YES(?,POLY)

'Pop* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,POLY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  g(s(x)) -> f(x)
     , f(0()) -> s(0())
     , f(s(x)) -> s(s(g(x)))
     , g(0()) -> 0()}

Proof Output:    
  The input was oriented with the instance of POP* as induced by the precedence
  
   g ~ f
  
  and safe mapping
  
   safe(g) = {}, safe(s) = {1}, safe(f) = {}, safe(0) = {} .
  
  For your convenience, here is the input in predicative notation:
  
   Rules:
    {  g(s(; x);) -> f(x;)
     , f(0();) -> s(; 0())
     , f(s(; x);) -> s(; s(; g(x;)))
     , g(0();) -> 0()}