TRS:
 {   a__f(X) -> g(h(f(X))),
  mark(f(X)) -> a__f(mark(X)),
  mark(g(X)) -> g(X),
  mark(h(X)) -> h(mark(X)),
     a__f(X) -> f(X)}
 POP*:
  Precedence:
  a__f > g, 
  a__f > h, 
  a__f > f, 
  mark > a__f, 
  mark > h
  empty
  
Normal:
   pi(mark) = [1]
  
Safe:
   pi(a__f) = [1], pi(f) = [1], pi(h) = [1], pi(g) = [1]
  
Predicative System:
   {    a__f(;X) -> g(;h(;f(;X))),
    mark(f(;X);) -> a__f(;mark(X;)),
    mark(g(;X);) -> g(;X),
    mark(h(;X);) -> h(;mark(X;)),
        a__f(;X) -> f(;X)}
  Qed