NO

1 decompositions
 #0 -----------
   1: a() -> h(a(),f(b()))
   2: f(f(h(a(),a()))) -> f(f(f(a())))
   3: f(h(a(),h(a(),a()))) -> f(a())
   4: f(h(h(b(),a()),h(f(c()),c()))) -> c()

unjoinable peak
    f(f(h(h(a(),f(b())),a())))
*<- f(f(h(a(),a()))) ->*
    f(f(f(h(a(),f(b())))))