TRS:
 {a(b(x)) -> a(c(b(x)))}
 POP* + Boolean Semantic Labelling:
  Normal positions:
  pi(a_sl=1) = [1], pi(a_sl=0) = [1]
  
Safe positions:
   pi(b_sl=1) = [1], pi(b_sl=0) = [1], pi(c_sl=1) = [1], pi(c_sl=0) = [1]
  
Precedence:
   a_sl=1 > a_sl=0, 
   a_sl=1 > c_sl=1
   empty
  
Interpretation:
   a^(1):
   0 | 0
   1 | 0
   c^(1):
   0 | 1
   1 | 0
   b^(1):
   0 | 0
   1 | 0
   
  
Labelling:
   a^(1):
   0 | 1
   1 | 0
   c^(1):
   0 | 1
   1 | 0
   b^(1):
   0 | 0
   1 | 0
   
  
Labelled predicative System:
   {a_sl=1(b_sl=0(;x);) -> a_sl=0(c_sl=1(;b_sl=0(;x));),
    a_sl=1(b_sl=0(;x);) -> a_sl=0(c_sl=1(;b_sl=0(;x));)}
  

  Qed