YES(?,POLY)

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

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