YES(?,POLY)

'Pop* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,POLY)
Input Problem:    innermost relative runtime-complexity with respect to
  Strict Rules:
    {  t(f(x), g(y), f(z())) -> t(z(), g(x), g(y))
     , t(g(x), g(y), f(z())) -> t(f(y), f(z()), x)}
  Weak Rules:
    {  f(g(x)) -> g(f(x))
     , g(f(x)) -> f(g(x))
     , f(f(x)) -> g(g(x))
     , g(g(x)) -> f(f(x))}

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