We consider the following Problem:

  Strict Trs:
    {  fst(0(), Z) -> nil()
     , fst(s(X), cons(Y, Z)) ->
       cons(Y, n__fst(activate(X), activate(Z)))
     , from(X) -> cons(X, n__from(n__s(X)))
     , add(0(), X) -> X
     , add(s(X), Y) -> s(n__add(activate(X), Y))
     , len(nil()) -> 0()
     , len(cons(X, Z)) -> s(n__len(activate(Z)))
     , fst(X1, X2) -> n__fst(X1, X2)
     , from(X) -> n__from(X)
     , s(X) -> n__s(X)
     , add(X1, X2) -> n__add(X1, X2)
     , len(X) -> n__len(X)
     , activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
     , activate(n__from(X)) -> from(activate(X))
     , activate(n__s(X)) -> s(X)
     , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2))
     , activate(n__len(X)) -> len(activate(X))
     , activate(X) -> X}
  StartTerms: basic terms
  Strategy: innermost

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

Proof:
  Arguments of following rules are not normal-forms:
  {  fst(s(X), cons(Y, Z)) ->
     cons(Y, n__fst(activate(X), activate(Z)))
   , add(s(X), Y) -> s(n__add(activate(X), Y))}
  
  All above mentioned rules can be savely removed.
  
  We consider the following Problem:
  
    Strict Trs:
      {  fst(0(), Z) -> nil()
       , from(X) -> cons(X, n__from(n__s(X)))
       , add(0(), X) -> X
       , len(nil()) -> 0()
       , len(cons(X, Z)) -> s(n__len(activate(Z)))
       , fst(X1, X2) -> n__fst(X1, X2)
       , from(X) -> n__from(X)
       , s(X) -> n__s(X)
       , add(X1, X2) -> n__add(X1, X2)
       , len(X) -> n__len(X)
       , activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
       , activate(n__from(X)) -> from(activate(X))
       , activate(n__s(X)) -> s(X)
       , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2))
       , activate(n__len(X)) -> len(activate(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:
      {  fst(0(), Z) -> nil()
       , len(nil()) -> 0()
       , len(cons(X, Z)) -> s(n__len(activate(Z)))}
    
    Interpretation of nonconstant growth:
    -------------------------------------
      The following argument positions are usable:
        Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(cons) = {},
        Uargs(n__fst) = {}, Uargs(activate) = {}, Uargs(from) = {1},
        Uargs(n__from) = {}, Uargs(n__s) = {}, Uargs(add) = {1, 2},
        Uargs(n__add) = {}, Uargs(len) = {1}, Uargs(n__len) = {1}
      We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
      Interpretation Functions:
       fst(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                     [0 0]      [0 0]      [1]
       0() = [0]
             [0]
       nil() = [0]
               [0]
       s(x1) = [1 0] x1 + [1]
               [0 0]      [1]
       cons(x1, x2) = [1 1] x1 + [0 0] x2 + [1]
                      [0 0]      [1 1]      [1]
       n__fst(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                        [0 1]      [0 1]      [0]
       activate(x1) = [1 1] x1 + [0]
                      [0 0]      [1]
       from(x1) = [1 1] x1 + [0]
                  [0 0]      [1]
       n__from(x1) = [0 0] x1 + [0]
                     [1 1]      [0]
       n__s(x1) = [0 0] x1 + [0]
                  [1 0]      [0]
       add(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                     [0 0]      [0 0]      [1]
       n__add(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                        [0 1]      [0 1]      [0]
       len(x1) = [1 1] x1 + [1]
                 [0 0]      [1]
       n__len(x1) = [1 0] x1 + [0]
                    [0 1]      [0]
    
    The strictly oriented rules are moved into the weak component.
    
