  The implicit signature k consists of the multiplication and the
({\omega}-1)-power. We describe a procedure to transform each {\kappa}-term
over a finite alphabet A into a certain canonical form and show that different
canonical forms have different interpretations over some finite semigroup. The
procedure of construction of the canonical forms, which is inspired in
McCammond's normal form algorithm for {\omega}-terms interpreted over the
pseudovariety A of all finite aperiodic semigroups, consists in applying
elementary changes determined by an elementary set {\Sigma} of
pseudoidentities. As an application, we deduce that the variety of
{\kappa}-semigroups generated by the pseudovariety S of all finite semigroups
is defined by the set {\Sigma} and that the free {\kappa}-semigroup generated
by the alphabet A in that variety has decidable word problem. Furthermore, we
show that each {\omega}-term has a unique {\omega}-term in canonical form with
the same value over A. In particular, the canonical forms provide new, simpler,
representatives for {\omega}-terms interpreted over that pseudovariety.
