NO

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

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