NO

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

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