NO

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

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