NO

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

unjoinable peak
    f(x4,x6)
*<- f(f(x4,1()),x6) ->*
    f(x4,f(1(),x6))