    We consider the following Problem:
    
      Strict Trs:
        {  from(X) -> cons(X, n__from(n__s(X)))
         , add(0(), X) -> X
         , fst(X1, X2) -> n__fst(X1, X2)
         , from(X) -> n__from(X)
         , s(X) -> n__s(X)
         , add(X1, X2) -> n__add(X1, X2)
         , len(X) -> n__len(X)
         , activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
         , activate(n__from(X)) -> from(activate(X))
         , activate(n__s(X)) -> s(X)
         , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2))
         , activate(n__len(X)) -> len(activate(X))
         , activate(X) -> X}
      Weak Trs:
        {  fst(0(), Z) -> nil()
         , len(nil()) -> 0()
         , len(cons(X, Z)) -> s(n__len(activate(Z)))}
      StartTerms: basic terms
      Strategy: innermost
    
    Certificate: YES(?,O(n^2))
    
    Proof:
      The weightgap principle applies, where following rules are oriented strictly:
      
      TRS Component: {activate(n__s(X)) -> s(X)}
      
      Interpretation of nonconstant growth:
      -------------------------------------
        The following argument positions are usable:
          Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(cons) = {},
          Uargs(n__fst) = {}, Uargs(activate) = {}, Uargs(from) = {1},
          Uargs(n__from) = {}, Uargs(n__s) = {}, Uargs(add) = {1, 2},
          Uargs(n__add) = {}, Uargs(len) = {1}, Uargs(n__len) = {1}
        We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
        Interpretation Functions:
         fst(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                       [0 0]      [0 0]      [1]
         0() = [0]
               [0]
         nil() = [0]
                 [0]
         s(x1) = [1 0] x1 + [0]
                 [0 0]      [1]
         cons(x1, x2) = [1 1] x1 + [0 0] x2 + [1]
                        [0 0]      [1 1]      [1]
         n__fst(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                          [0 1]      [0 1]      [0]
         activate(x1) = [1 1] x1 + [1]
                        [0 0]      [1]
         from(x1) = [1 1] x1 + [1]
                    [0 0]      [1]
         n__from(x1) = [0 0] x1 + [0]
                       [1 1]      [0]
         n__s(x1) = [0 0] x1 + [0]
                    [1 0]      [0]
         add(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                       [0 0]      [0 0]      [1]
         n__add(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                          [0 1]      [0 1]      [0]
         len(x1) = [1 1] x1 + [1]
                   [0 0]      [1]
         n__len(x1) = [1 0] x1 + [0]
                      [0 1]      [0]
      
      The strictly oriented rules are moved into the weak component.
      
      We consider the following Problem:
      
        Strict Trs:
          {  from(X) -> cons(X, n__from(n__s(X)))
           , add(0(), X) -> X
           , fst(X1, X2) -> n__fst(X1, X2)
           , from(X) -> n__from(X)
           , s(X) -> n__s(X)
           , add(X1, X2) -> n__add(X1, X2)
           , len(X) -> n__len(X)
           , activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
           , activate(n__from(X)) -> from(activate(X))
           , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2))
           , activate(n__len(X)) -> len(activate(X))
           , activate(X) -> X}
        Weak Trs:
          {  activate(n__s(X)) -> s(X)
           , fst(0(), Z) -> nil()
           , len(nil()) -> 0()
           , len(cons(X, Z)) -> s(n__len(activate(Z)))}
        StartTerms: basic terms
        Strategy: innermost
      
      Certificate: YES(?,O(n^2))
      
      Proof:
        The weightgap principle applies, where following rules are oriented strictly:
        
