NO

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

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

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

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