We consider the following Problem:

  Strict Trs:
    {  __(__(X, Y), Z) -> __(X, __(Y, Z))
     , __(X, nil()) -> X
     , __(nil(), X) -> X
     , and(tt(), X) -> activate(X)
     , isNePal(__(I, __(P, I))) -> tt()
     , activate(X) -> X}
  StartTerms: basic terms
  Strategy: innermost

Certificate: YES(?,O(n^1))

Proof:
  We consider the following Problem:
  
    Strict Trs:
      {  __(__(X, Y), Z) -> __(X, __(Y, Z))
       , __(X, nil()) -> X
       , __(nil(), X) -> X
       , and(tt(), X) -> activate(X)
       , isNePal(__(I, __(P, I))) -> tt()
       , activate(X) -> X}
    StartTerms: basic terms
    Strategy: innermost
  
  Certificate: YES(?,O(n^1))
  
  Proof:
    The weightgap principle applies, where following rules are oriented strictly:
    
    TRS Component:
      {  and(tt(), X) -> activate(X)
       , isNePal(__(I, __(P, I))) -> tt()}
    
    Interpretation of nonconstant growth:
    -------------------------------------
      The following argument positions are usable:
        Uargs(__) = {2}, Uargs(and) = {}, Uargs(activate) = {},
        Uargs(isNePal) = {}
      We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
      Interpretation Functions:
       __(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                    [0 1]      [0 0]      [0]
       nil() = [0]
               [0]
       and(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
                     [0 0]      [0 0]      [1]
       tt() = [0]
              [0]
       activate(x1) = [1 0] x1 + [0]
                      [0 0]      [0]
       isNePal(x1) = [0 0] x1 + [1]
                     [0 0]      [1]
    
    The strictly oriented rules are moved into the weak component.
    
    We consider the following Problem:
    
      Strict Trs:
        {  __(__(X, Y), Z) -> __(X, __(Y, Z))
         , __(X, nil()) -> X
         , __(nil(), X) -> X
         , activate(X) -> X}
      Weak Trs:
        {  and(tt(), X) -> activate(X)
         , isNePal(__(I, __(P, I))) -> tt()}
      StartTerms: basic terms
      Strategy: innermost
    
    Certificate: YES(?,O(n^1))
    
    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(__) = {2}, Uargs(and) = {}, Uargs(activate) = {},
          Uargs(isNePal) = {}
        We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
        Interpretation Functions:
         __(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                      [0 1]      [0 0]      [0]
         nil() = [0]
                 [0]
         and(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
                       [0 0]      [0 1]      [1]
         tt() = [0]
                [0]
         activate(x1) = [1 0] x1 + [1]
                        [0 1]      [0]
         isNePal(x1) = [0 0] x1 + [1]
                       [0 0]      [1]
      
      The strictly oriented rules are moved into the weak component.
      
      We consider the following Problem:
      
        Strict Trs:
          {  __(__(X, Y), Z) -> __(X, __(Y, Z))
           , __(X, nil()) -> X
           , __(nil(), X) -> X}
        Weak Trs:
          {  activate(X) -> X
           , and(tt(), X) -> activate(X)
           , isNePal(__(I, __(P, I))) -> tt()}
        StartTerms: basic terms
        Strategy: innermost
      
      Certificate: YES(?,O(n^1))
      
      Proof:
        The weightgap principle applies, where following rules are oriented strictly:
        
        TRS Component: {__(X, nil()) -> X}
        
        Interpretation of nonconstant growth:
        -------------------------------------
          The following argument positions are usable:
            Uargs(__) = {2}, Uargs(and) = {}, Uargs(activate) = {},
            Uargs(isNePal) = {}
          We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
          Interpretation Functions:
           __(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                        [0 1]      [0 0]      [0]
           nil() = [2]
                   [0]
           and(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
                         [0 0]      [0 1]      [1]
           tt() = [0]
                  [0]
           activate(x1) = [1 0] x1 + [0]
                          [0 1]      [0]
           isNePal(x1) = [0 0] x1 + [1]
                         [0 0]      [1]
        
        The strictly oriented rules are moved into the weak component.
        
        We consider the following Problem:
        
          Strict Trs:
            {  __(__(X, Y), Z) -> __(X, __(Y, Z))
             , __(nil(), X) -> X}
          Weak Trs:
            {  __(X, nil()) -> X
             , activate(X) -> X
             , and(tt(), X) -> activate(X)
             , isNePal(__(I, __(P, I))) -> tt()}
          StartTerms: basic terms
          Strategy: innermost
        
        Certificate: YES(?,O(n^1))
        
        Proof:
          The weightgap principle applies, where following rules are oriented strictly:
          
          TRS Component: {__(nil(), X) -> X}
          
          Interpretation of nonconstant growth:
          -------------------------------------
            The following argument positions are usable:
              Uargs(__) = {2}, Uargs(and) = {}, Uargs(activate) = {},
              Uargs(isNePal) = {}
            We have the following EDA-non-satisfying and IDA(1)-non-satisfying matrix interpretation:
            Interpretation Functions:
             __(x1, x2) = [1 0] x1 + [1 0] x2 + [0]
                          [1 1]      [0 1]      [0]
             nil() = [2]
                     [0]
             and(x1, x2) = [0 0] x1 + [1 0] x2 + [1]
                           [0 0]      [0 1]      [1]
             tt() = [0]
                    [0]
             activate(x1) = [1 0] x1 + [0]
                            [0 1]      [0]
             isNePal(x1) = [0 0] x1 + [1]
                           [0 0]      [1]
          
          The strictly oriented rules are moved into the weak component.
          
          We consider the following Problem:
          
            Strict Trs: {__(__(X, Y), Z) -> __(X, __(Y, Z))}
            Weak Trs:
              {  __(nil(), X) -> X
               , __(X, nil()) -> X
               , activate(X) -> X
               , and(tt(), X) -> activate(X)
               , isNePal(__(I, __(P, I))) -> tt()}
            StartTerms: basic terms
            Strategy: innermost
          
          Certificate: YES(?,O(n^1))
          
          Proof:
            We consider the following Problem:
            
              Strict Trs: {__(__(X, Y), Z) -> __(X, __(Y, Z))}
              Weak Trs:
                {  __(nil(), X) -> X
                 , __(X, nil()) -> X
                 , activate(X) -> X
                 , and(tt(), X) -> activate(X)
                 , isNePal(__(I, __(P, I))) -> tt()}
              StartTerms: basic terms
              Strategy: innermost
            
            Certificate: YES(?,O(n^1))
            
            Proof:
              The problem is match-bounded by 0.
              The enriched problem is compatible with the following automaton:
              {  ___0(2, 2) -> 1
               , nil_0() -> 1
               , nil_0() -> 2
               , and_0(2, 2) -> 1
               , tt_0() -> 1
               , tt_0() -> 2
               , activate_0(2) -> 1
               , isNePal_0(2) -> 1}

Hurray, we answered YES(?,O(n^1))