NO

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

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