That approach is quite nice. Here's a unsightly twist on it: 
#!/usr/bin/perl -wl
use strict;
use warnings;
sub Prefix {
   my $p = shift;
   ($p)=$_=~join'','\A',map("(\Q$_",split//,$p),join'?',(')')x length(
+$p)or return'' for @_;
   $p
}

while (<DATA>) {
   print "$_=> ", Prefix(split ' ',$_);
}
__DATA__
model4run1 model2run1 model4run2 model1run1
model4run1 model2run1 model4run2 abbot
model4run1 model2run1 abbot model1run1
model4run1 model2run1 model4run2 monk
model4run1 model2run1 monk model1run1
testing terse testing time

[download]
but I prefer the chop.

In reply to Re^3: Find common prefix from a list of strings by ysth
in thread Find common prefix from a list of strings by Albannach

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