The Solvability of the Word Problem for Certain Semigroups

This paper establishes the solvability of the word problem for semigroups with one defining relation if that relation is of the form <!-- MATH $A \sim BtC$ --> where (1) and are words on the generators of the semigroup but the generator does not occur in or and (2) the length of is greater than the <!-- MATH $\max \;(\operatorname{length} B,\operatorname{length} C)$ --> .