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