self, $mark, $current_chain) = @_;
    if ($self->{MARK} != $mark) {
        $self->{MARK} = $mark;
        my $called;
        foreach $called (@{$self->{CALLED}}) {
            push @{$current_chain}, $called->{NAME};
            $result |= $called->mark($mark, $current_chain);
        }
    } else {
        $result = 1;
        print(join("->", @{$current_chain})."\n");
    }
    pop @{$current_chain};
    $self->{MARK} = 0;
    return $result;
}

1;

func.pl:
use func;
use Data::Dumper;

use strict;

my %funcs;
while (<DATA>) {
    chomp;
    my ($calling, $called) = split(' ');
    if (!exists($funcs{$calling})) {
        $funcs{$calling} = new func($calling);
    }
    if (!exists($funcs{$called})) {
        $funcs{$called} = new func($called);
    }
    $funcs{$calling}->call($funcs{$called});
}

my $mark = 0;
my $func;
print "Bad calling chains:\n";
foreach $func (keys %funcs) {
    $mark ++;
    my $current_chain = [];
    push @{$current_chain}, $func;
    $funcs{$func}->mark($mark, $current_chain);
}
print "End of bad calling chains\n";

__DATA__
aaa bbb
aaa ccc
bbb ccc
ccc bbb
ddd aaa
ddd eee


testing result
Bad calling chains:
bbb->ccc->bbb
aaa->bbb->ccc->bbb
aaa->ccc->bbb->ccc
ccc->bbb->ccc
ddd->aaa->bbb->ccc->bbb
ddd->aaa->ccc->bbb->ccc
End of bad calling chains
[download]

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