NO

1 decompositions
 #0 -----------
   1: f(g(x,a(),b())) -> x
   2: p(a()) -> c()
   3: g(f(h(c(),d())),x,y) -> h(p(x),q(x))
   4: q(b()) -> d()

unjoinable peak
    f(h(p(a()),q(a())))
*<- f(g(f(h(c(),d())),a(),b())) ->*
    f(h(c(),d()))