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* + Boolean Semantic Labelling:
  Normal positions:
  pi(mark_sl=1) = [1], pi(mark_sl=0) = [1], pi(a__f_sl=0) = [1]
  
Safe positions:
   pi(a__f_sl=1) = [1], pi(f_sl=1) = [1], pi(f_sl=0) = [1], pi(h_sl=1) = [1], pi(h_sl=0) = [1], pi(g_sl=1) = [1], pi(g_sl=0) = [1]
  
Precedence:
   a__f_sl=1 > g_sl=0, 
   a__f_sl=1 > h_sl=0, 
   a__f_sl=1 > f_sl=0, 
   a__f_sl=0 > g_sl=0, 
   a__f_sl=0 > h_sl=0, 
   a__f_sl=0 > f_sl=0, 
   mark_sl=1 > mark_sl=0, 
   mark_sl=1 > a__f_sl=1, 
   mark_sl=1 > a__f_sl=0, 
   mark_sl=1 > h_sl=0
   empty
  
Interpretation:
   g^(1):
   0 | 0
   1 | 0
   h^(1):
   0 | 0
   1 | 0
   f^(1):
   0 | 0
   1 | 0
   a__f^(1):
   0 | 0
   1 | 0
   mark^(1):
   0 | 0
   1 | 1
   
  
Labelling:
   g^(1):
   0 | 0
   1 | 0
   h^(1):
   0 | 0
   1 | 0
   f^(1):
   0 | 0
   1 | 0
   a__f^(1):
   0 | 1
   1 | 0
   mark^(1):
   0 | 1
   1 | 0
   
  
Labelled predicative System:
   {         a__f_sl=1(;X) -> g_sl=0(;h_sl=0(;f_sl=0(;X))),
             a__f_sl=0(X;) -> g_sl=0(;h_sl=0(;f_sl=0(;X))),
    mark_sl=1(f_sl=0(;X);) -> a__f_sl=1(;mark_sl=1(X;)),
    mark_sl=1(f_sl=0(;X);) -> a__f_sl=0(mark_sl=0(X;);),
    mark_sl=1(g_sl=0(;X);) -> g_sl=0(;X),
    mark_sl=1(g_sl=0(;X);) -> g_sl=0(;X),
    mark_sl=1(h_sl=0(;X);) -> h_sl=0(;mark_sl=1(X;)),
    mark_sl=1(h_sl=0(;X);) -> h_sl=0(;mark_sl=0(X;)),
             a__f_sl=1(;X) -> f_sl=0(;X),
             a__f_sl=0(X;) -> f_sl=0(;X)}
  

  Qed