NO

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

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