And here is rather ugly but working code:

#!/usr/bin/perl -w
use strict;

use Algorithm::Diff 1.19 ();

Main( @ARGV );
exit( 0 );

{
    package DiffToMerge;

    sub new
    {
        my $class= shift @_;
        my $diff= Algorithm::Diff->new( @_ );
        $diff->Next();  # Start out at first chunk
        my $me= bless {
            diff => $diff,
            offset => 0,
        }, $class;
        if(  $diff->Diff()  ) {
            $me->{sublist}= [ $diff->Items( 1 ) ];
            $me->{suboff}= $diff->Min( 1 );
        }
        return $me;
    }

    sub Same
    {
        my( $me, $off )= @_;
        for(  $me->{offset}  ) {
            die   if  $off < $_;
            die   if  $_+1 < $off;
            $_= $off;
        }
        my $diff= $me->{diff};
        if(  $diff->Max(2) < $off  ) {
            die   if  ! $diff->Next();
            if(  $diff->Diff()  ) {
                $me->{sublist}= [ $diff->Items( 1 ) ];
                $me->{suboff}= $diff->Min( 1 );
            }
            if(  ! $diff->Range(2)  ) {
                die   if  $off <= $diff->Max(2);
                die   if  ! $diff->Next();
            }
            die   if  $off < $diff->Min(2);
            die   if  $diff->Max(2) < $off;
        }
        return $diff->Same();
    }

    sub Shift
    {
        my( $me )= @_;
        my $diff= $me->{diff};
        die   if  ! $diff->Same();
        return  $diff->Min(1) + $me->{offset}++ - $diff->Min(2);
    }

    sub Sublist
    {
        my( $me )= @_;
        my $sublist= $me->{sublist};
        return   if  ! $sublist  ||  ! @$sublist;
        return $sublist;
    }

    sub SublistOffset
    {
        my( $me, $offset )= @_;
        return undef   if  ! defined $offset;
        shift @{ $me->{sublist} };
        return $me->{suboff}++;
    }

    sub SublistIdxs
    {
        my( $me )= @_;
        my $beg= $me->{suboff};
        $me->{suboff} += @{ $me->{sublist} || [] };
        $me->{sublist}= [];
        return $beg .. $me->{suboff}-1;
    }
}


sub FlushSublist
{
    my( $avOut, $d, $diff )= @_;
    for(  $diff->SublistIdxs()  ) {
        my @row;
        $row[$d]= $_;
        push @$avOut, \@row;
    }
}

sub DiffMerge
{
    my( $finish, @seq )= @_;
    my @diff= map {
        DiffToMerge->new( $_, $seq[-1] )
    }   @seq[ 0 .. $#seq-1 ];
    my @out;
    for my $i (  0 .. $#{ $seq[-1] }  ) {
        my @row;
        my %sublists;
        my @flush;
        for my $d (  0 .. $#diff  ) {
            my $same= $diff[$d]->Same($i);
            for(  $diff[$d]->Sublist()  ) {
                $sublists{$d}= $_   if  $_;
            }
            if(  $same  ) {
                push @flush, $d   if  $sublists{$d};
                $row[$d]= $diff[$d]->Shift();
            }
        }
        if(  @flush  ) {
            for my $row (  DiffMerge( 0, values %sublists )  ) {
                my @subrow;
                for my $d (  keys %sublists  ) {
                    $subrow[$d]= $diff[$d]->SublistOffset( shift @$row
+ );
                }
                push @out, \@subrow;
            }
            FlushSublist( \@out, $_, $diff[$_] )
                for  @flush;
        }
        $row[@diff]= $i;
        push @out, \@row;
    }
    if(  $finish  ) {
        for(  0 .. $#diff  ) {
            FlushSublist( \@out, $_, $diff[$_] )
                if  $diff[$_]->Sublist();
        }
    }
    return @out;
}

sub Main
{
    my @seq= @_;
    @seq= qw( abdefhi azcdfghi abcjkgnhi )
        if  ! @seq;
    @seq= map [ /./gs ], @seq;
    my @out= DiffMerge( 1, @seq );
    for( @seq ) {
        push @$_, '-';
    }
    for( @out ) {
        for( @$_ ) {
            $_= '-'   if  ! defined $_;
        }
        print "( @$_ )\n";
    }
    print $/;
    for(  @seq  ) {
        my @l= map shift @$_, @out;
        for(  @l  ) {
            $_= -1   if  ! defined $_  ||  '-' eq $_;
        }
        print "( @$_[@l] )\n";
    }
}
[download]

can be used as:

 % perl diffN.pl
( 0 0 0 )
( 1 - 1 )
( 2 - )
( 3 - )
( 4 - )
( - 1 )
( - 2 2 )
( - - 3 )
( - - 4 )
( - 3 )
( - 4 )
( - 5 5 )
( - - 6 )
( 5 6 7 )
( 6 7 8 )

( a b d e f - - - - - - - - h i )
( a - - - - z c - - d f g - h i )
( a b - - - - c j k - - g n h i )

 % perl diffN.pl tye says japhy asked
( - - 0 )
( - 0 )
( - 1 1 0 )
( - - 2 )
( - - 3 )
( 0 - - )
( 1 2 4 )
( - 3 - 1 )
( - - - 2 )
( 2 - - 3 )
( - - - 4 )

( - - - - - t y - - e - )
( - s a - - - y s - - - )
( j - a p h - y - - - - )
( - - a - - - - s k e d )
[download]

Update: And here is a case with a bug to be fixed:

 % perl diffN.pl encyclopedia cyclops enclosure wikipedia cyclone wick
+ed lonely
( - - - 0 - 0 )
( - - - 1 - 1 )
( 0 - 0 - - - )
( 1 - 1 - - - )
( 2 0 2 - 0 2 )
( - - - 2 - 3 )
( 3 )
( 4 )
( - 1 )
( - 2 )
( - - - - 1 )
( - - - - 2 )
( 5 3 3 - 3 - 0 )
( 6 4 4 - 4 - 1 )
( - - - - 5 - 2 )
( - - - 3 )
( 7 5 - 4 )
( - 6 5 - )
( - - 6 - )
( - - 7 - )
( 8 - 8 5 6 4 3 )
( - - - - - - 4 )
( - - - - - - 5 )
( 9 )
( 10 )
( 11 )
( - - - 6 )
( - - - 7 )
( - - - 8 )
( - - - - - 5 )

( - - e n c - y c - - - - l o - - p - - - e - - d i a - - - - )
( - - - - c - - - y c - - l o - - p s - - - - - - - - - - - - )
( - - e n c - - - - - - - l o - - - s u r e - - - - - - - - - )
( w i - - - k - - - - - - - - - i p - - - e - - - - - d i a - )
( - - - - c - - - - - y c l o n - - - - - e - - - - - - - - - )
( w i - - c k - - - - - - - - - - - - - - e - - - - - - - - d )
( - - - - - - - - - - - - l o n - - - - - e l y - - - - - - - )
#             ^ ^ ^ ^ ^ ^  <   should merge  >  ^ ^ ^ ^ ^ ^ ^
[download]

Playing around with some code for this, there are often multiple ways in which differences could be merged. For example, from your test above:

encyclo   pedia
enc  losur e
#or
encyclop   edia
enc  lo sure
[download]

To me, these are both equally legitimate, but is there any criteria upon which the one could be determined to be preferrable to the other?

---

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority".

In the absence of evidence, opinion is indistinguishable from prejudice.

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