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

  Qed