        TRS Component: {activate(n__len(X)) -> len(activate(X))}
        
        Interpretation of nonconstant growth:
        -------------------------------------
          The following argument positions are usable:
            Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(cons) = {},
            Uargs(n__fst) = {}, Uargs(activate) = {}, Uargs(from) = {1},
            Uargs(n__from) = {}, Uargs(n__s) = {}, Uargs(add) = {1, 2},
            Uargs(n__add) = {}, Uargs(len) = {1}, Uargs(n__len) = {1}
          We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
          Interpretation Functions:
           fst(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                         [0 0]      [0 0]      [1]
           0() = [0]
                 [0]
           nil() = [0]
                   [0]
           s(x1) = [1 0] x1 + [0]
                   [0 0]      [1]
           cons(x1, x2) = [1 1] x1 + [0 0] x2 + [1]
                          [0 0]      [1 1]      [1]
           n__fst(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                            [0 1]      [0 1]      [0]
           activate(x1) = [1 1] x1 + [1]
                          [0 0]      [1]
           from(x1) = [1 1] x1 + [1]
                      [0 0]      [1]
           n__from(x1) = [0 0] x1 + [0]
                         [1 1]      [0]
           n__s(x1) = [0 0] x1 + [0]
                      [1 0]      [0]
           add(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                         [0 0]      [0 0]      [1]
           n__add(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                            [0 1]      [0 1]      [0]
           len(x1) = [1 1] x1 + [0]
                     [0 0]      [1]
           n__len(x1) = [1 0] x1 + [0]
                        [0 1]      [2]
        
        The strictly oriented rules are moved into the weak component.
        
        We consider the following Problem:
        
          Strict Trs:
            {  from(X) -> cons(X, n__from(n__s(X)))
             , add(0(), X) -> X
             , fst(X1, X2) -> n__fst(X1, X2)
             , from(X) -> n__from(X)
             , s(X) -> n__s(X)
             , add(X1, X2) -> n__add(X1, X2)
             , len(X) -> n__len(X)
             , activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
             , activate(n__from(X)) -> from(activate(X))
             , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2))
             , activate(X) -> X}
          Weak Trs:
            {  activate(n__len(X)) -> len(activate(X))
             , activate(n__s(X)) -> s(X)
             , fst(0(), Z) -> nil()
             , len(nil()) -> 0()
             , len(cons(X, Z)) -> s(n__len(activate(Z)))}
          StartTerms: basic terms
          Strategy: innermost
        
        Certificate: YES(?,O(n^2))
        
        Proof:
          The weightgap principle applies, where following rules are oriented strictly:
          
          TRS Component: {add(0(), X) -> X}
          
          Interpretation of nonconstant growth:
          -------------------------------------
            The following argument positions are usable:
              Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(cons) = {},
              Uargs(n__fst) = {}, Uargs(activate) = {}, Uargs(from) = {1},
              Uargs(n__from) = {}, Uargs(n__s) = {}, Uargs(add) = {1, 2},
              Uargs(n__add) = {}, Uargs(len) = {1}, Uargs(n__len) = {1}
            We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
            Interpretation Functions:
             fst(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                           [0 1]      [0 0]      [0]
             0() = [0]
                   [0]
             nil() = [0]
                     [0]
             s(x1) = [1 0] x1 + [0]
                     [0 0]      [1]
             cons(x1, x2) = [1 1] x1 + [0 0] x2 + [1]
                            [0 0]      [1 1]      [1]
             n__fst(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                              [0 1]      [0 1]      [0]
             activate(x1) = [1 1] x1 + [1]
                            [0 0]      [1]
             from(x1) = [1 1] x1 + [1]
                        [0 0]      [1]
             n__from(x1) = [0 0] x1 + [0]
                           [1 1]      [0]
             n__s(x1) = [0 0] x1 + [0]
                        [1 0]      [0]
             add(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                           [0 0]      [0 1]      [1]
             n__add(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                              [0 1]      [0 1]      [0]
             len(x1) = [1 1] x1 + [1]
                       [0 0]      [1]
             n__len(x1) = [1 0] x1 + [0]
                          [0 1]      [2]
          
          The strictly oriented rules are moved into the weak component.
          
          We consider the following Problem:
          
            Strict Trs:
              {  from(X) -> cons(X, n__from(n__s(X)))
               , fst(X1, X2) -> n__fst(X1, X2)
               , from(X) -> n__from(X)
               , s(X) -> n__s(X)
               , add(X1, X2) -> n__add(X1, X2)
               , len(X) -> n__len(X)
               , activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
               , activate(n__from(X)) -> from(activate(X))
               , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2))
               , activate(X) -> X}
            Weak Trs:
              {  add(0(), X) -> X
               , activate(n__len(X)) -> len(activate(X))
               , activate(n__s(X)) -> s(X)
               , fst(0(), Z) -> nil()
               , len(nil()) -> 0()
               , len(cons(X, Z)) -> s(n__len(activate(Z)))}
            StartTerms: basic terms
            Strategy: innermost
          
