
92 Algebraic Operads: An Algorithmic Companion
Two planar rooted trees that have an overlap can be merged along it by iden-
tifying the vertices of τ
0
1
with the corresponding vertices of τ
0
2
, and consider
the naturally induced parent function and planar structure. The overlap con-
ditions guarantee that the result of that identification is a planar rooted tree
again.
Example 3.5.1.2. Let us consider the three trees
, ,
from Example 3.4.2.2. Each two of those trees form an overlap (the dashed
edges mark the common parts). Merging the first and the second one (respec-
tively, the first and the third one, the second and the third one) along their
overlap, we ...