NO

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

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