          Certificate: YES(?,O(n^2))
          
          Proof:
            The weightgap principle applies, where following rules are oriented strictly:
            
            TRS Component: {fst(X1, X2) -> n__fst(X1, X2)}
            
            Interpretation of nonconstant growth:
            -------------------------------------
              The following argument positions are usable:
                Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(cons) = {},
                Uargs(n__fst) = {}, Uargs(activate) = {}, Uargs(from) = {1},
                Uargs(n__from) = {}, Uargs(n__s) = {}, Uargs(add) = {1, 2},
                Uargs(n__add) = {}, Uargs(len) = {1}, Uargs(n__len) = {1}
              We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
              Interpretation Functions:
               fst(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                             [0 1]      [0 1]      [1]
               0() = [0]
                     [0]
               nil() = [0]
                       [0]
               s(x1) = [1 0] x1 + [0]
                       [0 0]      [0]
               cons(x1, x2) = [1 1] x1 + [0 0] x2 + [1]
                              [0 0]      [1 1]      [1]
               n__fst(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                                [0 1]      [0 1]      [0]
               activate(x1) = [1 1] x1 + [1]
                              [0 0]      [0]
               from(x1) = [1 1] x1 + [0]
                          [0 0]      [1]
               n__from(x1) = [0 0] x1 + [0]
                             [1 1]      [0]
               n__s(x1) = [0 0] x1 + [0]
                          [1 0]      [0]
               add(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                             [0 0]      [0 1]      [1]
               n__add(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                                [0 1]      [0 1]      [0]
               len(x1) = [1 1] x1 + [0]
                         [0 0]      [0]
               n__len(x1) = [1 0] x1 + [0]
                            [0 1]      [0]
            
            The strictly oriented rules are moved into the weak component.
            
            We consider the following Problem:
            
              Strict Trs:
                {  from(X) -> cons(X, n__from(n__s(X)))
                 , from(X) -> n__from(X)
                 , s(X) -> n__s(X)
                 , add(X1, X2) -> n__add(X1, X2)
                 , len(X) -> n__len(X)
                 , activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
                 , activate(n__from(X)) -> from(activate(X))
                 , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2))
                 , activate(X) -> X}
              Weak Trs:
                {  fst(X1, X2) -> n__fst(X1, X2)
                 , add(0(), X) -> X
                 , activate(n__len(X)) -> len(activate(X))
                 , activate(n__s(X)) -> s(X)
                 , fst(0(), Z) -> nil()
                 , len(nil()) -> 0()
                 , len(cons(X, Z)) -> s(n__len(activate(Z)))}
              StartTerms: basic terms
              Strategy: innermost
            
            Certificate: YES(?,O(n^2))
            
            Proof:
              The weightgap principle applies, where following rules are oriented strictly:
              
              TRS Component: {add(X1, X2) -> n__add(X1, X2)}
              
              Interpretation of nonconstant growth:
              -------------------------------------
                The following argument positions are usable:
                  Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(cons) = {},
                  Uargs(n__fst) = {}, Uargs(activate) = {}, Uargs(from) = {1},
                  Uargs(n__from) = {}, Uargs(n__s) = {}, Uargs(add) = {1, 2},
                  Uargs(n__add) = {}, Uargs(len) = {1}, Uargs(n__len) = {1}
                We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
                Interpretation Functions:
                 fst(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                               [0 1]      [0 1]      [1]
                 0() = [0]
                       [0]
                 nil() = [0]
                         [0]
                 s(x1) = [1 0] x1 + [0]
                         [0 0]      [0]
                 cons(x1, x2) = [1 1] x1 + [0 0] x2 + [1]
                                [0 0]      [1 1]      [1]
                 n__fst(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                                  [0 1]      [0 1]      [0]
                 activate(x1) = [1 1] x1 + [1]
                                [0 0]      [0]
                 from(x1) = [1 1] x1 + [3]
                            [0 0]      [1]
                 n__from(x1) = [0 0] x1 + [0]
                               [1 1]      [0]
                 n__s(x1) = [0 0] x1 + [0]
                            [1 0]      [0]
                 add(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                               [0 1]      [0 1]      [1]
                 n__add(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                                  [0 1]      [0 1]      [0]
                 len(x1) = [1 1] x1 + [0]
                           [0 0]      [0]
                 n__len(x1) = [1 0] x1 + [0]
                              [0 1]      [0]
              
