You'll want that exec to be something like...

exec("shell_script < $input_file") unless $pid;
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...since otherwise the parent will exec as well. FWIW, when I use fork() most of the time I write it in the following "template", comments and all ...

my $pid = fork();
die "failed to fork: $!" unless defined $pid;
unless ($pid) {
   # child
   die;
}
# parent
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... and then fill in the code later. That way it's harder for me to mess it up. :-)