NO

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

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

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

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