              The strictly oriented rules are moved into the weak component.
              
              We consider the following Problem:
              
                Strict Trs:
                  {  from(X) -> cons(X, n__from(n__s(X)))
                   , from(X) -> n__from(X)
                   , s(X) -> n__s(X)
                   , len(X) -> n__len(X)
                   , activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
                   , activate(n__from(X)) -> from(activate(X))
                   , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2))
                   , activate(X) -> X}
                Weak Trs:
                  {  add(X1, X2) -> n__add(X1, X2)
                   , fst(X1, X2) -> n__fst(X1, X2)
                   , add(0(), X) -> X
                   , activate(n__len(X)) -> len(activate(X))
                   , activate(n__s(X)) -> s(X)
                   , fst(0(), Z) -> nil()
                   , len(nil()) -> 0()
                   , len(cons(X, Z)) -> s(n__len(activate(Z)))}
                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) -> n__from(X)}
                
                Interpretation of nonconstant growth:
                -------------------------------------
                  The following argument positions are usable:
                    Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(cons) = {},
                    Uargs(n__fst) = {}, Uargs(activate) = {}, Uargs(from) = {1},
                    Uargs(n__from) = {}, Uargs(n__s) = {}, Uargs(add) = {1, 2},
                    Uargs(n__add) = {}, Uargs(len) = {1}, Uargs(n__len) = {1}
                  We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
                  Interpretation Functions:
                   fst(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                                 [0 0]      [0 0]      [0]
                   0() = [1]
                         [0]
                   nil() = [2]
                           [0]
                   s(x1) = [1 0] x1 + [0]
                           [1 0]      [0]
                   cons(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
                                  [1 1]      [1 1]      [1]
                   n__fst(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                                    [0 0]      [0 0]      [0]
                   activate(x1) = [1 0] x1 + [0]
                                  [1 1]      [0]
                   from(x1) = [1 0] x1 + [1]
                              [0 0]      [1]
                   n__from(x1) = [1 0] x1 + [0]
                                 [0 0]      [0]
                   n__s(x1) = [1 0] x1 + [0]
                              [0 0]      [0]
                   add(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                                 [0 0]      [0 1]      [0]
                   n__add(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                                    [0 0]      [0 0]      [0]
                   len(x1) = [1 0] x1 + [0]
                             [1 0]      [0]
                   n__len(x1) = [1 0] x1 + [1]
                                [0 0]      [3]
                
                The strictly oriented rules are moved into the weak component.
                
                We consider the following Problem:
                
                  Strict Trs:
                    {  from(X) -> cons(X, n__from(n__s(X)))
                     , s(X) -> n__s(X)
                     , len(X) -> n__len(X)
                     , activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
                     , activate(n__from(X)) -> from(activate(X))
                     , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2))
                     , activate(X) -> X}
                  Weak Trs:
                    {  from(X) -> n__from(X)
                     , add(X1, X2) -> n__add(X1, X2)
                     , fst(X1, X2) -> n__fst(X1, X2)
                     , add(0(), X) -> X
                     , activate(n__len(X)) -> len(activate(X))
                     , activate(n__s(X)) -> s(X)
                     , fst(0(), Z) -> nil()
                     , len(nil()) -> 0()
                     , len(cons(X, Z)) -> s(n__len(activate(Z)))}
                  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(n__s(X)))}
                  
