We consider the following Problem:

  Strict Trs:
    {  from(X) -> cons(X, n__from(s(X)))
     , after(0(), XS) -> XS
     , after(s(N), cons(X, XS)) -> after(N, activate(XS))
     , from(X) -> n__from(X)
     , activate(n__from(X)) -> from(X)
     , activate(X) -> X}
  StartTerms: basic terms
  Strategy: innermost

Certificate: YES(?,O(n^2))

Proof:
  We consider the following Problem:
  
    Strict Trs:
      {  from(X) -> cons(X, n__from(s(X)))
       , after(0(), XS) -> XS
       , after(s(N), cons(X, XS)) -> after(N, activate(XS))
       , from(X) -> n__from(X)
       , activate(n__from(X)) -> from(X)
       , activate(X) -> X}
    StartTerms: basic terms
    Strategy: innermost
  
  Certificate: YES(?,O(n^2))
  
  Proof:
    The weightgap principle applies, where following rules are oriented strictly:
    
    TRS Component: {from(X) -> cons(X, n__from(s(X)))}
    
    Interpretation of nonconstant growth:
    -------------------------------------
      The following argument positions are usable:
        Uargs(from) = {}, Uargs(cons) = {}, Uargs(n__from) = {},
        Uargs(s) = {}, Uargs(after) = {2}, Uargs(activate) = {}
      We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
      Interpretation Functions:
       from(x1) = [1 1] x1 + [2]
                  [0 0]      [2]
       cons(x1, x2) = [1 1] x1 + [0 0] x2 + [1]
                      [0 0]      [1 0]      [1]
       n__from(x1) = [0 0] x1 + [0]
                     [1 1]      [0]
       s(x1) = [0 0] x1 + [0]
               [0 0]      [0]
       after(x1, x2) = [0 0] x1 + [1 1] x2 + [1]
                       [0 0]      [0 0]      [1]
       0() = [0]
             [0]
       activate(x1) = [1 1] x1 + [0]
                      [0 0]      [0]
    
    The strictly oriented rules are moved into the weak component.
    
    We consider the following Problem:
    
      Strict Trs:
        {  after(0(), XS) -> XS
         , after(s(N), cons(X, XS)) -> after(N, activate(XS))
         , from(X) -> n__from(X)