NO

1 decompositions
 #1 -----------
   2: a() -> b()
   3: f(a(),a()) -> f(b(),f(f(a(),b()),a()))

unjoinable peak
    f(b(),b())
*<- f(a(),a()) ->*
    f(b(),f(f(a(),b()),a()))
NOTE: input TRS is reduced

original is
   1: a() -> a()
   2: a() -> b()
   3: f(a(),a()) -> f(b(),f(f(a(),b()),a()))

reduced to
   2: a() -> b()
   3: f(a(),a()) -> f(b(),f(f(a(),b()),a()))