my $mutex  = Mutex->new;
...

my $rg = sub {
    my $name = shift || die;
    print "(rg)" if ( $name eq "fork1" );
    print "[rg]" if ( $name eq "fork2" );

    $mutex->enter( sub {
        $t{$name}->{r}++;
        $t{$name}->{rg}++;
        $t{$name}->{g}++;

        $t{cur} = "rg";
        $t{index}->{ $t{prev} }{ $t{cur} }++;
        $t{prev} = "rg";
    });

    $sleep_inside->();
};

my $ry = sub {
    my $name = shift || die;
    print "(ry)" if ( $name eq "fork1" );
    print "[ry]" if ( $name eq "fork2" );

    $mutex->enter( sub {
        $t{$name}->{r}++;
        $t{$name}->{ry}++;
        $t{$name}->{y}++;

        $t{cur} = "ry";
        $t{index}->{ $t{prev} }{ $t{cur} }++;
        $t{prev} = "ry";
    });

    $sleep_inside->();
};

my $rgy = sub {
    my $name = shift || die;
    say "{rgy}" if ( $name eq "mothersbaugh" );

    $mutex->enter( sub {
        $t{$name}->{r}++;
        $t{$name}->{rg}++;
        $t{$name}->{g}++;
        $t{$name}->{gy}++;
        $t{$name}->{rgy}++;

        $t{cur} = "rgy";
        $t{index}->{ $t{prev} }{ $t{cur} }++;
        $t{prev} = "rgy";
    });

    $sleep_inside->();
};