Substitution of bounded rational cone

We study the family S of rational cones obtained by iterated substitutions from rational cones L1, .., Ln. This family is a semi-group and to every non empty word u defined on the alphabet {L1, ..., Ln}, corresponds a rational cone U of S. We give sufficient conditions for S to be free (U = U′ implies u = u′) and to verify the subpattern property (U ⊂ U′ implies u is a subpattern of u′). We study, more particularly, the case where L1, ..., Ln are bounded rational cones.