NO

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

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