NO

1 decompositions
 #0 -----------
   1: f(f(x,y),z) -> f(x,f(y,z))
   2: f(x,1()) -> x

unjoinable peak
    f(_y5,_y7)
*<- f(f(_y5,1()),_y7) ->*
    f(_y5,f(1(),_y7))