YES(?,POLY)

'Pop* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,POLY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  f(X) -> g(n__h(n__f(X)))
     , h(X) -> n__h(X)
     , f(X) -> n__f(X)
     , activate(n__h(X)) -> h(activate(X))
     , activate(n__f(X)) -> f(activate(X))
     , activate(X) -> X}

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