NO

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

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

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

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