YES(?,POLY)

'Pop* with parameter subtitution (timeout of 60.0 seconds)'
-----------------------------------------------------------
Answer:           YES(?,POLY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  first(0(), X) -> nil()
     , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
     , from(X) -> cons(X, n__from(s(X)))
     , first(X1, X2) -> n__first(X1, X2)
     , from(X) -> n__from(X)
     , activate(n__first(X1, X2)) -> first(X1, X2)
     , activate(n__from(X)) -> from(X)
     , activate(X) -> X}

Proof Output:    
  The input was oriented with the instance of POP* as induced by the precedence
  
   first > from, activate > from, first ~ activate
  
  and safe mapping
  
   safe(first) = {}, safe(0) = {}, safe(nil) = {}, safe(s) = {1},
   safe(cons) = {1, 2}, safe(n__first) = {1, 2}, safe(activate) = {},
   safe(from) = {1}, safe(n__from) = {1} .
  
  For your convenience, here is the input in predicative notation:
  
   Rules:
    {  first(0(), X;) -> nil()
     , first(s(; X), cons(; Y, Z);) ->
       cons(; Y, n__first(; X, activate(Z;)))
     , from(; X) -> cons(; X, n__from(; s(; X)))
     , first(X1, X2;) -> n__first(; X1, X2)
     , from(; X) -> n__from(; X)
     , activate(n__first(; X1, X2);) -> first(X1, X2;)
     , activate(n__from(; X);) -> from(; X)
     , activate(X;) -> X}