NO

1 decompositions
 #0 -----------
   1: f(g(x)) -> g(f(f(x)))
   2: f(h(x)) -> h(h(f(x)))
   3: f(x) -> x
   4: g(x) -> x

unjoinable peak
    h(h(f(x)))
*<- f(h(x)) ->*
    h(x)