TRS:
 { f(0()) -> 1(),
  f(s(x)) -> g(f(x)),
     g(x) -> +(x, s(x)),
  f(s(x)) -> +(f(x), s(f(x)))}
 LMPO:
  Quasi-Precedence:
  f > g
  empty
  
Normal:
   pi(f) = [1]
  
Safe:
   pi(g) = [1]
  
Predicative System:
   {  f(0();) -> 1(),
    f(s(x;);) -> g(;f(x;)),
        g(;x) -> +(x,s(x;);),
    f(s(x;);) -> +(f(x;),s(f(x;););)}
  

   
  

  Qed