TRS:
 {f(g(i(a(), b(), b'()), c()), d()) -> if(e(), f(.(b(), c()), d'()), f(.(b'(), c()), d'())),
        f(g(h(a(), b()), c()), d()) -> if(e(), f(.(b(), g(h(a(), b()), c())), d()), f(c(), d'()))}
 POP* + Boolean Semantic Labelling:
  Normal positions:
  pi(f_sl=1) = [1,2], pi(f_sl=0) = [1,2]
  
Safe positions:
   pi(h_sl=1) = [1,2], pi(h_sl=0) = [1,2], pi(i_sl=1) = [1,2,3], pi(i_sl=0) = [1,2,3], pi(g_sl=1) = [1,2], pi(g_sl=0) = [1,2], pi(._sl=1) = [1,2], pi(._sl=0) = [1,2], pi(if_sl=1) = [1,2,3], pi(if_sl=0) = [1,2,3]
  
Precedence:
   f_sl=1 > if_sl=0, 
   f_sl=1 > f_sl=0, 
   f_sl=1 > e_sl=1, 
   f_sl=1 > ._sl=0, 
   f_sl=1 > d'_sl=0
   empty
  
Interpretation:
   if^(3):
   000 | 0
   001 | 0
   010 | 0
   011 | 0
   100 | 0
   101 | 0
   110 | 0
   111 | 0
   e^(0):
    | 0
   f^(2):
   00 | 0
   01 | 0
   10 | 0
   11 | 0
   .^(2):
   00 | 0
   01 | 0
   10 | 0
   11 | 0
   b^(0):
    | 0
   c^(0):
    | 0
   d'^(0):
    | 0
   b'^(0):
    | 0
   g^(2):
   00 | 1
   01 | 0
   10 | 0
   11 | 0
   i^(3):
   000 | 0
   001 | 0
   010 | 0
   011 | 0
   100 | 0
   101 | 0
   110 | 0
   111 | 0
   a^(0):
    | 0
   d^(0):
    | 0
   h^(2):
   00 | 0
   01 | 0
   10 | 0
   11 | 0
   
  
Labelling:
   if^(3):
   000 | 0
   001 | 0
   010 | 0
   011 | 0
   100 | 0
   101 | 0
   110 | 0
   111 | 0
   e^(0):
    | 1
   f^(2):
   00 | 0
   01 | 0
   10 | 1
   11 | 0
   .^(2):
   00 | 0
   01 | 0
   10 | 0
   11 | 0
   b^(0):
    | 0
   c^(0):
    | 0
   d'^(0):
    | 0
   b'^(0):
    | 0
   g^(2):
   00 | 0
   01 | 0
   10 | 0
   11 | 0
   i^(3):
   000 | 0
   001 | 0
   010 | 0
   011 | 0
   100 | 0
   101 | 0
   110 | 0
   111 | 0
   a^(0):
    | 0
   d^(0):
    | 0
   h^(2):
   00 | 0
   01 | 0
   10 | 0
   11 | 0
   
  
Labelled predicative System:
   {f_sl=1(g_sl=0(;i_sl=0(;a_sl=0(),b_sl=0(),b'_sl=0()),c_sl=0()),d_sl=0();) -> if_sl=0(;e_sl=1(),f_sl=0(._sl=0(;b_sl=0(),c_sl=0()),d'_sl=0();),f_sl=0(._sl=0(;b'_sl=0(),c_sl=0()),d'_sl=0();)),
              f_sl=1(g_sl=0(;h_sl=0(;a_sl=0(),b_sl=0()),c_sl=0()),d_sl=0();) -> if_sl=0(;e_sl=1(),f_sl=0(._sl=0(;b_sl=0(),g_sl=0(;h_sl=0(;a_sl=0(),b_sl=0()),c_sl=0())),d_sl=0();),f_sl=0(c_sl=0(),d'_sl=0();))}
  

  Qed