NO

1 decompositions
 #1 -----------
   2: f(f(x1,a()),a()) -> b()

unjoinable peak
    f(b(),a())
*<- f(f(f(x1,a()),a()),a()) ->*
    b()
NOTE: input TRS is reduced

original is
   1: a() -> a()
   2: f(f(x1,a()),a()) -> b()

reduced to
   2: f(f(x1,a()),a()) -> b()