  We show that Joseph-Lamprou's path model for representations of generalized
Kac-Moody algebras can be embedded into Littelmann's path model for certain
Kac-Moody algebras. Using this embedding, for Joseph-Lamprou's path crystals,
we give a decomposition rule for tensor product and a branching rule for
restriction to Levi subalgebras. Also, we obtain a characterization of standard
paths in terms of a certain monoid, which can be thought of as a generalization
of a Coxeter group.
