NO

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

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