NO

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

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