NO

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

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

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

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