Quiver in fear, for here is my unholy answer :)

#!/usr/bin/perl -w

use strict;

my @stack=qw(d b f a e c 6);  # <-- bottom .. top -->

# You are not allowed to modify this.
sub rotate_up {
    local($a,$b);
    $a=$_[0];
    $a--;
    return if $a<1;
    $b=pop @stack;
    splice(@stack, -$a, 0, $b);
}

sub sortIt {
    print "before stack is ",(join ", ",@stack),"\n";
    my $initLen=pop @stack;
    my $currLen=$initLen;

    # strategy: find the largest element, push it to bottom.
    # reduce size by one, repeat
    while($currLen) {
        my $max;
        my $rot=$currLen;
        my $maxLoc=-1;
        #print "Len $currLen, stack is ",(join ",", @stack),"\n";

        # find largest element, and save its position
        while($rot>=1) {
            my $x=pop @stack;
            if (!defined $max || ($x gt $max)) {
                $maxLoc=$rot;
                $max=$x;
            }
            push @stack, $x;

            
            rotate_up($rot) if($rot>1);
            $rot--;

            #print "examined $x, max is ($maxLoc, $max), stack is ",(j
+oin ",", @stack),"\n";
        }

        # bring largest elem back up to top
        while($maxLoc>1) {
            rotate_up($maxLoc--);
            #print "bumping up, stack is ",(join ",", @stack),"\n";
        }

        # push it to bottom
        rotate_up($currLen--);
    }

    push @stack, $initLen;
    print "Finished, ending stack is ",(join ", ",@stack),"\n";
}

# initial test case
sortIt();

# test reversed
@stack=qw(a b c d e f 6);  # <-- bottom .. top -->
sortIt();

# test sorted
sortIt();

# test 1 element stack
@stack=qw(f 1);  # <-- bottom .. top -->
sortIt();
@stack=qw(a a f a a 5);  # <-- bottom .. top -->
sortIt();

# empty stack
@stack=qw(0);  # <-- bottom .. top -->
sortIt();

# make sure items below stack aren't touched
@stack=qw(dontmoveme1 dontmoveme2 a a f a a 5);  # <-- bottom .. top -
+->
sortIt();
[download]

Works for me!
--
Mike
(Edit: Updated with comments, added test cases, made the sort code into a subroutine to make testing simpler, added "before and after" printouts for testing)

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