We will consider the problem whether two loops on an
oriented surface are Hamiltonianly diffeomorphic.
This problem is a specifical case of the classification problem
of Lagrangian submanifolds in a symplectic manifold.
Our goal of this talk is to construct a psuedo-distance between
two loops satisfying a certain condition, and to show a property
that the distance between two loops is zero if they are
Hamiltonianly diffeomorphic to each other. This psuedo-distance would
be considered as a counterpart of the Hofer distance, which is known as
a non-degenerate one between Hamiltonianly diffeomorphic loops.
We will define the (combinatorial) Floer complex for a pair of loops by
counting areas of "lobes", and explain the condition under which the
construction of our psuedo-distance works well.