                  Interpretation of nonconstant growth:
                  -------------------------------------
                    The following argument positions are usable:
                      Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(cons) = {},
                      Uargs(n__fst) = {}, Uargs(activate) = {}, Uargs(from) = {1},
                      Uargs(n__from) = {}, Uargs(n__s) = {}, Uargs(add) = {1, 2},
                      Uargs(n__add) = {}, Uargs(len) = {1}, Uargs(n__len) = {1}
                    We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
                    Interpretation Functions:
                     fst(x1, x2) = [1 0] x1 + [1 0] x2 + [3]
                                   [0 1]      [0 0]      [1]
                     0() = [1]
                           [0]
                     nil() = [0]
                             [0]
                     s(x1) = [1 0] x1 + [0]
                             [0 0]      [0]
                     cons(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
                                    [0 1]      [0 0]      [1]
                     n__fst(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                                      [0 0]      [0 0]      [0]
                     activate(x1) = [1 0] x1 + [1]
                                    [0 0]      [1]
                     from(x1) = [1 0] x1 + [2]
                                [0 1]      [3]
                     n__from(x1) = [1 0] x1 + [0]
                                   [0 0]      [0]
                     n__s(x1) = [1 0] x1 + [0]
                                [0 0]      [0]
                     add(x1, x2) = [1 0] x1 + [1 0] x2 + [3]
                                   [0 0]      [0 1]      [1]
                     n__add(x1, x2) = [1 0] x1 + [1 0] x2 + [3]
                                      [0 0]      [0 0]      [0]
                     len(x1) = [1 0] x1 + [1]
                               [0 0]      [0]
                     n__len(x1) = [1 0] x1 + [1]
                                  [0 0]      [0]
                  
                  The strictly oriented rules are moved into the weak component.
                  
                  We consider the following Problem:
                  
                    Strict Trs:
                      {  s(X) -> n__s(X)
                       , len(X) -> n__len(X)
                       , activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
                       , activate(n__from(X)) -> from(activate(X))
                       , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2))
                       , activate(X) -> X}
                    Weak Trs:
                      {  from(X) -> cons(X, n__from(n__s(X)))
                       , from(X) -> n__from(X)
                       , add(X1, X2) -> n__add(X1, X2)
                       , fst(X1, X2) -> n__fst(X1, X2)
                       , add(0(), X) -> X
                       , activate(n__len(X)) -> len(activate(X))
                       , activate(n__s(X)) -> s(X)
                       , fst(0(), Z) -> nil()
                       , len(nil()) -> 0()
                       , len(cons(X, Z)) -> s(n__len(activate(Z)))}
                    StartTerms: basic terms
                    Strategy: innermost
                  
                  Certificate: YES(?,O(n^2))
                  
                  Proof:
                    The weightgap principle applies, where following rules are oriented strictly:
                    
                    TRS Component: {s(X) -> n__s(X)}
                    
                    Interpretation of nonconstant growth:
                    -------------------------------------
                      The following argument positions are usable:
                        Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(cons) = {},
                        Uargs(n__fst) = {}, Uargs(activate) = {}, Uargs(from) = {1},
                        Uargs(n__from) = {}, Uargs(n__s) = {}, Uargs(add) = {1, 2},
                        Uargs(n__add) = {}, Uargs(len) = {1}, Uargs(n__len) = {1}
                      We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
                      Interpretation Functions:
                       fst(x1, x2) = [1 0] x1 + [1 1] x2 + [0]
                                     [0 1]      [0 0]      [0]
                       0() = [0]
                             [0]
                       nil() = [0]
                               [0]
                       s(x1) = [1 2] x1 + [1]
                               [0 0]      [1]
                       cons(x1, x2) = [0 0] x1 + [1 0] x2 + [0]
                                      [0 0]      [0 1]      [3]
                       n__fst(x1, x2) = [1 0] x1 + [1 1] x2 + [0]
                                        [0 1]      [0 0]      [0]
                       activate(x1) = [1 1] x1 + [0]
                                      [0 0]      [1]
                       from(x1) = [1 2] x1 + [2]
                                  [0 0]      [3]
                       n__from(x1) = [1 1] x1 + [0]
                                     [0 0]      [0]
                       n__s(x1) = [1 2] x1 + [0]
                                  [0 0]      [1]
                       add(x1, x2) = [1 1] x1 + [1 0] x2 + [0]
                                     [0 0]      [0 1]      [0]
                       n__add(x1, x2) = [1 1] x1 + [1 0] x2 + [0]
                                        [0 0]      [0 1]      [0]
                       len(x1) = [1 2] x1 + [0]
                                 [0 0]      [1]
                       n__len(x1) = [1 0] x1 + [2]
                                    [0 1]      [0]
                    
