> The code is much easier then.

Yep!

use strict;
use warnings;
use Data::Dump qw/pp dd/;


my $goal  = [3,1,'goal'];
my $start = [0,0,'start'];

pp "OLD: ",[$start,$goal];

($start,$goal) = map old2new($_), ($start,$goal);

pp "NEW: ",[$start,$goal];
my ($gl,$gr) = @$goal;



my @results;
pathfinder( $start );
pp \@$_ for @results;


sub pathfinder {
    my ( $last ) = @_;

    my ( $l, $r ) = @$last ;

    if ( $gl == $l and $gr == $r) {
        push @results, [ map new2old($_), reverse @_ ];
        return;
    }

    pathfinder( [$l+1,$r   ,"left" ], @_ ) if $l < $gl;

    pathfinder( [$l  ,$r+1 ,"right"], @_ ) if $r < $gr;
}


# --------------------------------------------------
# coordinate transformations


sub old2new {                           # left = level - right
    my ($a_old)=@_;
    my @new = @$a_old;
    $new[0] = $new[0] - $new[1];
    return \@new;
}

sub new2old {                           # level = left + right
    my ($a_new)=@_;
    my @old = @$a_new;
    $old[0] = $old[0] + $old[1];
    return \@old;
}
[download]

Compilation started at Thu Mar 22 16:09:33

C:/Perl_64/bin\perl.exe  d:/tmp/pascale_path.pl 
("OLD: ", [[0, 0, "start"], [3, 1, "goal"]])
("NEW: ", [[0, 0, "start"], [2, 1, "goal"]])
[
  [0, 0, "start"],
  [1, 0, "left"],
  [2, 0, "left"],
  [3, 1, "right"],
]
[
  [0, 0, "start"],
  [1, 0, "left"],
  [2, 1, "right"],
  [3, 1, "left"],
]
[
  [0, 0, "start"],
  [1, 1, "right"],
  [2, 1, "left"],
  [3, 1, "left"],
]

Compilation finished at Thu Mar 22 16:09:33
[download]