NO

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

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