NO

1 decompositions
 #1 -----------
   1: f(f(x1,x2),x3) -> f(x1,f(x2,x3))
   2: f(x4,1()) -> x4

unjoinable peak
    f(x9,x11)
*<- f(f(x9,1()),x11) ->*
    f(x9,f(1(),x11))