State 1: y,ys,sy,,s,ys,sy,
State 2: s,sy,sy,,y,sy,ys,
State 3: y,ys,ys,,s,ys,sy,
State 4: y,sy,ys,,s,ys,sy,
State 2: s,sy,sy,,y,sy,ys,
...
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That it has a distinct "initializing" state could seen as an advantage. If not, change the initial string to one of states 2, 3 or 4 to get a purely three state engine.

State 1: y,sy,ys,,s,ys,sy,
State 2: s,sy,sy,,y,sy,ys,
State 3: y,ys,ys,,s,ys,sy,
State 1: y,sy,ys,,s,ys,sy,
...
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Modified engine that tracks the states:

use strict;
use warnings;

local $_ = 'y,ys,sy,,s,ys,sy,';

my %h;
my $i;

for my $n (1 .. $ARGV[0] || 12) {
   $h{$_} ||= ++$i;
   print("State $h{$_}: $_\n");
   eval;
}
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As for your question, longer is trivial. Shorter, on the other hand...

State 1: y/123/231/
State 2: y/231/312/
State 3: y/312/123/
State 1: y/123/231/
...
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And with an "initializing" state:

State 1: y/123i/231/
State 2: y/2311/312/
State 3: y/3122/123/
State 4: y/1233/231/
State 2: y/2311/312/
[download]