Universal terms of complexity three

If there is a function g such that g ^m mapsX/C bijectively ontoX, wherem is a positive integer and whereC is a finite subset ofX, thenm is a factor of |C|. This fact serves to establish the necessary and sufficient conditions for the wordA ^kB^mAⁿ to represent the successor and the predecessor functions on ε. These conditions entail that there is no nontrivial point universal word of complexity three.