NO

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

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