The word problem for Pride groups

Pride groups are defined by means of finite (simplicial) graphs and examples include Artin groups, Coxeter groups and generalized tetrahedron groups. Under suitable conditions we calculate an upper bound of the first order Dehn function for a finitely presented Pride group. We thus obtain sufficient conditions for when finitely presented Pride groups have solvable word problems. As a corollary to our main results we show that the first order Dehn function of a generalized tetrahedron groups, containing finite generalized triangle groups, is at most cubic.