sub up
  {
  my ($row, $col) = split /-/, $_[0];
  return $_[0] eq '0-0' ? "@_\n" :
    ($row * $col > 0 && up( ~-$row . '-' . ~-$col, @_ ) ) .
      ($row > $col && up( ~-$row . '-' . $col, @_ ) );
  }

##</code><code>##

sub up{
		# indent to evidentiate the recursive function level
		# using the last index of the arguments array
		my $ind = ' ' x $#_ x 4;
		print $ind."\@_ = [@_]\n";
		my ($row, $col) = split /-/, $_[0];
		# if the first argument is 0-0 we are arrived to 
		# the upper edge: time to return the result
		if ($_[0] eq '0-0'){
			print $ind."RETURNING: \@_ is a valid path [@_]\n";
			return   "@_\n"
		}
		else{
			# check A 
			if ($row * $col > 0){
				# show what happens if check A pass
				print $ind."$row * $col > 0 ".
						"&& up(",$row-1,'-',$col-1,", ",(join ', ',@_),
						') # decremented both row and column are passed plus original @_ ',"\n";
			}
			else{
				print $ind."$row * $col > 0 is FALSE...\n";	
			}
			# execute the code if check A pass as shown above
			($row * $col > 0 && up( ~-$row . '-' . ~-$col, @_ ) ) .
			(	
				# check B
				eval{
					# show what happens if check B pass
					if ($row > $col){
						print $ind."$row > $col ".
							"&& up(",$row-1,'-',$col,", ",(join ', ',@_),
							') # decremented row and original column are passed plus original @_ ',"\n";
					}
					else{print $ind."$row > $col is FALSE...\n"}
					# the eval block return empty string
					# to not pollute the output of the function
					'';
				}				 
			).
			# execute the code if check B pass as shown above
			($row > $col && up( ~-$row . '-' . $col, @_ ) );
		} 
}

##</code><code>##

@_ = [3-1]
3 * 1 > 0 && up(2-0, 3-1) # decremented both row and column are passed plus original @_
    @_ = [2-0 3-1]
    2 * 0 > 0 is FALSE...
    2 > 0 && up(1-0, 2-0, 3-1) # decremented row and original column are passed plus original @_
        @_ = [1-0 2-0 3-1]
        1 * 0 > 0 is FALSE...
        1 > 0 && up(0-0, 1-0, 2-0, 3-1) # decremented row and original column are passed plus original @_
            @_ = [0-0 1-0 2-0 3-1]
            RETURNING: @_ is a valid path [0-0 1-0 2-0 3-1]
3 > 1 && up(2-1, 3-1) # decremented row and original column are passed plus original @_
    @_ = [2-1 3-1]
    2 * 1 > 0 && up(1-0, 2-1, 3-1) # decremented both row and column are passed plus original @_
        @_ = [1-0 2-1 3-1]
        1 * 0 > 0 is FALSE...
        1 > 0 && up(0-0, 1-0, 2-1, 3-1) # decremented row and original column are passed plus original @_
            @_ = [0-0 1-0 2-1 3-1]
            RETURNING: @_ is a valid path [0-0 1-0 2-1 3-1]
    2 > 1 && up(1-1, 2-1, 3-1) # decremented row and original column are passed plus original @_
        @_ = [1-1 2-1 3-1]
        1 * 1 > 0 && up(0-0, 1-1, 2-1, 3-1) # decremented both row and column are passed plus original @_
            @_ = [0-0 1-1 2-1 3-1]
            RETURNING: @_ is a valid path [0-0 1-1 2-1 3-1]
        1 > 1 is FALSE...
"0-0 1-0 2-0 3-1\n0-0 1-0 2-1 3-1\n0-0 1-1 2-1 3-1\n"

##</code><code>##

# receives and returns aoa
 sub up_modified{
	my $ind = ' ' x $#{$_[0]} x 4;
	print  $ind."\@_ is ";
	dd @_;
	my ($row, $col) = ($_[0][0][0],$_[0][0][1]);
	print $ind."receiving row $row col $col \n";
	
	if ($row == 0 and $col == 0){
		print  $ind."RETURNING: ";
		dd @_;
		return @_;
	}
	else{
		(
			$row * $col > 0 && up_modified( [[~-$row, ~-$col],map {@$_}@_] ) 
		).
		(
			$row > $col && up_modified( [[~-$row, $col], map {@$_}@_] )
		);
	}	
}

##</code><code>##

@_ is [[3, 1]]
receiving row 3 col 1
    @_ is [[2, 0], [3, 1]]
    receiving row 2 col 0
        @_ is [[1, 0], [2, 0], [3, 1]]
        receiving row 1 col 0
            @_ is [[0, 0], [1, 0], [2, 0], [3, 1]]
            receiving row 0 col 0
            RETURNING: [[0, 0], [1, 0], [2, 0], [3, 1]]
    @_ is [[2, 1], [3, 1]]
    receiving row 2 col 1
        @_ is [[1, 0], [2, 1], [3, 1]]
        receiving row 1 col 0
            @_ is [[0, 0], [1, 0], [2, 1], [3, 1]]
            receiving row 0 col 0
            RETURNING: [[0, 0], [1, 0], [2, 1], [3, 1]]
        @_ is [[1, 1], [2, 1], [3, 1]]
        receiving row 1 col 1
            @_ is [[0, 0], [1, 1], [2, 1], [3, 1]]
            receiving row 0 col 0
            RETURNING: [[0, 0], [1, 1], [2, 1], [3, 1]]

##</code><code>##

 sub up_modified_bis{
	my $ind = ' ' x $#_ x 4;
	print  $ind."\@_ is ";
	dd @_;
	my ($row, $col) = ($_[0][0],$_[0][1]);
	print $ind."receiving row $row col $col \n";
	
	if ($row == 0 and $col == 0){
		print  $ind."RETURNING: ";
		dd @_;
		return @_;
	}
	else{
		(
			$row * $col > 0 && up_modified_bis( [~-$row, ~-$col],map {[@$_]}@_ ) 
		).
		(
			$row > $col && up_modified_bis( [~-$row, $col], map {[@$_]}@_ )
		);
	}	
}


#output of called; up_modified_bis ([(3,1)]);

@_ is [3, 1]
receiving row 3 col 1
    @_ is ([2, 0], [3, 1])
    receiving row 2 col 0
        @_ is ([1, 0], [2, 0], [3, 1])
        receiving row 1 col 0
            @_ is ([0, 0], [1, 0], [2, 0], [3, 1])
            receiving row 0 col 0
            RETURNING: ([0, 0], [1, 0], [2, 0], [3, 1])
    @_ is ([2, 1], [3, 1])
    receiving row 2 col 1
        @_ is ([1, 0], [2, 1], [3, 1])
        receiving row 1 col 0
            @_ is ([0, 0], [1, 0], [2, 1], [3, 1])
            receiving row 0 col 0
            RETURNING: ([0, 0], [1, 0], [2, 1], [3, 1])
        @_ is ([1, 1], [2, 1], [3, 1])
        receiving row 1 col 1
            @_ is ([0, 0], [1, 1], [2, 1], [3, 1])
            receiving row 0 col 0
            RETURNING: ([0, 0], [1, 1], [2, 1], [3, 1])