                    The strictly oriented rules are moved into the weak component.
                    
                    We consider the following Problem:
                    
                      Strict Trs:
                        {  len(X) -> n__len(X)
                         , activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
                         , activate(n__from(X)) -> from(activate(X))
                         , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2))
                         , activate(X) -> X}
                      Weak Trs:
                        {  s(X) -> n__s(X)
                         , from(X) -> cons(X, n__from(n__s(X)))
                         , from(X) -> n__from(X)
                         , add(X1, X2) -> n__add(X1, X2)
                         , fst(X1, X2) -> n__fst(X1, X2)
                         , add(0(), X) -> X
                         , activate(n__len(X)) -> len(activate(X))
                         , activate(n__s(X)) -> s(X)
                         , fst(0(), Z) -> nil()
                         , len(nil()) -> 0()
                         , len(cons(X, Z)) -> s(n__len(activate(Z)))}
                      StartTerms: basic terms
                      Strategy: innermost
                    
                    Certificate: YES(?,O(n^2))
                    
                    Proof:
                      The weightgap principle applies, where following rules are oriented strictly:
                      
                      TRS Component: {activate(X) -> X}
                      
                      Interpretation of nonconstant growth:
                      -------------------------------------
                        The following argument positions are usable:
                          Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(cons) = {},
                          Uargs(n__fst) = {}, Uargs(activate) = {}, Uargs(from) = {1},
                          Uargs(n__from) = {}, Uargs(n__s) = {}, Uargs(add) = {1, 2},
                          Uargs(n__add) = {}, Uargs(len) = {1}, Uargs(n__len) = {1}
                        We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
                        Interpretation Functions:
                         fst(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                                       [0 0]      [0 0]      [0]
                         0() = [0]
                               [0]
                         nil() = [0]
                                 [0]
                         s(x1) = [1 0] x1 + [0]
                                 [0 0]      [0]
                         cons(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
                                        [0 0]      [0 1]      [0]
                         n__fst(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                                          [0 0]      [0 0]      [0]
                         activate(x1) = [1 0] x1 + [1]
                                        [0 1]      [0]
                         from(x1) = [1 0] x1 + [2]
                                    [0 0]      [0]
                         n__from(x1) = [1 0] x1 + [0]
                                       [0 0]      [0]
                         n__s(x1) = [1 0] x1 + [0]
                                    [0 0]      [0]
                         add(x1, x2) = [1 0] x1 + [1 0] x2 + [1]
                                       [0 0]      [0 1]      [0]
                         n__add(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                                          [0 0]      [0 0]      [0]
                         len(x1) = [1 0] x1 + [0]
                                   [0 0]      [0]
                         n__len(x1) = [1 0] x1 + [0]
                                      [0 0]      [0]
                      
                      The strictly oriented rules are moved into the weak component.
                      
                      We consider the following Problem:
                      
                        Strict Trs:
                          {  len(X) -> n__len(X)
                           , activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
                           , activate(n__from(X)) -> from(activate(X))
                           , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2))}
                        Weak Trs:
                          {  activate(X) -> X
                           , s(X) -> n__s(X)
                           , from(X) -> cons(X, n__from(n__s(X)))
                           , from(X) -> n__from(X)
                           , add(X1, X2) -> n__add(X1, X2)
                           , fst(X1, X2) -> n__fst(X1, X2)
                           , add(0(), X) -> X
                           , activate(n__len(X)) -> len(activate(X))
                           , activate(n__s(X)) -> s(X)
                           , fst(0(), Z) -> nil()
                           , len(nil()) -> 0()
                           , len(cons(X, Z)) -> s(n__len(activate(Z)))}
                        StartTerms: basic terms
                        Strategy: innermost
                      
