  For a class C of operations on a nonempty base set A, an operation f is
called a C-subfunction of an operation g, if f = g(h_1, ..., h_n), where all
the inner functions h_i are members of C. Two operations are C-equivalent if
they are C-subfunctions of each other. The C-subfunction relation is a
quasiorder if and only if the defining class C is a clone. The C-subfunction
relations defined by clones that contain all unary operations on a finite base
set are examined. For each such clone it is determined whether the
corresponding partial order satisfies the descending chain condition and
whether it contains infinite antichains.
