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use strict;
use warnings;
...
        return ackermann($i-1, ackermann($i,$j-1));
    } 
}

$ perl  pseudo_acker.pl 3 4
Iteration 1: i = 3, j = 4
Iteration 2: i = 3, j = 3
...
Iteration 38: i = 1, j = inf
Iteration 39: i = 1, j = inf
Iteration 40: i = 1, j = inf

return 2**$j;

sub acker {
    my ($m, $n) = @_;
...
    return acker( $m-1, 1) if $n == 0;
    return acker ($m - 1, acker ($m, $n - 1));
}