                      Certificate: YES(?,O(n^2))
                      
                      Proof:
                        We consider the following Problem:
                        
                          Strict Trs:
                            {  len(X) -> n__len(X)
                             , activate(n__fst(X1, X2)) -> fst(activate(X1), activate(X2))
                             , activate(n__from(X)) -> from(activate(X))
                             , activate(n__add(X1, X2)) -> add(activate(X1), activate(X2))}
                          Weak Trs:
                            {  activate(X) -> X
                             , s(X) -> n__s(X)
                             , from(X) -> cons(X, n__from(n__s(X)))
                             , from(X) -> n__from(X)
                             , add(X1, X2) -> n__add(X1, X2)
                             , fst(X1, X2) -> n__fst(X1, X2)
                             , add(0(), X) -> X
                             , activate(n__len(X)) -> len(activate(X))
                             , activate(n__s(X)) -> s(X)
                             , fst(0(), Z) -> nil()
                             , len(nil()) -> 0()
                             , len(cons(X, Z)) -> s(n__len(activate(Z)))}
                          StartTerms: basic terms
                          Strategy: innermost
                        
                        Certificate: YES(?,O(n^2))
                        
                        Proof:
                          The following argument positions are usable:
                            Uargs(fst) = {1, 2}, Uargs(s) = {1}, Uargs(cons) = {},
                            Uargs(n__fst) = {}, Uargs(activate) = {}, Uargs(from) = {1},
                            Uargs(n__from) = {}, Uargs(n__s) = {}, Uargs(add) = {1, 2},
                            Uargs(n__add) = {}, Uargs(len) = {1}, Uargs(n__len) = {1}
                          We have the following constructor-based EDA-non-satisfying and IDA(2)-non-satisfying matrix interpretation:
                          Interpretation Functions:
                           fst(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [1]
                                         [0 1 0]      [0 1 0]      [2]
                                         [0 0 1]      [0 1 1]      [0]
                           0() = [0]
                                 [0]
                                 [0]
                           nil() = [0]
                                   [0]
                                   [0]
                           s(x1) = [1 0 0] x1 + [0]
                                   [0 0 0]      [0]
                                   [0 0 0]      [0]
                           cons(x1, x2) = [0 0 0] x1 + [1 1 2] x2 + [0]
                                          [0 1 0]      [0 1 0]      [0]
                                          [0 0 1]      [0 0 0]      [0]
                           n__fst(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
                                            [0 1 0]      [0 1 0]      [2]
                                            [0 0 1]      [0 1 1]      [0]
                           activate(x1) = [1 2 2] x1 + [0]
                                          [0 1 0]      [0]
                                          [0 0 1]      [0]
                           from(x1) = [1 0 0] x1 + [1]
                                      [0 1 0]      [1]
                                      [0 0 1]      [0]
                           n__from(x1) = [1 0 0] x1 + [0]
                                         [0 1 0]      [1]
                                         [0 0 1]      [0]
                           n__s(x1) = [1 0 0] x1 + [0]
                                      [0 0 0]      [0]
                                      [0 0 0]      [0]
                           add(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [1]
                                         [0 0 0]      [0 1 0]      [1]
                                         [0 1 1]      [0 0 1]      [1]
                           n__add(x1, x2) = [1 0 0] x1 + [1 0 0] x2 + [0]
                                            [0 0 0]      [0 1 0]      [1]
                                            [0 1 1]      [0 0 1]      [1]
                           len(x1) = [1 1 0] x1 + [2]
                                     [0 1 0]      [0]
                                     [0 1 1]      [2]
                           n__len(x1) = [1 0 0] x1 + [0]
                                        [0 1 0]      [0]
                                        [0 1 1]      [2]

Hurray, we answered YES(?,O(n^2))