NO

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

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