sub no_dups {
  my $in = join( '', sort split '', shift );
  ( my $out = $in ) =~ y/smtwhfa/smtwhfa/s;
  $out =~ y/smtwhfa//cd;
  print "no dupes $in\n" if length $in == length $out;
}

no_dups( 'afhwtms' );
no_dups( 'smtthfa' );
no_dups( 'smatwhfa' );
no_dups( 'afhwtmsz' );
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Update: Ooop, didn't consider characters not in the allowed alphabet. Added second y/// to correct.