ABSTRACT
Now t h a t we h a ve an explicit calculation of jfiCH), let us consider some special cases. 1) Suppose h,k : [1] —» [n] are n - a r y operations. Then, using jg we obtain jB(h) = JB^) iff for all u n a r y operations f, for all n - tuples of te rm s( t r ee s ) (x i ,x 2 ,....xn ): f (h (x i ,x 2 ,....,xn )) € B iff f(k(xi,x 2 ,- . ,xn )) € B
2) Let us simplify this first example to w here n = 0, i.e. h and k a re trees. If T= srf([l],[0]) is the free srf-algebra of all stf-trees, then we obtain from jg the congruence on T defined by (h,k) € iff JB(h) = j s (k ) iff for all u n a r y opera t ions f, f(h) € B iff f(k) € B.
